/////////////////////////////////////////////////////////////////////////////// // // // TetGen // // // // A Quality Tetrahedral Mesh Generator and A 3D Delaunay Triangulator // // // // Version 1.5 // // August 18, 2018 // // // // Copyright (C) 2002--2018 // // // // TetGen is freely available through the website: http://www.tetgen.org. // // It may be copied, modified, and redistributed for non-commercial use. // // Please consult the file LICENSE for the detailed copyright notices. // // // /////////////////////////////////////////////////////////////////////////////// #include "tetgen.h" //// io_cxx /////////////////////////////////////////////////////////////////// //// //// //// //// /////////////////////////////////////////////////////////////////////////////// // // // load_node_call() Read a list of points from a file. // // // // 'infile' is the file handle contains the node list. It may point to a // // .node, or .poly or .smesh file. 'markers' indicates each node contains an // // additional marker (integer) or not. 'uvflag' indicates each node contains // // u,v coordinates or not. It is reuqired by a PSC. 'infilename' is the name // // of the file being read, it is only used in error messages. // // // // The 'firstnumber' (0 or 1) is automatically determined by the number of // // the first index of the first point. // // // /////////////////////////////////////////////////////////////////////////////// bool tetgenio::load_node_call(FILE* infile, int markers, int uvflag, char* infilename) { char inputline[INPUTLINESIZE]; char* stringptr; REAL x, y, z, attrib; int firstnode, currentmarker; int index, attribindex; int i, j; // Initialize 'pointlist', 'pointattributelist', and 'pointmarkerlist'. pointlist = new REAL[numberofpoints * 3]; if (pointlist == (REAL*)NULL) { terminatetetgen(NULL, 1); } if (numberofpointattributes > 0) { pointattributelist = new REAL[numberofpoints * numberofpointattributes]; if (pointattributelist == (REAL*)NULL) { terminatetetgen(NULL, 1); } } if (markers) { pointmarkerlist = new int[numberofpoints]; if (pointmarkerlist == (int*)NULL) { terminatetetgen(NULL, 1); } } if (uvflag) { pointparamlist = new pointparam[numberofpoints]; if (pointparamlist == NULL) { terminatetetgen(NULL, 1); } } // Read the point section. index = 0; attribindex = 0; for (i = 0; i < numberofpoints; i++) { stringptr = readnumberline(inputline, infile, infilename); if (useindex) { if (i == 0) { firstnode = (int)strtol(stringptr, &stringptr, 0); if ((firstnode == 0) || (firstnode == 1)) { firstnumber = firstnode; } } stringptr = findnextnumber(stringptr); } // if (useindex) if (*stringptr == '\0') { printf("Error: Point %d has no x coordinate.\n", firstnumber + i); break; } x = (REAL)strtod(stringptr, &stringptr); stringptr = findnextnumber(stringptr); if (*stringptr == '\0') { printf("Error: Point %d has no y coordinate.\n", firstnumber + i); break; } y = (REAL)strtod(stringptr, &stringptr); if (mesh_dim == 3) { stringptr = findnextnumber(stringptr); if (*stringptr == '\0') { printf("Error: Point %d has no z coordinate.\n", firstnumber + i); break; } z = (REAL)strtod(stringptr, &stringptr); } else { z = 0.0; // mesh_dim == 2; } pointlist[index++] = x; pointlist[index++] = y; pointlist[index++] = z; // Read the point attributes. for (j = 0; j < numberofpointattributes; j++) { stringptr = findnextnumber(stringptr); if (*stringptr == '\0') { attrib = 0.0; } else { attrib = (REAL)strtod(stringptr, &stringptr); } pointattributelist[attribindex++] = attrib; } if (markers) { // Read a point marker. stringptr = findnextnumber(stringptr); if (*stringptr == '\0') { currentmarker = 0; } else { currentmarker = (int)strtol(stringptr, &stringptr, 0); } pointmarkerlist[i] = currentmarker; } if (uvflag) { // Read point paramteters. stringptr = findnextnumber(stringptr); if (*stringptr == '\0') { printf("Error: Point %d has no uv[0].\n", firstnumber + i); break; } pointparamlist[i].uv[0] = (REAL)strtod(stringptr, &stringptr); stringptr = findnextnumber(stringptr); if (*stringptr == '\0') { printf("Error: Point %d has no uv[1].\n", firstnumber + i); break; } pointparamlist[i].uv[1] = (REAL)strtod(stringptr, &stringptr); stringptr = findnextnumber(stringptr); if (*stringptr == '\0') { printf("Error: Point %d has no tag.\n", firstnumber + i); break; } pointparamlist[i].tag = (int)strtol(stringptr, &stringptr, 0); stringptr = findnextnumber(stringptr); if (*stringptr == '\0') { printf("Error: Point %d has no type.\n", firstnumber + i); break; } pointparamlist[i].type = (int)strtol(stringptr, &stringptr, 0); if ((pointparamlist[i].type < 0) || (pointparamlist[i].type > 2)) { printf("Error: Point %d has an invalid type.\n", firstnumber + i); break; } } } if (i < numberofpoints) { // Failed to read points due to some error. delete[] pointlist; pointlist = (REAL*)NULL; if (markers) { delete[] pointmarkerlist; pointmarkerlist = (int*)NULL; } if (numberofpointattributes > 0) { delete[] pointattributelist; pointattributelist = (REAL*)NULL; } if (uvflag) { delete[] pointparamlist; pointparamlist = NULL; } numberofpoints = 0; return false; } return true; } /////////////////////////////////////////////////////////////////////////////// // // // load_node() Load a list of points from a .node file. // // // /////////////////////////////////////////////////////////////////////////////// bool tetgenio::load_node(char* filebasename) { FILE* infile; char innodefilename[FILENAMESIZE]; char inputline[INPUTLINESIZE]; char* stringptr; bool okflag; int markers; int uvflag; // for psc input. // Assembling the actual file names we want to open. strcpy(innodefilename, filebasename); strcat(innodefilename, ".node"); // Try to open a .node file. infile = fopen(innodefilename, "r"); if (infile == (FILE*)NULL) { printf(" Cannot access file %s.\n", innodefilename); return false; } printf("Opening %s.\n", innodefilename); // Set initial flags. mesh_dim = 3; numberofpointattributes = 0; // no point attribute. markers = 0; // no boundary marker. uvflag = 0; // no uv parameters (required by a PSC). // Read the first line of the file. stringptr = readnumberline(inputline, infile, innodefilename); // Does this file contain an index column? stringptr = strstr(inputline, "rbox"); if (stringptr == NULL) { // Read number of points, number of dimensions, number of point // attributes, and number of boundary markers. stringptr = inputline; numberofpoints = (int)strtol(stringptr, &stringptr, 0); stringptr = findnextnumber(stringptr); if (*stringptr != '\0') { mesh_dim = (int)strtol(stringptr, &stringptr, 0); } stringptr = findnextnumber(stringptr); if (*stringptr != '\0') { numberofpointattributes = (int)strtol(stringptr, &stringptr, 0); } stringptr = findnextnumber(stringptr); if (*stringptr != '\0') { markers = (int)strtol(stringptr, &stringptr, 0); } stringptr = findnextnumber(stringptr); if (*stringptr != '\0') { uvflag = (int)strtol(stringptr, &stringptr, 0); } } else { // It is a rbox (qhull) input file. stringptr = inputline; // Get the dimension. mesh_dim = (int)strtol(stringptr, &stringptr, 0); // Get the number of points. stringptr = readnumberline(inputline, infile, innodefilename); numberofpoints = (int)strtol(stringptr, &stringptr, 0); // There is no index column. useindex = 0; } // Load the list of nodes. okflag = load_node_call(infile, markers, uvflag, innodefilename); fclose(infile); return okflag; } /////////////////////////////////////////////////////////////////////////////// // // // load_edge() Load a list of edges from a .edge file. // // // /////////////////////////////////////////////////////////////////////////////// bool tetgenio::load_edge(char* filebasename) { FILE* infile; char inedgefilename[FILENAMESIZE]; char inputline[INPUTLINESIZE]; char* stringptr; int markers, corner; int index; int i, j; strcpy(inedgefilename, filebasename); strcat(inedgefilename, ".edge"); infile = fopen(inedgefilename, "r"); if (infile != (FILE*)NULL) { printf("Opening %s.\n", inedgefilename); } else { // printf(" Cannot access file %s.\n", inedgefilename); return false; } // Read number of boundary edges. stringptr = readnumberline(inputline, infile, inedgefilename); numberofedges = (int)strtol(stringptr, &stringptr, 0); if (numberofedges > 0) { edgelist = new int[numberofedges * 2]; if (edgelist == (int*)NULL) { terminatetetgen(NULL, 1); } stringptr = findnextnumber(stringptr); if (*stringptr == '\0') { markers = 0; // Default value. } else { markers = (int)strtol(stringptr, &stringptr, 0); } if (markers > 0) { edgemarkerlist = new int[numberofedges]; } } // Read the list of edges. index = 0; for (i = 0; i < numberofedges; i++) { // Read edge index and the edge's two endpoints. stringptr = readnumberline(inputline, infile, inedgefilename); for (j = 0; j < 2; j++) { stringptr = findnextnumber(stringptr); if (*stringptr == '\0') { printf("Error: Edge %d is missing vertex %d in %s.\n", i + firstnumber, j + 1, inedgefilename); terminatetetgen(NULL, 1); } corner = (int)strtol(stringptr, &stringptr, 0); if (corner < firstnumber || corner >= numberofpoints + firstnumber) { printf("Error: Edge %d has an invalid vertex index.\n", i + firstnumber); terminatetetgen(NULL, 1); } edgelist[index++] = corner; } if (numberofcorners == 10) { // Skip an extra vertex (generated by a previous -o2 option). stringptr = findnextnumber(stringptr); } // Read the edge marker if it has. if (markers) { stringptr = findnextnumber(stringptr); edgemarkerlist[i] = (int)strtol(stringptr, &stringptr, 0); } } fclose(infile); return true; } /////////////////////////////////////////////////////////////////////////////// // // // load_face() Load a list of faces (triangles) from a .face file. // // // /////////////////////////////////////////////////////////////////////////////// bool tetgenio::load_face(char* filebasename) { FILE* infile; char infilename[FILENAMESIZE]; char inputline[INPUTLINESIZE]; char* stringptr; REAL attrib; int markers, corner; int index; int i, j; strcpy(infilename, filebasename); strcat(infilename, ".face"); infile = fopen(infilename, "r"); if (infile != (FILE*)NULL) { printf("Opening %s.\n", infilename); } else { return false; } // Read number of faces, boundary markers. stringptr = readnumberline(inputline, infile, infilename); numberoftrifaces = (int)strtol(stringptr, &stringptr, 0); stringptr = findnextnumber(stringptr); if (mesh_dim == 2) { // Skip a number. stringptr = findnextnumber(stringptr); } if (*stringptr == '\0') { markers = 0; // Default there is no marker per face. } else { markers = (int)strtol(stringptr, &stringptr, 0); } if (numberoftrifaces > 0) { trifacelist = new int[numberoftrifaces * 3]; if (trifacelist == (int*)NULL) { terminatetetgen(NULL, 1); } if (markers) { trifacemarkerlist = new int[numberoftrifaces]; if (trifacemarkerlist == (int*)NULL) { terminatetetgen(NULL, 1); } } } // Read the list of faces. index = 0; for (i = 0; i < numberoftrifaces; i++) { // Read face index and the face's three corners. stringptr = readnumberline(inputline, infile, infilename); for (j = 0; j < 3; j++) { stringptr = findnextnumber(stringptr); if (*stringptr == '\0') { printf("Error: Face %d is missing vertex %d in %s.\n", i + firstnumber, j + 1, infilename); terminatetetgen(NULL, 1); } corner = (int)strtol(stringptr, &stringptr, 0); if (corner < firstnumber || corner >= numberofpoints + firstnumber) { printf("Error: Face %d has an invalid vertex index.\n", i + firstnumber); terminatetetgen(NULL, 1); } trifacelist[index++] = corner; } if (numberofcorners == 10) { // Skip 3 extra vertices (generated by a previous -o2 option). for (j = 0; j < 3; j++) { stringptr = findnextnumber(stringptr); } } // Read the boundary marker if it exists. if (markers) { stringptr = findnextnumber(stringptr); if (*stringptr == '\0') { attrib = 0.0; } else { attrib = (REAL)strtod(stringptr, &stringptr); } trifacemarkerlist[i] = (int)attrib; } } fclose(infile); return true; } /////////////////////////////////////////////////////////////////////////////// // // // load_tet() Load a list of tetrahedra from a .ele file. // // // /////////////////////////////////////////////////////////////////////////////// bool tetgenio::load_tet(char* filebasename) { FILE* infile; char infilename[FILENAMESIZE]; char inputline[INPUTLINESIZE]; char* stringptr; REAL attrib; int corner; int index, attribindex; int i, j; strcpy(infilename, filebasename); strcat(infilename, ".ele"); infile = fopen(infilename, "r"); if (infile != (FILE*)NULL) { printf("Opening %s.\n", infilename); } else { return false; } // Read number of elements, number of corners (4 or 10), number of // element attributes. stringptr = readnumberline(inputline, infile, infilename); numberoftetrahedra = (int)strtol(stringptr, &stringptr, 0); if (numberoftetrahedra <= 0) { printf("Error: Invalid number of tetrahedra.\n"); fclose(infile); return false; } stringptr = findnextnumber(stringptr); if (*stringptr == '\0') { numberofcorners = 4; // Default read 4 nodes per element. } else { numberofcorners = (int)strtol(stringptr, &stringptr, 0); } stringptr = findnextnumber(stringptr); if (*stringptr == '\0') { numberoftetrahedronattributes = 0; // Default no attribute. } else { numberoftetrahedronattributes = (int)strtol(stringptr, &stringptr, 0); } if (numberofcorners != 4 && numberofcorners != 10) { printf("Error: Wrong number of corners %d (should be 4 or 10).\n", numberofcorners); fclose(infile); return false; } // Allocate memory for tetrahedra. tetrahedronlist = new int[numberoftetrahedra * numberofcorners]; if (tetrahedronlist == (int*)NULL) { terminatetetgen(NULL, 1); } // Allocate memory for output tetrahedron attributes if necessary. if (numberoftetrahedronattributes > 0) { tetrahedronattributelist = new REAL[numberoftetrahedra * numberoftetrahedronattributes]; if (tetrahedronattributelist == (REAL*)NULL) { terminatetetgen(NULL, 1); } } // Read the list of tetrahedra. index = 0; attribindex = 0; for (i = 0; i < numberoftetrahedra; i++) { // Read tetrahedron index and the tetrahedron's corners. stringptr = readnumberline(inputline, infile, infilename); for (j = 0; j < numberofcorners; j++) { stringptr = findnextnumber(stringptr); if (*stringptr == '\0') { printf("Error: Tetrahedron %d is missing vertex %d in %s.\n", i + firstnumber, j + 1, infilename); terminatetetgen(NULL, 1); } corner = (int)strtol(stringptr, &stringptr, 0); if (corner < firstnumber || corner >= numberofpoints + firstnumber) { printf("Error: Tetrahedron %d has an invalid vertex index.\n", i + firstnumber); terminatetetgen(NULL, 1); } tetrahedronlist[index++] = corner; } // Read the tetrahedron's attributes. for (j = 0; j < numberoftetrahedronattributes; j++) { stringptr = findnextnumber(stringptr); if (*stringptr == '\0') { attrib = 0.0; } else { attrib = (REAL)strtod(stringptr, &stringptr); } tetrahedronattributelist[attribindex++] = attrib; } } fclose(infile); return true; } /////////////////////////////////////////////////////////////////////////////// // // // load_vol() Load a list of volume constraints from a .vol file. // // // /////////////////////////////////////////////////////////////////////////////// bool tetgenio::load_vol(char* filebasename) { FILE* infile; char inelefilename[FILENAMESIZE]; char infilename[FILENAMESIZE]; char inputline[INPUTLINESIZE]; char* stringptr; REAL volume; int volelements; int i; strcpy(infilename, filebasename); strcat(infilename, ".vol"); infile = fopen(infilename, "r"); if (infile != (FILE*)NULL) { printf("Opening %s.\n", infilename); } else { return false; } // Read number of tetrahedra. stringptr = readnumberline(inputline, infile, infilename); volelements = (int)strtol(stringptr, &stringptr, 0); if (volelements != numberoftetrahedra) { strcpy(inelefilename, filebasename); strcat(infilename, ".ele"); printf("Warning: %s and %s disagree on number of tetrahedra.\n", inelefilename, infilename); fclose(infile); return false; } tetrahedronvolumelist = new REAL[volelements]; if (tetrahedronvolumelist == (REAL*)NULL) { terminatetetgen(NULL, 1); } // Read the list of volume constraints. for (i = 0; i < volelements; i++) { stringptr = readnumberline(inputline, infile, infilename); stringptr = findnextnumber(stringptr); if (*stringptr == '\0') { volume = -1.0; // No constraint on this tetrahedron. } else { volume = (REAL)strtod(stringptr, &stringptr); } tetrahedronvolumelist[i] = volume; } fclose(infile); return true; } /////////////////////////////////////////////////////////////////////////////// // // // load_var() Load constraints applied on facets, segments, and nodes // // from a .var file. // // // /////////////////////////////////////////////////////////////////////////////// bool tetgenio::load_var(char* filebasename) { FILE* infile; char varfilename[FILENAMESIZE]; char inputline[INPUTLINESIZE]; char* stringptr; int index; int i; // Variant constraints are saved in file "filename.var". strcpy(varfilename, filebasename); strcat(varfilename, ".var"); infile = fopen(varfilename, "r"); if (infile != (FILE*)NULL) { printf("Opening %s.\n", varfilename); } else { return false; } // Read the facet constraint section. stringptr = readnumberline(inputline, infile, varfilename); if (stringptr == NULL) { // No region list, return. fclose(infile); return true; } if (*stringptr != '\0') { numberoffacetconstraints = (int)strtol(stringptr, &stringptr, 0); } else { numberoffacetconstraints = 0; } if (numberoffacetconstraints > 0) { // Initialize 'facetconstraintlist'. facetconstraintlist = new REAL[numberoffacetconstraints * 2]; index = 0; for (i = 0; i < numberoffacetconstraints; i++) { stringptr = readnumberline(inputline, infile, varfilename); stringptr = findnextnumber(stringptr); if (*stringptr == '\0') { printf("Error: facet constraint %d has no facet marker.\n", firstnumber + i); break; } else { facetconstraintlist[index++] = (REAL)strtod(stringptr, &stringptr); } stringptr = findnextnumber(stringptr); if (*stringptr == '\0') { printf("Error: facet constraint %d has no maximum area bound.\n", firstnumber + i); break; } else { facetconstraintlist[index++] = (REAL)strtod(stringptr, &stringptr); } } if (i < numberoffacetconstraints) { // This must be caused by an error. fclose(infile); return false; } } // Read the segment constraint section. stringptr = readnumberline(inputline, infile, varfilename); if (stringptr == NULL) { // No segment list, return. fclose(infile); return true; } if (*stringptr != '\0') { numberofsegmentconstraints = (int)strtol(stringptr, &stringptr, 0); } else { numberofsegmentconstraints = 0; } if (numberofsegmentconstraints > 0) { // Initialize 'segmentconstraintlist'. segmentconstraintlist = new REAL[numberofsegmentconstraints * 3]; index = 0; for (i = 0; i < numberofsegmentconstraints; i++) { stringptr = readnumberline(inputline, infile, varfilename); stringptr = findnextnumber(stringptr); if (*stringptr == '\0') { printf("Error: segment constraint %d has no frist endpoint.\n", firstnumber + i); break; } else { segmentconstraintlist[index++] = (REAL)strtod(stringptr, &stringptr); } stringptr = findnextnumber(stringptr); if (*stringptr == '\0') { printf("Error: segment constraint %d has no second endpoint.\n", firstnumber + i); break; } else { segmentconstraintlist[index++] = (REAL)strtod(stringptr, &stringptr); } stringptr = findnextnumber(stringptr); if (*stringptr == '\0') { printf("Error: segment constraint %d has no maximum length bound.\n", firstnumber + i); break; } else { segmentconstraintlist[index++] = (REAL)strtod(stringptr, &stringptr); } } if (i < numberofsegmentconstraints) { // This must be caused by an error. fclose(infile); return false; } } fclose(infile); return true; } /////////////////////////////////////////////////////////////////////////////// // // // load_mtr() Load a size specification map from a .mtr file. // // // /////////////////////////////////////////////////////////////////////////////// bool tetgenio::load_mtr(char* filebasename) { FILE* infile; char mtrfilename[FILENAMESIZE]; char inputline[INPUTLINESIZE]; char* stringptr; REAL mtr; int ptnum; int mtrindex; int i, j; strcpy(mtrfilename, filebasename); strcat(mtrfilename, ".mtr"); infile = fopen(mtrfilename, "r"); if (infile != (FILE*)NULL) { printf("Opening %s.\n", mtrfilename); } else { return false; } // Read the number of points. stringptr = readnumberline(inputline, infile, mtrfilename); ptnum = (int)strtol(stringptr, &stringptr, 0); if (ptnum != numberofpoints) { printf(" !! Point numbers are not equal. Ignored.\n"); fclose(infile); return false; } // Read the number of columns (1, 3, or 6). stringptr = findnextnumber(stringptr); // Skip number of points. if (*stringptr != '\0') { numberofpointmtrs = (int)strtol(stringptr, &stringptr, 0); } if ((numberofpointmtrs != 1) && (numberofpointmtrs != 3) && (numberofpointmtrs != 6)) { // Column number doesn't match. numberofpointmtrs = 0; printf(" !! Metric size does not match (1, 3, or 6). Ignored.\n"); fclose(infile); return false; } // Allocate space for pointmtrlist. pointmtrlist = new REAL[numberofpoints * numberofpointmtrs]; if (pointmtrlist == (REAL*)NULL) { terminatetetgen(NULL, 1); } mtrindex = 0; for (i = 0; i < numberofpoints; i++) { // Read metrics. stringptr = readnumberline(inputline, infile, mtrfilename); for (j = 0; j < numberofpointmtrs; j++) { if (*stringptr == '\0') { printf("Error: Metric %d is missing value #%d in %s.\n", i + firstnumber, j + 1, mtrfilename); terminatetetgen(NULL, 1); } mtr = (REAL)strtod(stringptr, &stringptr); pointmtrlist[mtrindex++] = mtr; stringptr = findnextnumber(stringptr); } } fclose(infile); return true; } /////////////////////////////////////////////////////////////////////////////// // // // load_poly() Load a PL complex from a .poly or a .smesh file. // // // /////////////////////////////////////////////////////////////////////////////// bool tetgenio::load_poly(char* filebasename) { FILE* infile; char inpolyfilename[FILENAMESIZE]; char insmeshfilename[FILENAMESIZE]; char inputline[INPUTLINESIZE]; char *stringptr, *infilename; int smesh, markers, uvflag, currentmarker; int index; int i, j, k; // Assembling the actual file names we want to open. strcpy(inpolyfilename, filebasename); strcpy(insmeshfilename, filebasename); strcat(inpolyfilename, ".poly"); strcat(insmeshfilename, ".smesh"); // First assume it is a .poly file. smesh = 0; // Try to open a .poly file. infile = fopen(inpolyfilename, "r"); if (infile == (FILE*)NULL) { // .poly doesn't exist! Try to open a .smesh file. infile = fopen(insmeshfilename, "r"); if (infile == (FILE*)NULL) { printf(" Cannot access file %s and %s.\n", inpolyfilename, insmeshfilename); return false; } else { printf("Opening %s.\n", insmeshfilename); infilename = insmeshfilename; } smesh = 1; } else { printf("Opening %s.\n", inpolyfilename); infilename = inpolyfilename; } // Initialize the default values. mesh_dim = 3; // Three-dimensional coordinates. numberofpointattributes = 0; // no point attribute. markers = 0; // no boundary marker. uvflag = 0; // no uv parameters (required by a PSC). // Read number of points, number of dimensions, number of point // attributes, and number of boundary markers. stringptr = readnumberline(inputline, infile, infilename); numberofpoints = (int)strtol(stringptr, &stringptr, 0); stringptr = findnextnumber(stringptr); if (*stringptr != '\0') { mesh_dim = (int)strtol(stringptr, &stringptr, 0); } stringptr = findnextnumber(stringptr); if (*stringptr != '\0') { numberofpointattributes = (int)strtol(stringptr, &stringptr, 0); } stringptr = findnextnumber(stringptr); if (*stringptr != '\0') { markers = (int)strtol(stringptr, &stringptr, 0); } if (*stringptr != '\0') { uvflag = (int)strtol(stringptr, &stringptr, 0); } if (numberofpoints > 0) { // Load the list of nodes. if (!load_node_call(infile, markers, uvflag, infilename)) { fclose(infile); return false; } } else { // If the .poly or .smesh file claims there are zero points, that // means the points should be read from a separate .node file. if (!load_node(filebasename)) { fclose(infile); return false; } } if ((mesh_dim != 3) && (mesh_dim != 2)) { printf("Input error: TetGen only works for 2D & 3D point sets.\n"); fclose(infile); return false; } if (numberofpoints < (mesh_dim + 1)) { printf("Input error: TetGen needs at least %d points.\n", mesh_dim + 1); fclose(infile); return false; } facet* f; polygon* p; if (mesh_dim == 3) { // Read number of facets and number of boundary markers. stringptr = readnumberline(inputline, infile, infilename); if (stringptr == NULL) { // No facet list, return. fclose(infile); return true; } numberoffacets = (int)strtol(stringptr, &stringptr, 0); if (numberoffacets <= 0) { // No facet list, return. fclose(infile); return true; } stringptr = findnextnumber(stringptr); if (*stringptr == '\0') { markers = 0; // no boundary marker. } else { markers = (int)strtol(stringptr, &stringptr, 0); } // Initialize the 'facetlist', 'facetmarkerlist'. facetlist = new facet[numberoffacets]; if (markers == 1) { facetmarkerlist = new int[numberoffacets]; } // Read data into 'facetlist', 'facetmarkerlist'. if (smesh == 0) { // Facets are in .poly file format. for (i = 1; i <= numberoffacets; i++) { f = &(facetlist[i - 1]); init(f); f->numberofholes = 0; currentmarker = 0; // Read number of polygons, number of holes, and a boundary marker. stringptr = readnumberline(inputline, infile, infilename); f->numberofpolygons = (int)strtol(stringptr, &stringptr, 0); stringptr = findnextnumber(stringptr); if (*stringptr != '\0') { f->numberofholes = (int)strtol(stringptr, &stringptr, 0); if (markers == 1) { stringptr = findnextnumber(stringptr); if (*stringptr != '\0') { currentmarker = (int)strtol(stringptr, &stringptr, 0); } } } // Initialize facetmarker if it needs. if (markers == 1) { facetmarkerlist[i - 1] = currentmarker; } // Each facet should has at least one polygon. if (f->numberofpolygons <= 0) { printf("Error: Wrong number of polygon in %d facet.\n", i); break; } // Initialize the 'f->polygonlist'. f->polygonlist = new polygon[f->numberofpolygons]; // Go through all polygons, read in their vertices. for (j = 1; j <= f->numberofpolygons; j++) { p = &(f->polygonlist[j - 1]); init(p); // Read number of vertices of this polygon. stringptr = readnumberline(inputline, infile, infilename); p->numberofvertices = (int)strtol(stringptr, &stringptr, 0); if (p->numberofvertices < 1) { printf("Error: Wrong polygon %d in facet %d\n", j, i); break; } // Initialize 'p->vertexlist'. p->vertexlist = new int[p->numberofvertices]; // Read all vertices of this polygon. for (k = 1; k <= p->numberofvertices; k++) { stringptr = findnextnumber(stringptr); if (*stringptr == '\0') { // Try to load another non-empty line and continue to read the // rest of vertices. stringptr = readnumberline(inputline, infile, infilename); if (*stringptr == '\0') { printf("Error: Missing %d endpoints of polygon %d in facet %d", p->numberofvertices - k, j, i); break; } } p->vertexlist[k - 1] = (int)strtol(stringptr, &stringptr, 0); } } if (j <= f->numberofpolygons) { // This must be caused by an error. However, there're j - 1 // polygons have been read. Reset the 'f->numberofpolygon'. if (j == 1) { // This is the first polygon. delete[] f->polygonlist; } f->numberofpolygons = j - 1; // No hole will be read even it exists. f->numberofholes = 0; break; } // If this facet has hole pints defined, read them. if (f->numberofholes > 0) { // Initialize 'f->holelist'. f->holelist = new REAL[f->numberofholes * 3]; // Read the holes' coordinates. index = 0; for (j = 1; j <= f->numberofholes; j++) { stringptr = readnumberline(inputline, infile, infilename); for (k = 1; k <= 3; k++) { stringptr = findnextnumber(stringptr); if (*stringptr == '\0') { printf("Error: Hole %d in facet %d has no coordinates", j, i); break; } f->holelist[index++] = (REAL)strtod(stringptr, &stringptr); } if (k <= 3) { // This must be caused by an error. break; } } if (j <= f->numberofholes) { // This must be caused by an error. break; } } } if (i <= numberoffacets) { // This must be caused by an error. numberoffacets = i - 1; fclose(infile); return false; } } else { // poly == 0 // Read the facets from a .smesh file. for (i = 1; i <= numberoffacets; i++) { f = &(facetlist[i - 1]); init(f); // Initialize 'f->facetlist'. In a .smesh file, each facetlist only // contains exactly one polygon, no hole. f->numberofpolygons = 1; f->polygonlist = new polygon[f->numberofpolygons]; p = &(f->polygonlist[0]); init(p); // Read number of vertices of this polygon. stringptr = readnumberline(inputline, infile, insmeshfilename); p->numberofvertices = (int)strtol(stringptr, &stringptr, 0); if (p->numberofvertices < 1) { printf("Error: Wrong number of vertex in facet %d\n", i); break; } // Initialize 'p->vertexlist'. p->vertexlist = new int[p->numberofvertices]; for (k = 1; k <= p->numberofvertices; k++) { stringptr = findnextnumber(stringptr); if (*stringptr == '\0') { // Try to load another non-empty line and continue to read the // rest of vertices. stringptr = readnumberline(inputline, infile, infilename); if (*stringptr == '\0') { printf("Error: Missing %d endpoints in facet %d", p->numberofvertices - k, i); break; } } p->vertexlist[k - 1] = (int)strtol(stringptr, &stringptr, 0); } if (k <= p->numberofvertices) { // This must be caused by an error. break; } // Read facet's boundary marker at last. if (markers == 1) { stringptr = findnextnumber(stringptr); if (*stringptr == '\0') { currentmarker = 0; } else { currentmarker = (int)strtol(stringptr, &stringptr, 0); } facetmarkerlist[i - 1] = currentmarker; } } if (i <= numberoffacets) { // This must be caused by an error. numberoffacets = i - 1; fclose(infile); return false; } } // Read the hole section. stringptr = readnumberline(inputline, infile, infilename); if (stringptr == NULL) { // No hole list, return. fclose(infile); return true; } if (*stringptr != '\0') { numberofholes = (int)strtol(stringptr, &stringptr, 0); } else { numberofholes = 0; } if (numberofholes > 0) { // Initialize 'holelist'. holelist = new REAL[numberofholes * 3]; for (i = 0; i < 3 * numberofholes; i += 3) { stringptr = readnumberline(inputline, infile, infilename); stringptr = findnextnumber(stringptr); if (*stringptr == '\0') { printf("Error: Hole %d has no x coord.\n", firstnumber + (i / 3)); break; } else { holelist[i] = (REAL)strtod(stringptr, &stringptr); } stringptr = findnextnumber(stringptr); if (*stringptr == '\0') { printf("Error: Hole %d has no y coord.\n", firstnumber + (i / 3)); break; } else { holelist[i + 1] = (REAL)strtod(stringptr, &stringptr); } stringptr = findnextnumber(stringptr); if (*stringptr == '\0') { printf("Error: Hole %d has no z coord.\n", firstnumber + (i / 3)); break; } else { holelist[i + 2] = (REAL)strtod(stringptr, &stringptr); } } if (i < 3 * numberofholes) { // This must be caused by an error. fclose(infile); return false; } } // Read the region section. The 'region' section is optional, if we // don't reach the end-of-file, try read it in. stringptr = readnumberline(inputline, infile, NULL); if (stringptr != (char*)NULL && *stringptr != '\0') { numberofregions = (int)strtol(stringptr, &stringptr, 0); } else { numberofregions = 0; } if (numberofregions > 0) { // Initialize 'regionlist'. regionlist = new REAL[numberofregions * 5]; index = 0; for (i = 0; i < numberofregions; i++) { stringptr = readnumberline(inputline, infile, infilename); stringptr = findnextnumber(stringptr); if (*stringptr == '\0') { printf("Error: Region %d has no x coordinate.\n", firstnumber + i); break; } else { regionlist[index++] = (REAL)strtod(stringptr, &stringptr); } stringptr = findnextnumber(stringptr); if (*stringptr == '\0') { printf("Error: Region %d has no y coordinate.\n", firstnumber + i); break; } else { regionlist[index++] = (REAL)strtod(stringptr, &stringptr); } stringptr = findnextnumber(stringptr); if (*stringptr == '\0') { printf("Error: Region %d has no z coordinate.\n", firstnumber + i); break; } else { regionlist[index++] = (REAL)strtod(stringptr, &stringptr); } stringptr = findnextnumber(stringptr); if (*stringptr == '\0') { printf("Error: Region %d has no region attrib.\n", firstnumber + i); break; } else { regionlist[index++] = (REAL)strtod(stringptr, &stringptr); } stringptr = findnextnumber(stringptr); if (*stringptr == '\0') { regionlist[index] = regionlist[index - 1]; } else { regionlist[index] = (REAL)strtod(stringptr, &stringptr); } index++; } if (i < numberofregions) { // This must be caused by an error. fclose(infile); return false; } } } // End of reading poly/smesh file. fclose(infile); return true; } /////////////////////////////////////////////////////////////////////////////// // // // load_off() Load a polyhedron from a .off file. // // // // The .off format is one of file formats of the Geomview, an interactive // // program for viewing and manipulating geometric objects. More information // // is available form: http://www.geomview.org. // // // /////////////////////////////////////////////////////////////////////////////// bool tetgenio::load_off(char* filebasename) { FILE* fp; tetgenio::facet* f; tetgenio::polygon* p; char infilename[FILENAMESIZE]; char buffer[INPUTLINESIZE]; char* bufferp; double* coord; int nverts = 0, iverts = 0; int nfaces = 0, ifaces = 0; int nedges = 0; int line_count = 0, i; // Default, the off file's index is from '0'. We check it by remembering the // smallest index we found in the file. It should be either 0 or 1. int smallestidx = 0; strncpy(infilename, filebasename, 1024 - 1); infilename[FILENAMESIZE - 1] = '\0'; if (infilename[0] == '\0') { printf("Error: No filename.\n"); return false; } if (strcmp(&infilename[strlen(infilename) - 4], ".off") != 0) { strcat(infilename, ".off"); } if (!(fp = fopen(infilename, "r"))) { printf(" Unable to open file %s\n", infilename); return false; } printf("Opening %s.\n", infilename); while ((bufferp = readline(buffer, fp, &line_count)) != NULL) { // Check section if (nverts == 0) { // Read header bufferp = strstr(bufferp, "OFF"); if (bufferp != NULL) { // Read mesh counts bufferp = findnextnumber(bufferp); // Skip field "OFF". if (*bufferp == '\0') { // Read a non-empty line. bufferp = readline(buffer, fp, &line_count); } if ((sscanf(bufferp, "%d%d%d", &nverts, &nfaces, &nedges) != 3) || (nverts == 0)) { printf("Syntax error reading header on line %d in file %s\n", line_count, infilename); fclose(fp); return false; } // Allocate memory for 'tetgenio' if (nverts > 0) { numberofpoints = nverts; pointlist = new REAL[nverts * 3]; smallestidx = nverts + 1; // A bigger enough number. } if (nfaces > 0) { numberoffacets = nfaces; facetlist = new tetgenio::facet[nfaces]; } } } else if (iverts < nverts) { // Read vertex coordinates coord = &pointlist[iverts * 3]; for (i = 0; i < 3; i++) { if (*bufferp == '\0') { printf("Syntax error reading vertex coords on line %d in file %s\n", line_count, infilename); fclose(fp); return false; } coord[i] = (REAL)strtod(bufferp, &bufferp); bufferp = findnextnumber(bufferp); } iverts++; } else if (ifaces < nfaces) { // Get next face f = &facetlist[ifaces]; init(f); // In .off format, each facet has one polygon, no hole. f->numberofpolygons = 1; f->polygonlist = new tetgenio::polygon[1]; p = &f->polygonlist[0]; init(p); // Read the number of vertices, it should be greater than 0. p->numberofvertices = (int)strtol(bufferp, &bufferp, 0); if (p->numberofvertices == 0) { printf("Syntax error reading polygon on line %d in file %s\n", line_count, infilename); fclose(fp); return false; } // Allocate memory for face vertices p->vertexlist = new int[p->numberofvertices]; for (i = 0; i < p->numberofvertices; i++) { bufferp = findnextnumber(bufferp); if (*bufferp == '\0') { printf("Syntax error reading polygon on line %d in file %s\n", line_count, infilename); fclose(fp); return false; } p->vertexlist[i] = (int)strtol(bufferp, &bufferp, 0); // Detect the smallest index. if (p->vertexlist[i] < smallestidx) { smallestidx = p->vertexlist[i]; } } ifaces++; } else { // Should never get here printf("Found extra text starting at line %d in file %s\n", line_count, infilename); break; } } // Close file fclose(fp); // Decide the firstnumber of the index. if (smallestidx == 0) { firstnumber = 0; } else if (smallestidx == 1) { firstnumber = 1; } else { printf("A wrong smallest index (%d) was detected in file %s\n", smallestidx, infilename); return false; } if (iverts != nverts) { printf("Expected %d vertices, but read only %d vertices in file %s\n", nverts, iverts, infilename); return false; } if (ifaces != nfaces) { printf("Expected %d faces, but read only %d faces in file %s\n", nfaces, ifaces, infilename); return false; } return true; } /////////////////////////////////////////////////////////////////////////////// // // // load_ply() Load a polyhedron from a .ply file. // // // // This is a simplified version of reading .ply files, which only reads the // // set of vertices and the set of faces. Other informations (such as color, // // material, texture, etc) in .ply file are ignored. Complete routines for // // reading and writing ,ply files are available from: http://www.cc.gatech. // // edu/projects/large_models/ply.html. Except the header section, ply file // // format has exactly the same format for listing vertices and polygons as // // off file format. // // // /////////////////////////////////////////////////////////////////////////////// bool tetgenio::load_ply(char* filebasename) { FILE* fp; tetgenio::facet* f; tetgenio::polygon* p; char infilename[FILENAMESIZE]; char buffer[INPUTLINESIZE]; char *bufferp, *str; double* coord; int endheader = 0, format = 0; int nverts = 0, iverts = 0; int nfaces = 0, ifaces = 0; int line_count = 0, i; // Default, the ply file's index is from '0'. We check it by remembering the // smallest index we found in the file. It should be either 0 or 1. int smallestidx = 0; strncpy(infilename, filebasename, FILENAMESIZE - 1); infilename[FILENAMESIZE - 1] = '\0'; if (infilename[0] == '\0') { printf("Error: No filename.\n"); return false; } if (strcmp(&infilename[strlen(infilename) - 4], ".ply") != 0) { strcat(infilename, ".ply"); } if (!(fp = fopen(infilename, "r"))) { printf("Error: Unable to open file %s\n", infilename); return false; } printf("Opening %s.\n", infilename); while ((bufferp = readline(buffer, fp, &line_count)) != NULL) { if (!endheader) { // Find if it is the keyword "end_header". str = strstr(bufferp, "end_header"); // strstr() is case sensitive. if (!str) str = strstr(bufferp, "End_header"); if (!str) str = strstr(bufferp, "End_Header"); if (str) { // This is the end of the header section. endheader = 1; continue; } // Parse the number of vertices and the number of faces. if (nverts == 0 || nfaces == 0) { // Find if it si the keyword "element". str = strstr(bufferp, "element"); if (!str) str = strstr(bufferp, "Element"); if (str) { bufferp = findnextfield(str); if (*bufferp == '\0') { printf("Syntax error reading element type on line%d in file %s\n", line_count, infilename); fclose(fp); return false; } if (nverts == 0) { // Find if it is the keyword "vertex". str = strstr(bufferp, "vertex"); if (!str) str = strstr(bufferp, "Vertex"); if (str) { bufferp = findnextnumber(str); if (*bufferp == '\0') { printf("Syntax error reading vertex number on line"); printf(" %d in file %s\n", line_count, infilename); fclose(fp); return false; } nverts = (int)strtol(bufferp, &bufferp, 0); // Allocate memory for 'tetgenio' if (nverts > 0) { numberofpoints = nverts; pointlist = new REAL[nverts * 3]; smallestidx = nverts + 1; // A big enough index. } } } if (nfaces == 0) { // Find if it is the keyword "face". str = strstr(bufferp, "face"); if (!str) str = strstr(bufferp, "Face"); if (str) { bufferp = findnextnumber(str); if (*bufferp == '\0') { printf("Syntax error reading face number on line"); printf(" %d in file %s\n", line_count, infilename); fclose(fp); return false; } nfaces = (int)strtol(bufferp, &bufferp, 0); // Allocate memory for 'tetgenio' if (nfaces > 0) { numberoffacets = nfaces; facetlist = new tetgenio::facet[nfaces]; } } } } // It is not the string "element". } if (format == 0) { // Find the keyword "format". str = strstr(bufferp, "format"); if (!str) str = strstr(bufferp, "Format"); if (str) { format = 1; bufferp = findnextfield(str); // Find if it is the string "ascii". str = strstr(bufferp, "ascii"); if (!str) str = strstr(bufferp, "ASCII"); if (!str) { printf("This routine only reads ascii format of ply files.\n"); printf("Hint: You can convert the binary to ascii format by\n"); printf(" using the provided ply tools:\n"); printf(" ply2ascii < %s > ascii_%s\n", infilename, infilename); fclose(fp); return false; } } } } else if (iverts < nverts) { // Read vertex coordinates coord = &pointlist[iverts * 3]; for (i = 0; i < 3; i++) { if (*bufferp == '\0') { printf("Syntax error reading vertex coords on line %d in file %s\n", line_count, infilename); fclose(fp); return false; } coord[i] = (REAL)strtod(bufferp, &bufferp); bufferp = findnextnumber(bufferp); } iverts++; } else if (ifaces < nfaces) { // Get next face f = &facetlist[ifaces]; init(f); // In .off format, each facet has one polygon, no hole. f->numberofpolygons = 1; f->polygonlist = new tetgenio::polygon[1]; p = &f->polygonlist[0]; init(p); // Read the number of vertices, it should be greater than 0. p->numberofvertices = (int)strtol(bufferp, &bufferp, 0); if (p->numberofvertices == 0) { printf("Syntax error reading polygon on line %d in file %s\n", line_count, infilename); fclose(fp); return false; } // Allocate memory for face vertices p->vertexlist = new int[p->numberofvertices]; for (i = 0; i < p->numberofvertices; i++) { bufferp = findnextnumber(bufferp); if (*bufferp == '\0') { printf("Syntax error reading polygon on line %d in file %s\n", line_count, infilename); fclose(fp); return false; } p->vertexlist[i] = (int)strtol(bufferp, &bufferp, 0); if (p->vertexlist[i] < smallestidx) { smallestidx = p->vertexlist[i]; } } ifaces++; } else { // Should never get here printf("Found extra text starting at line %d in file %s\n", line_count, infilename); break; } } // Close file fclose(fp); // Decide the firstnumber of the index. if (smallestidx == 0) { firstnumber = 0; } else if (smallestidx == 1) { firstnumber = 1; } else { printf("A wrong smallest index (%d) was detected in file %s\n", smallestidx, infilename); return false; } if (iverts != nverts) { printf("Expected %d vertices, but read only %d vertices in file %s\n", nverts, iverts, infilename); return false; } if (ifaces != nfaces) { printf("Expected %d faces, but read only %d faces in file %s\n", nfaces, ifaces, infilename); return false; } return true; } /////////////////////////////////////////////////////////////////////////////// // // // load_stl() Load a surface mesh from a .stl file. // // // // The .stl or stereolithography format is an ASCII or binary file used in // // manufacturing. It is a list of the triangular surfaces that describe a // // computer generated solid model. This is the standard input for most rapid // // prototyping machines. // // // // Comment: A .stl file many contain many duplicated points. They will be // // unified during the Delaunay tetrahedralization process. // // // /////////////////////////////////////////////////////////////////////////////// void SwapBytes(char* array, int size, int n) { char* x = new char[size]; for (int i = 0; i < n; i++) { char* a = &array[i * size]; memcpy(x, a, size); for (int c = 0; c < size; c++) a[size - 1 - c] = x[c]; } delete[] x; } bool tetgenio::load_stl(char* filebasename) { FILE* fp; tetgenmesh::arraypool* plist; tetgenio::facet* f; tetgenio::polygon* p; char infilename[FILENAMESIZE]; char buffer[INPUTLINESIZE]; char *bufferp, *str; double* coord; int solid = 0; int nverts = 0, iverts = 0; int nfaces = 0; int line_count = 0, i; strncpy(infilename, filebasename, FILENAMESIZE - 1); infilename[FILENAMESIZE - 1] = '\0'; if (infilename[0] == '\0') { printf("Error: No filename.\n"); return false; } if (strcmp(&infilename[strlen(infilename) - 4], ".stl") != 0) { strcat(infilename, ".stl"); } if (!(fp = fopen(infilename, "rb"))) { printf("Error: Unable to open file %s\n", infilename); return false; } printf("Opening %s.\n", infilename); // "solid", or binary data header if (!fgets(buffer, sizeof(buffer), fp)) { fclose(fp); return 0; } bool binary = strncmp(buffer, "solid", 5) && strncmp(buffer, "SOLID", 5); // STL file has no number of points available. Use a list to read points. plist = new tetgenmesh::arraypool(sizeof(double) * 3, 10); if (!binary) { solid = 1; while ((bufferp = readline(buffer, fp, &line_count)) != NULL) { // The ASCII .stl file must start with the lower case keyword solid and // end with endsolid. if (solid == 0) { // Read header bufferp = strstr(bufferp, "solid"); if (bufferp != NULL) { solid = 1; } } else { // We're inside the block of the solid. str = bufferp; // Is this the end of the solid. bufferp = strstr(bufferp, "endsolid"); if (bufferp != NULL) { solid = 0; } else { // Read the XYZ coordinates if it is a vertex. bufferp = str; bufferp = strstr(bufferp, "vertex"); if (bufferp != NULL) { plist->newindex((void**)&coord); for (i = 0; i < 3; i++) { bufferp = findnextnumber(bufferp); if (*bufferp == '\0') { printf("Syntax error reading vertex coords on line %d\n", line_count); delete plist; fclose(fp); return false; } coord[i] = (REAL)strtod(bufferp, &bufferp); } } } } } } // if(!binary) else { rewind(fp); while (!feof(fp)) { char header[80]; if (!fread(header, sizeof(char), 80, fp)) break; unsigned int nfacets = 0; size_t ret = fread(&nfacets, sizeof(unsigned int), 1, fp); bool swap = false; if (nfacets > 100000000) { // Msg::Info("Swapping bytes from binary file"); swap = true; SwapBytes((char*)&nfacets, sizeof(unsigned int), 1); } if (ret && nfacets) { // points.resize(points.size() + 1); char* data = new char[nfacets * 50 * sizeof(char)]; ret = fread(data, sizeof(char), nfacets * 50, fp); if (ret == nfacets * 50) { for (unsigned int i = 0; i < nfacets; i++) { float* xyz = (float*)&data[i * 50 * sizeof(char)]; if (swap) SwapBytes((char*)xyz, sizeof(float), 12); for (int j = 0; j < 3; j++) { // SPoint3 p(xyz[3 + 3 * j], xyz[3 + 3 * j + 1], xyz[3 + 3 * j + 2]); // points.back().push_back(p); // bbox += p; plist->newindex((void**)&coord); coord[0] = xyz[3 + 3 * j]; coord[1] = xyz[3 + 3 * j + 1]; coord[2] = xyz[3 + 3 * j + 2]; } } } delete[] data; } } // while (!feof(fp)) } // binary fclose(fp); nverts = (int)plist->objects; // nverts should be an integer times 3 (every 3 vertices denote a face). if (nverts == 0 || (nverts % 3 != 0)) { printf("Error: Wrong number of vertices in file %s.\n", infilename); delete plist; return false; } numberofpoints = nverts; pointlist = new REAL[nverts * 3]; for (i = 0; i < nverts; i++) { coord = (double*)fastlookup(plist, i); iverts = i * 3; pointlist[iverts] = (REAL)coord[0]; pointlist[iverts + 1] = (REAL)coord[1]; pointlist[iverts + 2] = (REAL)coord[2]; } nfaces = (int)(nverts / 3); numberoffacets = nfaces; facetlist = new tetgenio::facet[nfaces]; // Default use '1' as the array starting index. firstnumber = 1; iverts = firstnumber; for (i = 0; i < nfaces; i++) { f = &facetlist[i]; init(f); // In .stl format, each facet has one polygon, no hole. f->numberofpolygons = 1; f->polygonlist = new tetgenio::polygon[1]; p = &f->polygonlist[0]; init(p); // Each polygon has three vertices. p->numberofvertices = 3; p->vertexlist = new int[p->numberofvertices]; p->vertexlist[0] = iverts; p->vertexlist[1] = iverts + 1; p->vertexlist[2] = iverts + 2; iverts += 3; } delete plist; return true; } /////////////////////////////////////////////////////////////////////////////// // // // load_medit() Load a surface mesh from a .mesh file. // // // // The .mesh format is the file format of Medit, a user-friendly interactive // // mesh viewer program. // // // /////////////////////////////////////////////////////////////////////////////// bool tetgenio::load_medit(char* filebasename, int istetmesh) { FILE* fp; tetgenio::facet *tmpflist, *f; tetgenio::polygon* p; char infilename[FILENAMESIZE]; char buffer[INPUTLINESIZE]; char *bufferp, *str; double* coord; int* tmpfmlist; int dimension = 0; int nverts = 0; int nfaces = 0; int ntets = 0; int line_count = 0; int corners = 0; // 3 (triangle) or 4 (quad). int* plist; int i, j; int smallestidx = 0; strncpy(infilename, filebasename, FILENAMESIZE - 1); infilename[FILENAMESIZE - 1] = '\0'; if (infilename[0] == '\0') { printf("Error: No filename.\n"); return false; } if (strcmp(&infilename[strlen(infilename) - 5], ".mesh") != 0) { strcat(infilename, ".mesh"); } if (!(fp = fopen(infilename, "r"))) { printf("Error: Unable to open file %s\n", infilename); return false; } printf("Opening %s.\n", infilename); while ((bufferp = readline(buffer, fp, &line_count)) != NULL) { if (*bufferp == '#') continue; // A comment line is skipped. if (dimension == 0) { // Find if it is the keyword "Dimension". str = strstr(bufferp, "Dimension"); if (!str) str = strstr(bufferp, "dimension"); if (!str) str = strstr(bufferp, "DIMENSION"); if (str) { // Read the dimensions bufferp = findnextnumber(str); // Skip field "Dimension". if (*bufferp == '\0') { // Read a non-empty line. bufferp = readline(buffer, fp, &line_count); } dimension = (int)strtol(bufferp, &bufferp, 0); if (dimension != 2 && dimension != 3) { printf("Unknown dimension in file on line %d in file %s\n", line_count, infilename); fclose(fp); return false; } mesh_dim = dimension; } } if (nverts == 0) { // Find if it is the keyword "Vertices". str = strstr(bufferp, "Vertices"); if (!str) str = strstr(bufferp, "vertices"); if (!str) str = strstr(bufferp, "VERTICES"); if (str) { // Read the number of vertices. bufferp = findnextnumber(str); // Skip field "Vertices". if (*bufferp == '\0') { // Read a non-empty line. bufferp = readline(buffer, fp, &line_count); } nverts = (int)strtol(bufferp, &bufferp, 0); // Initialize the smallest index. smallestidx = nverts + 1; // Allocate memory for 'tetgenio' if (nverts > 0) { numberofpoints = nverts; pointlist = new REAL[nverts * 3]; } // Read the follwoing node list. for (i = 0; i < nverts; i++) { bufferp = readline(buffer, fp, &line_count); if (bufferp == NULL) { printf("Unexpected end of file on line %d in file %s\n", line_count, infilename); fclose(fp); return false; } // Read vertex coordinates coord = &pointlist[i * 3]; for (j = 0; j < 3; j++) { if (*bufferp == '\0') { printf("Syntax error reading vertex coords on line"); printf(" %d in file %s\n", line_count, infilename); fclose(fp); return false; } if ((j < 2) || (dimension == 3)) { coord[j] = (REAL)strtod(bufferp, &bufferp); } else { coord[j] = 0.0; } bufferp = findnextnumber(bufferp); } } continue; } } if (ntets == 0) { // Find if it is the keyword "Tetrahedra" corners = 0; str = strstr(bufferp, "Tetrahedra"); if (!str) str = strstr(bufferp, "tetrahedra"); if (!str) str = strstr(bufferp, "TETRAHEDRA"); if (str) { corners = 4; } if (corners == 4) { // Read the number of tetrahedra bufferp = findnextnumber(str); // Skip field "Tetrahedra". if (*bufferp == '\0') { // Read a non-empty line. bufferp = readline(buffer, fp, &line_count); } ntets = strtol(bufferp, &bufferp, 0); if (ntets > 0) { // It is a tetrahedral mesh. numberoftetrahedra = ntets; numberofcorners = 4; numberoftetrahedronattributes = 1; tetrahedronlist = new int[ntets * 4]; tetrahedronattributelist = new REAL[ntets]; } } // if (corners == 4) // Read the list of tetrahedra. for (i = 0; i < numberoftetrahedra; i++) { plist = &(tetrahedronlist[i * 4]); bufferp = readline(buffer, fp, &line_count); if (bufferp == NULL) { printf("Unexpected end of file on line %d in file %s\n", line_count, infilename); fclose(fp); return false; } // Read the vertices of the tet. for (j = 0; j < corners; j++) { if (*bufferp == '\0') { printf("Syntax error reading face on line %d in file %s\n", line_count, infilename); fclose(fp); return false; } plist[j] = (int)strtol(bufferp, &bufferp, 0); // Remember the smallest index. if (plist[j] < smallestidx) smallestidx = plist[j]; bufferp = findnextnumber(bufferp); } // Read the attribute of the tet if it exists. tetrahedronattributelist[i] = 0; if (*bufferp != '\0') { tetrahedronattributelist[i] = (REAL)strtol(bufferp, &bufferp, 0); } } // i } // Tetrahedra if (nfaces == 0) { // Find if it is the keyword "Triangles" or "Quadrilaterals". corners = 0; str = strstr(bufferp, "Triangles"); if (!str) str = strstr(bufferp, "triangles"); if (!str) str = strstr(bufferp, "TRIANGLES"); if (str) { corners = 3; } else { str = strstr(bufferp, "Quadrilaterals"); if (!str) str = strstr(bufferp, "quadrilaterals"); if (!str) str = strstr(bufferp, "QUADRILATERALS"); if (str) { corners = 4; } } if (corners == 3 || corners == 4) { // Read the number of triangles (or quadrilaterals). bufferp = findnextnumber(str); // Skip field "Triangles". if (*bufferp == '\0') { // Read a non-empty line. bufferp = readline(buffer, fp, &line_count); } nfaces = strtol(bufferp, &bufferp, 0); // Allocate memory for 'tetgenio' if (nfaces > 0) { if (!istetmesh) { // It is a PLC surface mesh. if (numberoffacets > 0) { // facetlist has already been allocated. Enlarge arrays. // This happens when the surface mesh contains mixed cells. tmpflist = new tetgenio::facet[numberoffacets + nfaces]; tmpfmlist = new int[numberoffacets + nfaces]; // Copy the data of old arrays into new arrays. for (i = 0; i < numberoffacets; i++) { f = &(tmpflist[i]); tetgenio::init(f); *f = facetlist[i]; tmpfmlist[i] = facetmarkerlist[i]; } // Release old arrays. delete[] facetlist; delete[] facetmarkerlist; // Remember the new arrays. facetlist = tmpflist; facetmarkerlist = tmpfmlist; } else { // This is the first time to allocate facetlist. facetlist = new tetgenio::facet[nfaces]; facetmarkerlist = new int[nfaces]; } } else { if (corners == 3) { // It is a surface mesh of a tetrahedral mesh. numberoftrifaces = nfaces; trifacelist = new int[nfaces * 3]; trifacemarkerlist = new int[nfaces]; } } } // if (nfaces > 0) // Read the following list of faces. if (!istetmesh) { for (i = numberoffacets; i < numberoffacets + nfaces; i++) { bufferp = readline(buffer, fp, &line_count); if (bufferp == NULL) { printf("Unexpected end of file on line %d in file %s\n", line_count, infilename); fclose(fp); return false; } f = &facetlist[i]; tetgenio::init(f); // In .mesh format, each facet has one polygon, no hole. f->numberofpolygons = 1; f->polygonlist = new tetgenio::polygon[1]; p = &f->polygonlist[0]; tetgenio::init(p); p->numberofvertices = corners; // Allocate memory for face vertices p->vertexlist = new int[p->numberofvertices]; // Read the vertices of the face. for (j = 0; j < corners; j++) { if (*bufferp == '\0') { printf("Syntax error reading face on line %d in file %s\n", line_count, infilename); fclose(fp); return false; } p->vertexlist[j] = (int)strtol(bufferp, &bufferp, 0); // Remember the smallest index. if (p->vertexlist[j] < smallestidx) { smallestidx = p->vertexlist[j]; } bufferp = findnextnumber(bufferp); } // Read the marker of the face if it exists. facetmarkerlist[i] = 0; if (*bufferp != '\0') { facetmarkerlist[i] = (int)strtol(bufferp, &bufferp, 0); } } // Have read in a list of triangles/quads. numberoffacets += nfaces; nfaces = 0; } else { // It is a surface mesh of a tetrahedral mesh. if (corners == 3) { for (i = 0; i < numberoftrifaces; i++) { plist = &(trifacelist[i * 3]); bufferp = readline(buffer, fp, &line_count); if (bufferp == NULL) { printf("Unexpected end of file on line %d in file %s\n", line_count, infilename); fclose(fp); return false; } // Read the vertices of the face. for (j = 0; j < corners; j++) { if (*bufferp == '\0') { printf("Syntax error reading face on line %d in file %s\n", line_count, infilename); fclose(fp); return false; } plist[j] = (int)strtol(bufferp, &bufferp, 0); // Remember the smallest index. if (plist[j] < smallestidx) { smallestidx = plist[j]; } bufferp = findnextnumber(bufferp); } // Read the marker of the face if it exists. trifacemarkerlist[i] = 0; if (*bufferp != '\0') { trifacemarkerlist[i] = (int)strtol(bufferp, &bufferp, 0); } } // i } // if (corners == 3) } // if (b->refine) } // if (corners == 3 || corners == 4) } } // Close file fclose(fp); // Decide the firstnumber of the index. if (smallestidx == 0) { firstnumber = 0; } else if (smallestidx == 1) { firstnumber = 1; } else { printf("A wrong smallest index (%d) was detected in file %s\n", smallestidx, infilename); return false; } return true; } /////////////////////////////////////////////////////////////////////////////// // // // load_vtk() Load VTK surface mesh from file (.vtk ascii or binary). // // // // This function is contributed by: Bryn Lloyd, Computer Vision Laboratory, // // ETH, Zuerich. May 7, 2007. // // // /////////////////////////////////////////////////////////////////////////////// // Two inline functions used in read/write VTK files. void swapBytes(unsigned char* var, int size) { int i = 0; int j = size - 1; char c; while (i < j) { c = var[i]; var[i] = var[j]; var[j] = c; i++, j--; } } bool testIsBigEndian() { short word = 0x4321; if ((*(char*)&word) != 0x21) return true; else return false; } bool tetgenio::load_vtk(char* filebasename) { FILE* fp; tetgenio::facet* f; tetgenio::polygon* p; char infilename[FILENAMESIZE]; char line[INPUTLINESIZE]; char mode[128], id[256], fmt[64]; char* bufferp; double* coord; float _x, _y, _z; int nverts = 0; int nfaces = 0; int line_count = 0; int dummy; int id1, id2, id3; int nn = -1; int nn_old = -1; int i, j; bool ImALittleEndian = !testIsBigEndian(); int smallestidx = 0; strncpy(infilename, filebasename, FILENAMESIZE - 1); infilename[FILENAMESIZE - 1] = '\0'; if (infilename[0] == '\0') { printf("Error: No filename.\n"); return false; } if (strcmp(&infilename[strlen(infilename) - 4], ".vtk") != 0) { strcat(infilename, ".vtk"); } if (!(fp = fopen(infilename, "r"))) { printf("Error: Unable to open file %s\n", infilename); return false; } printf("Opening %s.\n", infilename); // Default uses the index starts from '0'. firstnumber = 0; strcpy(mode, "BINARY"); while ((bufferp = readline(line, fp, &line_count)) != NULL) { if (strlen(line) == 0) continue; // swallow lines beginning with a comment sign or white space if (line[0] == '#' || line[0] == '\n' || line[0] == 10 || line[0] == 13 || line[0] == 32) continue; sscanf(line, "%s", id); if (!strcmp(id, "ASCII")) { strcpy(mode, "ASCII"); } if (!strcmp(id, "POINTS")) { sscanf(line, "%s %d %s", id, &nverts, fmt); if (nverts > 0) { numberofpoints = nverts; pointlist = new REAL[nverts * 3]; smallestidx = nverts + 1; } if (!strcmp(mode, "BINARY")) { for (i = 0; i < nverts; i++) { coord = &pointlist[i * 3]; if (!strcmp(fmt, "double")) { fread((char*)(&(coord[0])), sizeof(double), 1, fp); fread((char*)(&(coord[1])), sizeof(double), 1, fp); fread((char*)(&(coord[2])), sizeof(double), 1, fp); if (ImALittleEndian) { swapBytes((unsigned char*)&(coord[0]), sizeof(coord[0])); swapBytes((unsigned char*)&(coord[1]), sizeof(coord[1])); swapBytes((unsigned char*)&(coord[2]), sizeof(coord[2])); } } else if (!strcmp(fmt, "float")) { fread((char*)(&_x), sizeof(float), 1, fp); fread((char*)(&_y), sizeof(float), 1, fp); fread((char*)(&_z), sizeof(float), 1, fp); if (ImALittleEndian) { swapBytes((unsigned char*)&_x, sizeof(_x)); swapBytes((unsigned char*)&_y, sizeof(_y)); swapBytes((unsigned char*)&_z, sizeof(_z)); } coord[0] = double(_x); coord[1] = double(_y); coord[2] = double(_z); } else { printf("Error: Only float or double formats are supported!\n"); return false; } } } else if (!strcmp(mode, "ASCII")) { for (i = 0; i < nverts; i++) { bufferp = readline(line, fp, &line_count); if (bufferp == NULL) { printf("Unexpected end of file on line %d in file %s\n", line_count, infilename); fclose(fp); return false; } // Read vertex coordinates coord = &pointlist[i * 3]; for (j = 0; j < 3; j++) { if (*bufferp == '\0') { printf("Syntax error reading vertex coords on line"); printf(" %d in file %s\n", line_count, infilename); fclose(fp); return false; } coord[j] = (REAL)strtod(bufferp, &bufferp); bufferp = findnextnumber(bufferp); } } } continue; } if (!strcmp(id, "POLYGONS")) { sscanf(line, "%s %d %d", id, &nfaces, &dummy); if (nfaces > 0) { numberoffacets = nfaces; facetlist = new tetgenio::facet[nfaces]; } if (!strcmp(mode, "BINARY")) { for (i = 0; i < nfaces; i++) { fread((char*)(&nn), sizeof(int), 1, fp); if (ImALittleEndian) { swapBytes((unsigned char*)&nn, sizeof(nn)); } if (i == 0) nn_old = nn; if (nn != nn_old) { printf("Error: No mixed cells are allowed.\n"); return false; } if (nn == 3) { fread((char*)(&id1), sizeof(int), 1, fp); fread((char*)(&id2), sizeof(int), 1, fp); fread((char*)(&id3), sizeof(int), 1, fp); if (ImALittleEndian) { swapBytes((unsigned char*)&id1, sizeof(id1)); swapBytes((unsigned char*)&id2, sizeof(id2)); swapBytes((unsigned char*)&id3, sizeof(id3)); } f = &facetlist[i]; init(f); // In .off format, each facet has one polygon, no hole. f->numberofpolygons = 1; f->polygonlist = new tetgenio::polygon[1]; p = &f->polygonlist[0]; init(p); // Set number of vertices p->numberofvertices = 3; // Allocate memory for face vertices p->vertexlist = new int[p->numberofvertices]; p->vertexlist[0] = id1; p->vertexlist[1] = id2; p->vertexlist[2] = id3; // Detect the smallest index. for (j = 0; j < 3; j++) { if (p->vertexlist[j] < smallestidx) { smallestidx = p->vertexlist[j]; } } } else { printf("Error: Only triangles are supported\n"); return false; } } } else if (!strcmp(mode, "ASCII")) { for (i = 0; i < nfaces; i++) { bufferp = readline(line, fp, &line_count); nn = (int)strtol(bufferp, &bufferp, 0); if (i == 0) nn_old = nn; if (nn != nn_old) { printf("Error: No mixed cells are allowed.\n"); return false; } if (nn == 3) { bufferp = findnextnumber(bufferp); // Skip the first field. id1 = (int)strtol(bufferp, &bufferp, 0); bufferp = findnextnumber(bufferp); id2 = (int)strtol(bufferp, &bufferp, 0); bufferp = findnextnumber(bufferp); id3 = (int)strtol(bufferp, &bufferp, 0); f = &facetlist[i]; init(f); // In .off format, each facet has one polygon, no hole. f->numberofpolygons = 1; f->polygonlist = new tetgenio::polygon[1]; p = &f->polygonlist[0]; init(p); // Set number of vertices p->numberofvertices = 3; // Allocate memory for face vertices p->vertexlist = new int[p->numberofvertices]; p->vertexlist[0] = id1; p->vertexlist[1] = id2; p->vertexlist[2] = id3; // Detect the smallest index. for (j = 0; j < 3; j++) { if (p->vertexlist[j] < smallestidx) { smallestidx = p->vertexlist[j]; } } } else { printf("Error: Only triangles are supported.\n"); return false; } } } fclose(fp); // Decide the firstnumber of the index. if (smallestidx == 0) { firstnumber = 0; } else if (smallestidx == 1) { firstnumber = 1; } else { printf("A wrong smallest index (%d) was detected in file %s\n", smallestidx, infilename); return false; } return true; } if (!strcmp(id, "LINES") || !strcmp(id, "CELLS")) { printf("Warning: load_vtk(): cannot read formats LINES, CELLS.\n"); } } // while () return true; } /////////////////////////////////////////////////////////////////////////////// // // // load_plc() Load a piecewise linear complex from file(s). // // // /////////////////////////////////////////////////////////////////////////////// bool tetgenio::load_plc(char* filebasename, int object) { bool success; if (object == (int)tetgenbehavior::NODES) { success = load_node(filebasename); } else if (object == (int)tetgenbehavior::POLY) { success = load_poly(filebasename); } else if (object == (int)tetgenbehavior::OFF) { success = load_off(filebasename); } else if (object == (int)tetgenbehavior::PLY) { success = load_ply(filebasename); } else if (object == (int)tetgenbehavior::STL) { success = load_stl(filebasename); } else if (object == (int)tetgenbehavior::MEDIT) { success = load_medit(filebasename, 0); } else if (object == (int)tetgenbehavior::VTK) { success = load_vtk(filebasename); } else { success = load_poly(filebasename); } if (success) { // Try to load the following files (.edge, .var, .mtr). load_edge(filebasename); load_var(filebasename); load_mtr(filebasename); } return success; } /////////////////////////////////////////////////////////////////////////////// // // // load_mesh() Load a tetrahedral mesh from file(s). // // // /////////////////////////////////////////////////////////////////////////////// bool tetgenio::load_tetmesh(char* filebasename, int object) { bool success; if (object == (int)tetgenbehavior::MEDIT) { success = load_medit(filebasename, 1); } else if (object == (int)tetgenbehavior::NEU_MESH) { // success = load_neumesh(filebasename, 1); } else { success = load_node(filebasename); if (success) { success = load_tet(filebasename); } if (success) { // Try to load the following files (.face, .edge, .vol). load_face(filebasename); load_edge(filebasename); load_vol(filebasename); } } // if (success) { // Try to load the following files (.var, .mtr). load_var(filebasename); load_mtr(filebasename); //} return success; } /////////////////////////////////////////////////////////////////////////////// // // // save_nodes() Save points to a .node file. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenio::save_nodes(char* filebasename) { FILE* fout; char outnodefilename[FILENAMESIZE]; char outmtrfilename[FILENAMESIZE]; int i, j; sprintf(outnodefilename, "%s.node", filebasename); printf("Saving nodes to %s\n", outnodefilename); fout = fopen(outnodefilename, "w"); fprintf(fout, "%d %d %d %d\n", numberofpoints, mesh_dim, numberofpointattributes, pointmarkerlist != NULL ? 1 : 0); for (i = 0; i < numberofpoints; i++) { if (mesh_dim == 2) { fprintf(fout, "%d %.16g %.16g", i + firstnumber, pointlist[i * 3], pointlist[i * 3 + 1]); } else { fprintf(fout, "%d %.16g %.16g %.16g", i + firstnumber, pointlist[i * 3], pointlist[i * 3 + 1], pointlist[i * 3 + 2]); } for (j = 0; j < numberofpointattributes; j++) { fprintf(fout, " %.16g", pointattributelist[i * numberofpointattributes + j]); } if (pointmarkerlist != NULL) { fprintf(fout, " %d", pointmarkerlist[i]); } fprintf(fout, "\n"); } fclose(fout); // If the point metrics exist, output them to a .mtr file. if ((numberofpointmtrs > 0) && (pointmtrlist != (REAL*)NULL)) { sprintf(outmtrfilename, "%s.mtr", filebasename); printf("Saving metrics to %s\n", outmtrfilename); fout = fopen(outmtrfilename, "w"); fprintf(fout, "%d %d\n", numberofpoints, numberofpointmtrs); for (i = 0; i < numberofpoints; i++) { for (j = 0; j < numberofpointmtrs; j++) { fprintf(fout, "%.16g ", pointmtrlist[i * numberofpointmtrs + j]); } fprintf(fout, "\n"); } fclose(fout); } } /////////////////////////////////////////////////////////////////////////////// // // // save_elements() Save elements to a .ele file. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenio::save_elements(char* filebasename) { FILE* fout; char outelefilename[FILENAMESIZE]; int i, j; sprintf(outelefilename, "%s.ele", filebasename); printf("Saving elements to %s\n", outelefilename); fout = fopen(outelefilename, "w"); if (mesh_dim == 3) { fprintf(fout, "%d %d %d\n", numberoftetrahedra, numberofcorners, numberoftetrahedronattributes); for (i = 0; i < numberoftetrahedra; i++) { fprintf(fout, "%d", i + firstnumber); for (j = 0; j < numberofcorners; j++) { fprintf(fout, " %5d", tetrahedronlist[i * numberofcorners + j]); } for (j = 0; j < numberoftetrahedronattributes; j++) { fprintf(fout, " %g", tetrahedronattributelist[i * numberoftetrahedronattributes + j]); } fprintf(fout, "\n"); } } else { // Save a two-dimensional mesh. fprintf(fout, "%d %d %d\n", numberoftrifaces, 3, trifacemarkerlist ? 1 : 0); for (i = 0; i < numberoftrifaces; i++) { fprintf(fout, "%d", i + firstnumber); for (j = 0; j < 3; j++) { fprintf(fout, " %5d", trifacelist[i * 3 + j]); } if (trifacemarkerlist != NULL) { fprintf(fout, " %d", trifacemarkerlist[i]); } fprintf(fout, "\n"); } } fclose(fout); } /////////////////////////////////////////////////////////////////////////////// // // // save_faces() Save faces to a .face file. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenio::save_faces(char* filebasename) { FILE* fout; char outfacefilename[FILENAMESIZE]; int i; sprintf(outfacefilename, "%s.face", filebasename); printf("Saving faces to %s\n", outfacefilename); fout = fopen(outfacefilename, "w"); fprintf(fout, "%d %d\n", numberoftrifaces, trifacemarkerlist != NULL ? 1 : 0); for (i = 0; i < numberoftrifaces; i++) { fprintf(fout, "%d %5d %5d %5d", i + firstnumber, trifacelist[i * 3], trifacelist[i * 3 + 1], trifacelist[i * 3 + 2]); if (trifacemarkerlist != NULL) { fprintf(fout, " %d", trifacemarkerlist[i]); } fprintf(fout, "\n"); } fclose(fout); } /////////////////////////////////////////////////////////////////////////////// // // // save_edges() Save egdes to a .edge file. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenio::save_edges(char* filebasename) { FILE* fout; char outedgefilename[FILENAMESIZE]; int i; sprintf(outedgefilename, "%s.edge", filebasename); printf("Saving edges to %s\n", outedgefilename); fout = fopen(outedgefilename, "w"); fprintf(fout, "%d %d\n", numberofedges, edgemarkerlist != NULL ? 1 : 0); for (i = 0; i < numberofedges; i++) { fprintf(fout, "%d %4d %4d", i + firstnumber, edgelist[i * 2], edgelist[i * 2 + 1]); if (edgemarkerlist != NULL) { fprintf(fout, " %d", edgemarkerlist[i]); } fprintf(fout, "\n"); } fclose(fout); } /////////////////////////////////////////////////////////////////////////////// // // // save_neighbors() Save egdes to a .neigh file. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenio::save_neighbors(char* filebasename) { FILE* fout; char outneighborfilename[FILENAMESIZE]; int i; sprintf(outneighborfilename, "%s.neigh", filebasename); printf("Saving neighbors to %s\n", outneighborfilename); fout = fopen(outneighborfilename, "w"); fprintf(fout, "%d %d\n", numberoftetrahedra, mesh_dim + 1); for (i = 0; i < numberoftetrahedra; i++) { if (mesh_dim == 2) { fprintf(fout, "%d %5d %5d %5d", i + firstnumber, neighborlist[i * 3], neighborlist[i * 3 + 1], neighborlist[i * 3 + 2]); } else { fprintf(fout, "%d %5d %5d %5d %5d", i + firstnumber, neighborlist[i * 4], neighborlist[i * 4 + 1], neighborlist[i * 4 + 2], neighborlist[i * 4 + 3]); } fprintf(fout, "\n"); } fclose(fout); } /////////////////////////////////////////////////////////////////////////////// // // // save_poly() Save segments or facets to a .poly file. // // // // It only save the facets, holes and regions. No .node file is saved. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenio::save_poly(char* filebasename) { FILE* fout; facet* f; polygon* p; char outpolyfilename[FILENAMESIZE]; int i, j, k; sprintf(outpolyfilename, "%s.poly", filebasename); printf("Saving poly to %s\n", outpolyfilename); fout = fopen(outpolyfilename, "w"); // The zero indicates that the vertices are in a separate .node file. // Followed by number of dimensions, number of vertex attributes, // and number of boundary markers (zero or one). fprintf(fout, "%d %d %d %d\n", 0, mesh_dim, numberofpointattributes, pointmarkerlist != NULL ? 1 : 0); // Save segments or facets. if (mesh_dim == 2) { // Number of segments, number of boundary markers (zero or one). fprintf(fout, "%d %d\n", numberofedges, edgemarkerlist != NULL ? 1 : 0); for (i = 0; i < numberofedges; i++) { fprintf(fout, "%d %4d %4d", i + firstnumber, edgelist[i * 2], edgelist[i * 2 + 1]); if (edgemarkerlist != NULL) { fprintf(fout, " %d", edgemarkerlist[i]); } fprintf(fout, "\n"); } } else { // Number of facets, number of boundary markers (zero or one). fprintf(fout, "%d %d\n", numberoffacets, facetmarkerlist != NULL ? 1 : 0); for (i = 0; i < numberoffacets; i++) { f = &(facetlist[i]); fprintf(fout, "%d %d %d # %d\n", f->numberofpolygons, f->numberofholes, facetmarkerlist != NULL ? facetmarkerlist[i] : 0, i + firstnumber); // Output polygons of this facet. for (j = 0; j < f->numberofpolygons; j++) { p = &(f->polygonlist[j]); fprintf(fout, "%d ", p->numberofvertices); for (k = 0; k < p->numberofvertices; k++) { if (((k + 1) % 10) == 0) { fprintf(fout, "\n "); } fprintf(fout, " %d", p->vertexlist[k]); } fprintf(fout, "\n"); } // Output holes of this facet. for (j = 0; j < f->numberofholes; j++) { fprintf(fout, "%d %.12g %.12g %.12g\n", j + firstnumber, f->holelist[j * 3], f->holelist[j * 3 + 1], f->holelist[j * 3 + 2]); } } } // Save holes. fprintf(fout, "%d\n", numberofholes); for (i = 0; i < numberofholes; i++) { // Output x, y coordinates. fprintf(fout, "%d %.12g %.12g", i + firstnumber, holelist[i * mesh_dim], holelist[i * mesh_dim + 1]); if (mesh_dim == 3) { // Output z coordinate. fprintf(fout, " %.12g", holelist[i * mesh_dim + 2]); } fprintf(fout, "\n"); } // Save regions. fprintf(fout, "%d\n", numberofregions); for (i = 0; i < numberofregions; i++) { if (mesh_dim == 2) { // Output the index, x, y coordinates, attribute (region number) // and maximum area constraint (maybe -1). fprintf(fout, "%d %.12g %.12g %.12g %.12g\n", i + firstnumber, regionlist[i * 4], regionlist[i * 4 + 1], regionlist[i * 4 + 2], regionlist[i * 4 + 3]); } else { // Output the index, x, y, z coordinates, attribute (region number) // and maximum volume constraint (maybe -1). fprintf(fout, "%d %.12g %.12g %.12g %.12g %.12g\n", i + firstnumber, regionlist[i * 5], regionlist[i * 5 + 1], regionlist[i * 5 + 2], regionlist[i * 5 + 3], regionlist[i * 5 + 4]); } } fclose(fout); } /////////////////////////////////////////////////////////////////////////////// // // // save_faces2smesh() Save triangular faces to a .smesh file. // // // // It only save the facets. No holes and regions. No .node file. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenio::save_faces2smesh(char* filebasename) { FILE* fout; char outsmeshfilename[FILENAMESIZE]; int i, j; sprintf(outsmeshfilename, "%s.smesh", filebasename); printf("Saving faces to %s\n", outsmeshfilename); fout = fopen(outsmeshfilename, "w"); // The zero indicates that the vertices are in a separate .node file. // Followed by number of dimensions, number of vertex attributes, // and number of boundary markers (zero or one). fprintf(fout, "%d %d %d %d\n", 0, mesh_dim, numberofpointattributes, pointmarkerlist != NULL ? 1 : 0); // Number of facets, number of boundary markers (zero or one). fprintf(fout, "%d %d\n", numberoftrifaces, trifacemarkerlist != NULL ? 1 : 0); // Output triangular facets. for (i = 0; i < numberoftrifaces; i++) { j = i * 3; fprintf(fout, "3 %d %d %d", trifacelist[j], trifacelist[j + 1], trifacelist[j + 2]); if (trifacemarkerlist != NULL) { fprintf(fout, " %d", trifacemarkerlist[i]); } fprintf(fout, "\n"); } // No holes and regions. fprintf(fout, "0\n"); fprintf(fout, "0\n"); fclose(fout); } /////////////////////////////////////////////////////////////////////////////// // // // readline() Read a nonempty line from a file. // // // // A line is considered "nonempty" if it contains something more than white // // spaces. If a line is considered empty, it will be dropped and the next // // line will be read, this process ends until reaching the end-of-file or a // // non-empty line. Return NULL if it is the end-of-file, otherwise, return // // a pointer to the first non-whitespace character of the line. // // // /////////////////////////////////////////////////////////////////////////////// char* tetgenio::readline(char* string, FILE* infile, int* linenumber) { char* result; // Search for a non-empty line. do { result = fgets(string, INPUTLINESIZE - 1, infile); if (linenumber) (*linenumber)++; if (result == (char*)NULL) { return (char*)NULL; } // Skip white spaces. while ((*result == ' ') || (*result == '\t')) result++; // If it's end of line, read another line and try again. } while ((*result == '\0') || (*result == '\r') || (*result == '\n')); return result; } /////////////////////////////////////////////////////////////////////////////// // // // findnextfield() Find the next field of a string. // // // // Jumps past the current field by searching for whitespace or a comma, then // // jumps past the whitespace or the comma to find the next field. // // // /////////////////////////////////////////////////////////////////////////////// char* tetgenio::findnextfield(char* string) { char* result; result = string; // Skip the current field. Stop upon reaching whitespace or a comma. while ((*result != '\0') && (*result != ' ') && (*result != '\t') && (*result != ',') && (*result != ';')) { result++; } // Now skip the whitespace or the comma, stop at anything else that looks // like a character, or the end of a line. while ((*result == ' ') || (*result == '\t') || (*result == ',') || (*result == ';')) { result++; } return result; } /////////////////////////////////////////////////////////////////////////////// // // // readnumberline() Read a nonempty number line from a file. // // // // A line is considered "nonempty" if it contains something that looks like // // a number. Comments (prefaced by `#') are ignored. // // // /////////////////////////////////////////////////////////////////////////////// char* tetgenio::readnumberline(char* string, FILE* infile, char* infilename) { char* result; // Search for something that looks like a number. do { result = fgets(string, INPUTLINESIZE, infile); if (result == (char*)NULL) { return result; } // Skip anything that doesn't look like a number, a comment, // or the end of a line. while ((*result != '\0') && (*result != '#') && (*result != '.') && (*result != '+') && (*result != '-') && ((*result < '0') || (*result > '9'))) { result++; } // If it's a comment or end of line, read another line and try again. } while ((*result == '#') || (*result == '\0')); return result; } /////////////////////////////////////////////////////////////////////////////// // // // findnextnumber() Find the next field of a number string. // // // // Jumps past the current field by searching for whitespace or a comma, then // // jumps past the whitespace or the comma to find the next field that looks // // like a number. // // // /////////////////////////////////////////////////////////////////////////////// char* tetgenio::findnextnumber(char* string) { char* result; result = string; // Skip the current field. Stop upon reaching whitespace or a comma. while ((*result != '\0') && (*result != '#') && (*result != ' ') && (*result != '\t') && (*result != ',')) { result++; } // Now skip the whitespace and anything else that doesn't look like a // number, a comment, or the end of a line. while ((*result != '\0') && (*result != '#') && (*result != '.') && (*result != '+') && (*result != '-') && ((*result < '0') || (*result > '9'))) { result++; } // Check for a comment (prefixed with `#'). if (*result == '#') { *result = '\0'; } return result; } //// //// //// //// //// io_cxx /////////////////////////////////////////////////////////////////// //// behavior_cxx ///////////////////////////////////////////////////////////// //// //// //// //// /////////////////////////////////////////////////////////////////////////////// // // // syntax() Print list of command line switches. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenbehavior::syntax() { printf(" tetgen [-pYrq_Aa_miO_S_T_XMwcdzfenvgkJBNEFICQVh] input_file\n"); printf(" -p Tetrahedralizes a piecewise linear complex (PLC).\n"); printf(" -Y Preserves the input surface mesh (does not modify it).\n"); printf(" -r Reconstructs a previously generated mesh.\n"); printf(" -q Refines mesh (to improve mesh quality).\n"); printf(" -R Mesh coarsening (to reduce the mesh elements).\n"); printf(" -A Assigns attributes to tetrahedra in different regions.\n"); printf(" -a Applies a maximum tetrahedron volume constraint.\n"); printf(" -m Applies a mesh sizing function.\n"); printf(" -i Inserts a list of additional points.\n"); printf(" -O Specifies the level of mesh optimization.\n"); printf(" -S Specifies maximum number of added points.\n"); printf(" -T Sets a tolerance for coplanar test (default 1e-8).\n"); printf(" -X Suppresses use of exact arithmetic.\n"); printf(" -M No merge of coplanar facets or very close vertices.\n"); printf(" -w Generates weighted Delaunay (regular) triangulation.\n"); printf(" -c Retains the convex hull of the PLC.\n"); printf(" -d Detects self-intersections of facets of the PLC.\n"); printf(" -z Numbers all output items starting from zero.\n"); printf(" -f Outputs all faces to .face file.\n"); printf(" -e Outputs all edges to .edge file.\n"); printf(" -n Outputs tetrahedra neighbors to .neigh file.\n"); printf(" -v Outputs Voronoi diagram to files.\n"); printf(" -g Outputs mesh to .mesh file for viewing by Medit.\n"); printf(" -k Outputs mesh to .vtk file for viewing by Paraview.\n"); printf(" -J No jettison of unused vertices from output .node file.\n"); printf(" -B Suppresses output of boundary information.\n"); printf(" -N Suppresses output of .node file.\n"); printf(" -E Suppresses output of .ele file.\n"); printf(" -F Suppresses output of .face and .edge file.\n"); printf(" -I Suppresses mesh iteration numbers.\n"); printf(" -C Checks the consistency of the final mesh.\n"); printf(" -Q Quiet: No terminal output except errors.\n"); printf(" -V Verbose: Detailed information, more terminal output.\n"); printf(" -h Help: A brief instruction for using TetGen.\n"); } /////////////////////////////////////////////////////////////////////////////// // // // usage() Print a brief instruction for using TetGen. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenbehavior::usage() { printf("TetGen\n"); printf("A Quality Tetrahedral Mesh Generator and 3D Delaunay "); printf("Triangulator\n"); printf("Version 1.5\n"); printf("August 18, 2018\n"); printf("\n"); printf("Copyright (C) 2002 - 2018\n"); printf("\n"); printf("What Can TetGen Do?\n"); printf("\n"); printf(" TetGen generates Delaunay tetrahedralizations, constrained\n"); printf(" Delaunay tetrahedralizations, and quality tetrahedral meshes.\n"); printf("\n"); printf("Command Line Syntax:\n"); printf("\n"); printf(" Below is the basic command line syntax of TetGen with a list of "); printf("short\n"); printf(" descriptions. Underscores indicate that numbers may optionally\n"); printf(" follow certain switches. Do not leave any space between a "); printf("switch\n"); printf(" and its numeric parameter. \'input_file\' contains input data\n"); printf(" depending on the switches you supplied which may be a "); printf(" piecewise\n"); printf(" linear complex or a list of nodes. File formats and detailed\n"); printf(" description of command line switches are found in user's "); printf("manual.\n"); printf("\n"); syntax(); printf("\n"); printf("Examples of How to Use TetGen:\n"); printf("\n"); printf(" \'tetgen object\' reads vertices from object.node, and writes "); printf("their\n Delaunay tetrahedralization to object.1.node, "); printf("object.1.ele\n (tetrahedra), and object.1.face"); printf(" (convex hull faces).\n"); printf("\n"); printf(" \'tetgen -p object\' reads a PLC from object.poly or object."); printf("smesh (and\n possibly object.node) and writes its constrained "); printf("Delaunay\n tetrahedralization to object.1.node, object.1.ele, "); printf("object.1.face,\n"); printf(" (boundary faces) and object.1.edge (boundary edges).\n"); printf("\n"); printf(" \'tetgen -pq1.414a.1 object\' reads a PLC from object.poly or\n"); printf(" object.smesh (and possibly object.node), generates a mesh "); printf("whose\n tetrahedra have radius-edge ratio smaller than 1.414 and "); printf("have volume\n of 0.1 or less, and writes the mesh to "); printf("object.1.node, object.1.ele,\n object.1.face, and object.1.edge\n"); printf("\n"); printf("Please send bugs/comments to Hang Si \n"); terminatetetgen(NULL, 0); } /////////////////////////////////////////////////////////////////////////////// // // // parse_commandline() Read the command line, identify switches, and set // // up options and file names. // // // // 'argc' and 'argv' are the same parameters passed to the function main() // // of a C/C++ program. They together represent the command line user invoked // // from an environment in which TetGen is running. // // // /////////////////////////////////////////////////////////////////////////////// bool tetgenbehavior::parse_commandline(int argc, char** argv) { int startindex; int increment; int meshnumber; int i, j, k; char workstring[1024]; // First determine the input style of the switches. if (argc == 0) { startindex = 0; // Switches are given without a dash. argc = 1; // For running the following for-loop once. commandline[0] = '\0'; } else { startindex = 1; strcpy(commandline, argv[0]); strcat(commandline, " "); } for (i = startindex; i < argc; i++) { // Remember the command line for output. strcat(commandline, argv[i]); strcat(commandline, " "); if (startindex == 1) { // Is this string a filename? if (argv[i][0] != '-') { strncpy(infilename, argv[i], 1024 - 1); infilename[1024 - 1] = '\0'; continue; } } // Parse the individual switch from the string. for (j = startindex; argv[i][j] != '\0'; j++) { if (argv[i][j] == 'p') { plc = 1; if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) || (argv[i][j + 1] == '.')) { k = 0; while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) || (argv[i][j + 1] == '.')) { j++; workstring[k] = argv[i][j]; k++; } workstring[k] = '\0'; facet_separate_ang_tol = (REAL)strtod(workstring, (char**)NULL); } if ((argv[i][j + 1] == '/') || (argv[i][j + 1] == ',')) { j++; if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) || (argv[i][j + 1] == '.')) { k = 0; while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) || (argv[i][j + 1] == '.') || (argv[i][j + 1] == 'e') || (argv[i][j + 1] == '-') || (argv[i][j + 1] == '+')) { j++; workstring[k] = argv[i][j]; k++; } workstring[k] = '\0'; facet_overlap_ang_tol = (REAL)strtod(workstring, (char**)NULL); } } if ((argv[i][j + 1] == '/') || (argv[i][j + 1] == ',')) { j++; if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) || (argv[i][j + 1] == '.')) { k = 0; while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) || (argv[i][j + 1] == '.')) { j++; workstring[k] = argv[i][j]; k++; } workstring[k] = '\0'; facet_small_ang_tol = (REAL)strtod(workstring, (char**)NULL); } } } else if (argv[i][j] == 's') { psc = 1; } else if (argv[i][j] == 'Y') { nobisect = 1; if ((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) { nobisect_nomerge = (argv[i][j + 1] - '0'); j++; } if ((argv[i][j + 1] == '/') || (argv[i][j + 1] == ',')) { j++; if ((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) { supsteiner_level = (argv[i][j + 1] - '0'); j++; } } if ((argv[i][j + 1] == '/') || (argv[i][j + 1] == ',')) { j++; if ((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) { addsteiner_algo = (argv[i][j + 1] - '0'); j++; } } } else if (argv[i][j] == 'r') { refine = 1; } else if (argv[i][j] == 'q') { quality = 1; if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) || (argv[i][j + 1] == '.')) { k = 0; while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) || (argv[i][j + 1] == '.')) { j++; workstring[k] = argv[i][j]; k++; } workstring[k] = '\0'; minratio = (REAL)strtod(workstring, (char**)NULL); } if ((argv[i][j + 1] == '/') || (argv[i][j + 1] == ',')) { j++; if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) || (argv[i][j + 1] == '.')) { k = 0; while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) || (argv[i][j + 1] == '.')) { j++; workstring[k] = argv[i][j]; k++; } workstring[k] = '\0'; mindihedral = (REAL)strtod(workstring, (char**)NULL); } } } else if (argv[i][j] == 'R') { coarsen = 1; if ((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) { coarsen_param = (argv[i][j + 1] - '0'); j++; } if ((argv[i][j + 1] == '/') || (argv[i][j + 1] == ',')) { j++; if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) || (argv[i][j + 1] == '.')) { k = 0; while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) || (argv[i][j + 1] == '.')) { j++; workstring[k] = argv[i][j]; k++; } workstring[k] = '\0'; coarsen_percent = (REAL)strtod(workstring, (char**)NULL); } } } else if (argv[i][j] == 'w') { weighted = 1; if ((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) { weighted_param = (argv[i][j + 1] - '0'); j++; } } else if (argv[i][j] == 'b') { // -b(brio_threshold/brio_ratio/hilbert_limit/hilbert_order) brio_hilbert = 1; if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) || (argv[i][j + 1] == '.')) { k = 0; while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) || (argv[i][j + 1] == '.')) { j++; workstring[k] = argv[i][j]; k++; } workstring[k] = '\0'; brio_threshold = (int)strtol(workstring, (char**)&workstring, 0); } if ((argv[i][j + 1] == '/') || (argv[i][j + 1] == ',')) { j++; if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) || (argv[i][j + 1] == '.')) { k = 0; while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) || (argv[i][j + 1] == '.')) { j++; workstring[k] = argv[i][j]; k++; } workstring[k] = '\0'; brio_ratio = (REAL)strtod(workstring, (char**)NULL); } } if ((argv[i][j + 1] == '/') || (argv[i][j + 1] == ',')) { j++; if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) || (argv[i][j + 1] == '.') || (argv[i][j + 1] == '-')) { k = 0; while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) || (argv[i][j + 1] == '.') || (argv[i][j + 1] == '-')) { j++; workstring[k] = argv[i][j]; k++; } workstring[k] = '\0'; hilbert_limit = (int)strtol(workstring, (char**)&workstring, 0); } } if ((argv[i][j + 1] == '/') || (argv[i][j + 1] == ',')) { j++; if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) || (argv[i][j + 1] == '.') || (argv[i][j + 1] == '-')) { k = 0; while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) || (argv[i][j + 1] == '.') || (argv[i][j + 1] == '-')) { j++; workstring[k] = argv[i][j]; k++; } workstring[k] = '\0'; hilbert_order = (REAL)strtod(workstring, (char**)NULL); } } if (brio_threshold == 0) { // -b0 brio_hilbert = 0; // Turn off BRIO-Hilbert sorting. } if (brio_ratio >= 1.0) { // -b/1 no_sort = 1; brio_hilbert = 0; // Turn off BRIO-Hilbert sorting. } } else if (argv[i][j] == 'l') { incrflip = 1; } else if (argv[i][j] == 'L') { flipinsert = 1; } else if (argv[i][j] == 'm') { metric = 1; } else if (argv[i][j] == 'a') { if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) || (argv[i][j + 1] == '.')) { fixedvolume = 1; k = 0; while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) || (argv[i][j + 1] == '.') || (argv[i][j + 1] == 'e') || (argv[i][j + 1] == '-') || (argv[i][j + 1] == '+')) { j++; workstring[k] = argv[i][j]; k++; } workstring[k] = '\0'; maxvolume = (REAL)strtod(workstring, (char**)NULL); } else { varvolume = 1; } } else if (argv[i][j] == 'A') { regionattrib = 1; } else if (argv[i][j] == 'D') { cdtrefine = 1; if (argv[i][j + 1] == 'l') { use_equatorial_lens = 1; } else if ((argv[i][j + 1] >= '1') && (argv[i][j + 1] <= '3')) { reflevel = (argv[i][j + 1] - '1') + 1; j++; } } else if (argv[i][j] == 'i') { insertaddpoints = 1; } else if (argv[i][j] == 'd') { diagnose = 1; } else if (argv[i][j] == 'c') { convex = 1; } else if (argv[i][j] == 'M') { nomergefacet = 1; nomergevertex = 1; if ((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '1')) { nomergefacet = (argv[i][j + 1] - '0'); j++; } if ((argv[i][j + 1] == '/') || (argv[i][j + 1] == ',')) { j++; if ((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '1')) { nomergevertex = (argv[i][j + 1] - '0'); j++; } } } else if (argv[i][j] == 'X') { if (argv[i][j + 1] == '1') { nostaticfilter = 1; j++; } else { noexact = 1; } } else if (argv[i][j] == 'z') { if (argv[i][j + 1] == '1') { // -z1 reversetetori = 1; j++; } else { zeroindex = 1; // -z } } else if (argv[i][j] == 'f') { facesout++; } else if (argv[i][j] == 'e') { edgesout++; } else if (argv[i][j] == 'n') { neighout++; } else if (argv[i][j] == 'v') { voroout = 1; } else if (argv[i][j] == 'g') { meditview = 1; } else if (argv[i][j] == 'k') { vtkview = 1; } else if (argv[i][j] == 'J') { nojettison = 1; } else if (argv[i][j] == 'B') { nobound = 1; } else if (argv[i][j] == 'N') { nonodewritten = 1; } else if (argv[i][j] == 'E') { noelewritten = 1; } else if (argv[i][j] == 'F') { nofacewritten = 1; } else if (argv[i][j] == 'I') { noiterationnum = 1; } else if (argv[i][j] == 'S') { if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) || (argv[i][j + 1] == '.')) { k = 0; while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) || (argv[i][j + 1] == '.') || (argv[i][j + 1] == 'e') || (argv[i][j + 1] == '-') || (argv[i][j + 1] == '+')) { j++; workstring[k] = argv[i][j]; k++; } workstring[k] = '\0'; steinerleft = (int)strtol(workstring, (char**)NULL, 0); } } else if (argv[i][j] == 'o') { if (argv[i][j + 1] == '2') { order = 2; j++; } if ((argv[i][j + 1] == '/') || (argv[i][j + 1] == ',')) { j++; if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) || (argv[i][j + 1] == '.')) { k = 0; while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) || (argv[i][j + 1] == '.')) { j++; workstring[k] = argv[i][j]; k++; } workstring[k] = '\0'; optmaxdihedral = (REAL)strtod(workstring, (char**)NULL); } } } else if (argv[i][j] == 'O') { if ((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) { optlevel = (argv[i][j + 1] - '0'); j++; } if ((argv[i][j + 1] == '/') || (argv[i][j + 1] == ',')) { j++; if ((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '7')) { optscheme = (argv[i][j + 1] - '0'); j++; } } } else if (argv[i][j] == 'T') { if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) || (argv[i][j + 1] == '.')) { k = 0; while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) || (argv[i][j + 1] == '.') || (argv[i][j + 1] == 'e') || (argv[i][j + 1] == '-') || (argv[i][j + 1] == '+')) { j++; workstring[k] = argv[i][j]; k++; } workstring[k] = '\0'; epsilon = (REAL)strtod(workstring, (char**)NULL); } } else if (argv[i][j] == 'C') { docheck++; } else if (argv[i][j] == 'Q') { quiet = 1; } else if (argv[i][j] == 'V') { verbose++; } else if (argv[i][j] == 'x') { if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) || (argv[i][j + 1] == '.')) { k = 0; while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) || (argv[i][j + 1] == '.') || (argv[i][j + 1] == 'e') || (argv[i][j + 1] == '-') || (argv[i][j + 1] == '+')) { j++; workstring[k] = argv[i][j]; k++; } workstring[k] = '\0'; tetrahedraperblock = (int)strtol(workstring, (char**)NULL, 0); if (tetrahedraperblock > 8188) { vertexperblock = tetrahedraperblock / 2; shellfaceperblock = vertexperblock / 2; } else { tetrahedraperblock = 8188; } } } else if (argv[i][j] == 'H') { if (argv[i + 1][0] != '-') { hole_mesh = 1; // It is a filename following by -H strncpy(hole_mesh_filename, argv[i + 1], 1024 - 1); hole_mesh_filename[1024 - 1] = '\0'; i++; // Skip the next string. break; // j } } else if (argv[i][j] == 'K') { apply_flow_bc = 1; } else if ((argv[i][j] == 'h') || // (argv[i][j] == 'H') (argv[i][j] == '?')) { usage(); } else { printf("Warning: Unknown switch -%c.\n", argv[i][j]); } } } if (startindex == 0) { // Set a temporary filename for debugging output. strcpy(infilename, "tetgen-tmpfile"); } else { if (infilename[0] == '\0') { // No input file name. Print the syntax and exit. syntax(); terminatetetgen(NULL, 0); } // Recognize the object from file extension if it is available. if (!strcmp(&infilename[strlen(infilename) - 5], ".node")) { infilename[strlen(infilename) - 5] = '\0'; object = NODES; } else if (!strcmp(&infilename[strlen(infilename) - 5], ".poly")) { infilename[strlen(infilename) - 5] = '\0'; object = POLY; plc = 1; } else if (!strcmp(&infilename[strlen(infilename) - 6], ".smesh")) { infilename[strlen(infilename) - 6] = '\0'; object = POLY; plc = 1; } else if (!strcmp(&infilename[strlen(infilename) - 4], ".off")) { infilename[strlen(infilename) - 4] = '\0'; object = OFF; plc = 1; } else if (!strcmp(&infilename[strlen(infilename) - 4], ".ply")) { infilename[strlen(infilename) - 4] = '\0'; object = PLY; plc = 1; } else if (!strcmp(&infilename[strlen(infilename) - 4], ".stl")) { infilename[strlen(infilename) - 4] = '\0'; object = STL; plc = 1; } else if (!strcmp(&infilename[strlen(infilename) - 5], ".mesh")) { infilename[strlen(infilename) - 5] = '\0'; object = MEDIT; if (!refine) plc = 1; } else if (!strcmp(&infilename[strlen(infilename) - 4], ".vtk")) { infilename[strlen(infilename) - 4] = '\0'; object = VTK; plc = 1; } else if (!strcmp(&infilename[strlen(infilename) - 4], ".ele")) { infilename[strlen(infilename) - 4] = '\0'; object = MESH; refine = 1; } else if (!strcmp(&infilename[strlen(infilename) - 4], ".neu")) { infilename[strlen(infilename) - 4] = '\0'; object = NEU_MESH; refine = 1; } } if (nobisect && (!plc && !refine)) { // -Y plc = 1; // Default -p option. } if (quality && (!plc && !refine)) { // -q plc = 1; // Default -p option. } if (diagnose && !plc) { // -d plc = 1; } if (refine && !quality) { // -r only // Reconstruct a mesh, no mesh optimization. optlevel = 0; } if (insertaddpoints && (optlevel == 0)) { // with -i option optlevel = 2; } if (coarsen && (optlevel == 0)) { // with -R option optlevel = 2; } // Detect improper combinations of switches. if ((refine || plc) && weighted) { printf("Error: Switches -w cannot use together with -p or -r.\n"); return false; } if (convex) { // -c if (plc && !regionattrib) { // -A (region attribute) is needed for marking exterior tets (-1). regionattrib = 1; } } // Note: -A must not used together with -r option. // Be careful not to add an extra attribute to each element unless the // input supports it (PLC in, but not refining a preexisting mesh). if (refine || !plc) { regionattrib = 0; } // Be careful not to allocate space for element area constraints that // will never be assigned any value (other than the default -1.0). if (!refine && !plc) { varvolume = 0; } // If '-a' or '-aa' is in use, enable '-q' option too. if (fixedvolume || varvolume) { if (quality == 0) { quality = 1; if (!plc && !refine) { plc = 1; // enable -p. } } } // No user-specified dihedral angle bound. Use default ones. if (!quality) { if (optmaxdihedral < 179.0) { if (nobisect) { // with -Y option optmaxdihedral = 179.0; } else { // -p only optmaxdihedral = 179.999; } } if (optminsmtdihed < 179.999) { optminsmtdihed = 179.999; } if (optminslidihed < 179.999) { optminslidihed = 179.999; } } increment = 0; strcpy(workstring, infilename); j = 1; while (workstring[j] != '\0') { if ((workstring[j] == '.') && (workstring[j + 1] != '\0')) { increment = j + 1; } j++; } meshnumber = 0; if (increment > 0) { j = increment; do { if ((workstring[j] >= '0') && (workstring[j] <= '9')) { meshnumber = meshnumber * 10 + (int)(workstring[j] - '0'); } else { increment = 0; } j++; } while (workstring[j] != '\0'); } if (noiterationnum) { strcpy(outfilename, infilename); } else if (increment == 0) { strcpy(outfilename, infilename); strcat(outfilename, ".1"); } else { workstring[increment] = '%'; workstring[increment + 1] = 'd'; workstring[increment + 2] = '\0'; sprintf(outfilename, workstring, meshnumber + 1); } // Additional input file name has the end ".a". strcpy(addinfilename, infilename); strcat(addinfilename, ".a"); // Background filename has the form "*.b.ele", "*.b.node", ... strcpy(bgmeshfilename, infilename); strcat(bgmeshfilename, ".b"); return true; } //// //// //// //// //// behavior_cxx ///////////////////////////////////////////////////////////// //// mempool_cxx ////////////////////////////////////////////////////////////// //// //// //// //// // Initialize fast lookup tables for mesh maniplulation primitives. int tetgenmesh::bondtbl[12][12] = { { 0, }, }; int tetgenmesh::enexttbl[12] = { 0, }; int tetgenmesh::eprevtbl[12] = { 0, }; int tetgenmesh::enextesymtbl[12] = { 0, }; int tetgenmesh::eprevesymtbl[12] = { 0, }; int tetgenmesh::eorgoppotbl[12] = { 0, }; int tetgenmesh::edestoppotbl[12] = { 0, }; int tetgenmesh::fsymtbl[12][12] = { { 0, }, }; int tetgenmesh::facepivot1[12] = { 0, }; int tetgenmesh::facepivot2[12][12] = { { 0, }, }; int tetgenmesh::tsbondtbl[12][6] = { { 0, }, }; int tetgenmesh::stbondtbl[12][6] = { { 0, }, }; int tetgenmesh::tspivottbl[12][6] = { { 0, }, }; int tetgenmesh::stpivottbl[12][6] = { { 0, }, }; // Table 'esymtbl' takes an directed edge (version) as input, returns the // inversed edge (version) of it. int tetgenmesh::esymtbl[12] = {9, 6, 11, 4, 3, 7, 1, 5, 10, 0, 8, 2}; // The following four tables give the 12 permutations of the set {0,1,2,3}. // An offset 4 is added to each element for a direct access of the points // in the tetrahedron data structure. int tetgenmesh::orgpivot[12] = {7, 7, 5, 5, 6, 4, 4, 6, 5, 6, 7, 4}; int tetgenmesh::destpivot[12] = {6, 4, 4, 6, 5, 6, 7, 4, 7, 7, 5, 5}; int tetgenmesh::apexpivot[12] = {5, 6, 7, 4, 7, 7, 5, 5, 6, 4, 4, 6}; int tetgenmesh::oppopivot[12] = {4, 5, 6, 7, 4, 5, 6, 7, 4, 5, 6, 7}; // The twelve versions correspond to six undirected edges. The following two // tables map a version to an undirected edge and vice versa. int tetgenmesh::ver2edge[12] = {0, 1, 2, 3, 3, 5, 1, 5, 4, 0, 4, 2}; int tetgenmesh::edge2ver[6] = {0, 1, 2, 3, 8, 5}; // Edge versions whose apex or opposite may be dummypoint. int tetgenmesh::epivot[12] = {4, 5, 2, 11, 4, 5, 2, 11, 4, 5, 2, 11}; // Table 'snextpivot' takes an edge version as input, returns the next edge // version in the same edge ring. int tetgenmesh::snextpivot[6] = {2, 5, 4, 1, 0, 3}; // The following three tables give the 6 permutations of the set {0,1,2}. // An offset 3 is added to each element for a direct access of the points // in the triangle data structure. int tetgenmesh::sorgpivot[6] = {3, 4, 4, 5, 5, 3}; int tetgenmesh::sdestpivot[6] = {4, 3, 5, 4, 3, 5}; int tetgenmesh::sapexpivot[6] = {5, 5, 3, 3, 4, 4}; /////////////////////////////////////////////////////////////////////////////// // // // inittable() Initialize the look-up tables. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::inittables() { int soffset, toffset; int i, j; // i = t1.ver; j = t2.ver; for (i = 0; i < 12; i++) { for (j = 0; j < 12; j++) { bondtbl[i][j] = (j & 3) + (((i & 12) + (j & 12)) % 12); } } // i = t1.ver; j = t2.ver for (i = 0; i < 12; i++) { for (j = 0; j < 12; j++) { fsymtbl[i][j] = (j + 12 - (i & 12)) % 12; } } for (i = 0; i < 12; i++) { facepivot1[i] = (esymtbl[i] & 3); } for (i = 0; i < 12; i++) { for (j = 0; j < 12; j++) { facepivot2[i][j] = fsymtbl[esymtbl[i]][j]; } } for (i = 0; i < 12; i++) { enexttbl[i] = (i + 4) % 12; eprevtbl[i] = (i + 8) % 12; } for (i = 0; i < 12; i++) { enextesymtbl[i] = esymtbl[enexttbl[i]]; eprevesymtbl[i] = esymtbl[eprevtbl[i]]; } for (i = 0; i < 12; i++) { eorgoppotbl[i] = eprevtbl[esymtbl[enexttbl[i]]]; edestoppotbl[i] = enexttbl[esymtbl[eprevtbl[i]]]; } // i = t.ver, j = s.shver for (i = 0; i < 12; i++) { for (j = 0; j < 6; j++) { if ((j & 1) == 0) { soffset = (6 - ((i & 12) >> 1)) % 6; toffset = (12 - ((j & 6) << 1)) % 12; } else { soffset = (i & 12) >> 1; toffset = (j & 6) << 1; } tsbondtbl[i][j] = (j & 1) + (((j & 6) + soffset) % 6); stbondtbl[i][j] = (i & 3) + (((i & 12) + toffset) % 12); } } // i = t.ver, j = s.shver for (i = 0; i < 12; i++) { for (j = 0; j < 6; j++) { if ((j & 1) == 0) { soffset = (i & 12) >> 1; toffset = (j & 6) << 1; } else { soffset = (6 - ((i & 12) >> 1)) % 6; toffset = (12 - ((j & 6) << 1)) % 12; } tspivottbl[i][j] = (j & 1) + (((j & 6) + soffset) % 6); stpivottbl[i][j] = (i & 3) + (((i & 12) + toffset) % 12); } } } /////////////////////////////////////////////////////////////////////////////// // // // restart() Deallocate all objects in this pool. // // // // The pool returns to a fresh state, like after it was initialized, except // // that no memory is freed to the operating system. Rather, the previously // // allocated blocks are ready to be used. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::arraypool::restart() { objects = 0l; } /////////////////////////////////////////////////////////////////////////////// // // // poolinit() Initialize an arraypool for allocation of objects. // // // // Before the pool may be used, it must be initialized by this procedure. // // After initialization, memory can be allocated and freed in this pool. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::arraypool::poolinit(int sizeofobject, int log2objperblk) { // Each object must be at least one byte long. objectbytes = sizeofobject > 1 ? sizeofobject : 1; log2objectsperblock = log2objperblk; // Compute the number of objects in each block. objectsperblock = ((int)1) << log2objectsperblock; objectsperblockmark = objectsperblock - 1; // No memory has been allocated. totalmemory = 0l; // The top array has not been allocated yet. toparray = (char**)NULL; toparraylen = 0; // Ready all indices to be allocated. restart(); } /////////////////////////////////////////////////////////////////////////////// // // // arraypool() The constructor and destructor. // // // /////////////////////////////////////////////////////////////////////////////// tetgenmesh::arraypool::arraypool(int sizeofobject, int log2objperblk) { poolinit(sizeofobject, log2objperblk); } tetgenmesh::arraypool::~arraypool() { int i; // Has anything been allocated at all? if (toparray != (char**)NULL) { // Walk through the top array. for (i = 0; i < toparraylen; i++) { // Check every pointer; NULLs may be scattered randomly. if (toparray[i] != (char*)NULL) { // Free an allocated block. free((void*)toparray[i]); } } // Free the top array. free((void*)toparray); } // The top array is no longer allocated. toparray = (char**)NULL; toparraylen = 0; objects = 0; totalmemory = 0; } /////////////////////////////////////////////////////////////////////////////// // // // getblock() Return (and perhaps create) the block containing the object // // with a given index. // // // // This function takes care of allocating or resizing the top array if nece- // // ssary, and of allocating the block if it hasn't yet been allocated. // // // // Return a pointer to the beginning of the block (NOT the object). // // // /////////////////////////////////////////////////////////////////////////////// char* tetgenmesh::arraypool::getblock(int objectindex) { char** newarray; char* block; int newsize; int topindex; int i; // Compute the index in the top array (upper bits). topindex = objectindex >> log2objectsperblock; // Does the top array need to be allocated or resized? if (toparray == (char**)NULL) { // Allocate the top array big enough to hold 'topindex', and NULL out // its contents. newsize = topindex + 128; toparray = (char**)malloc((size_t)(newsize * sizeof(char*))); toparraylen = newsize; for (i = 0; i < newsize; i++) { toparray[i] = (char*)NULL; } // Account for the memory. totalmemory = newsize * (uintptr_t)sizeof(char*); } else if (topindex >= toparraylen) { // Resize the top array, making sure it holds 'topindex'. newsize = 3 * toparraylen; if (topindex >= newsize) { newsize = topindex + 128; } // Allocate the new array, copy the contents, NULL out the rest, and // free the old array. newarray = (char**)malloc((size_t)(newsize * sizeof(char*))); for (i = 0; i < toparraylen; i++) { newarray[i] = toparray[i]; } for (i = toparraylen; i < newsize; i++) { newarray[i] = (char*)NULL; } free(toparray); // Account for the memory. totalmemory += (newsize - toparraylen) * sizeof(char*); toparray = newarray; toparraylen = newsize; } // Find the block, or learn that it hasn't been allocated yet. block = toparray[topindex]; if (block == (char*)NULL) { // Allocate a block at this index. block = (char*)malloc((size_t)(objectsperblock * objectbytes)); toparray[topindex] = block; // Account for the memory. totalmemory += objectsperblock * objectbytes; } // Return a pointer to the block. return block; } /////////////////////////////////////////////////////////////////////////////// // // // lookup() Return the pointer to the object with a given index, or NULL // // if the object's block doesn't exist yet. // // // /////////////////////////////////////////////////////////////////////////////// void* tetgenmesh::arraypool::lookup(int objectindex) { char* block; int topindex; // Has the top array been allocated yet? if (toparray == (char**)NULL) { return (void*)NULL; } // Compute the index in the top array (upper bits). topindex = objectindex >> log2objectsperblock; // Does the top index fit in the top array? if (topindex >= toparraylen) { return (void*)NULL; } // Find the block, or learn that it hasn't been allocated yet. block = toparray[topindex]; if (block == (char*)NULL) { return (void*)NULL; } // Compute a pointer to the object with the given index. Note that // 'objectsperblock' is a power of two, so the & operation is a bit mask // that preserves the lower bits. return (void*)(block + (objectindex & (objectsperblock - 1)) * objectbytes); } /////////////////////////////////////////////////////////////////////////////// // // // newindex() Allocate space for a fresh object from the pool. // // // // 'newptr' returns a pointer to the new object (it must not be a NULL). // // // /////////////////////////////////////////////////////////////////////////////// int tetgenmesh::arraypool::newindex(void** newptr) { // Allocate an object at index 'firstvirgin'. int newindex = objects; *newptr = (void*)(getblock(objects) + (objects & (objectsperblock - 1)) * objectbytes); objects++; return newindex; } /////////////////////////////////////////////////////////////////////////////// // // // memorypool() The constructors of memorypool. // // // /////////////////////////////////////////////////////////////////////////////// tetgenmesh::memorypool::memorypool() { firstblock = nowblock = (void**)NULL; nextitem = (void*)NULL; deaditemstack = (void*)NULL; pathblock = (void**)NULL; pathitem = (void*)NULL; alignbytes = 0; itembytes = itemwords = 0; itemsperblock = 0; items = maxitems = 0l; unallocateditems = 0; pathitemsleft = 0; } tetgenmesh::memorypool::memorypool(int bytecount, int itemcount, int wsize, int alignment) { poolinit(bytecount, itemcount, wsize, alignment); } /////////////////////////////////////////////////////////////////////////////// // // // ~memorypool() Free to the operating system all memory taken by a pool. // // // /////////////////////////////////////////////////////////////////////////////// tetgenmesh::memorypool::~memorypool() { while (firstblock != (void**)NULL) { nowblock = (void**)*(firstblock); free(firstblock); firstblock = nowblock; } } /////////////////////////////////////////////////////////////////////////////// // // // poolinit() Initialize a pool of memory for allocation of items. // // // // A `pool' is created whose records have size at least `bytecount'. Items // // will be allocated in `itemcount'-item blocks. Each item is assumed to be // // a collection of words, and either pointers or floating-point values are // // assumed to be the "primary" word type. (The "primary" word type is used // // to determine alignment of items.) If `alignment' isn't zero, all items // // will be `alignment'-byte aligned in memory. `alignment' must be either a // // multiple or a factor of the primary word size; powers of two are safe. // // `alignment' is normally used to create a few unused bits at the bottom of // // each item's pointer, in which information may be stored. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::memorypool::poolinit(int bytecount, int itemcount, int wordsize, int alignment) { // Find the proper alignment, which must be at least as large as: // - The parameter `alignment'. // - The primary word type, to avoid unaligned accesses. // - sizeof(void *), so the stack of dead items can be maintained // without unaligned accesses. if (alignment > wordsize) { alignbytes = alignment; } else { alignbytes = wordsize; } if ((int)sizeof(void*) > alignbytes) { alignbytes = (int)sizeof(void*); } itemwords = ((bytecount + alignbytes - 1) / alignbytes) * (alignbytes / wordsize); itembytes = itemwords * wordsize; itemsperblock = itemcount; // Allocate a block of items. Space for `itemsperblock' items and one // pointer (to point to the next block) are allocated, as well as space // to ensure alignment of the items. firstblock = (void**)malloc(itemsperblock * itembytes + sizeof(void*) + alignbytes); if (firstblock == (void**)NULL) { terminatetetgen(NULL, 1); } // Set the next block pointer to NULL. *(firstblock) = (void*)NULL; restart(); } /////////////////////////////////////////////////////////////////////////////// // // // restart() Deallocate all items in this pool. // // // // The pool is returned to its starting state, except that no memory is // // freed to the operating system. Rather, the previously allocated blocks // // are ready to be reused. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::memorypool::restart() { uintptr_t alignptr; items = 0; maxitems = 0; // Set the currently active block. nowblock = firstblock; // Find the first item in the pool. Increment by the size of (void *). alignptr = (uintptr_t)(nowblock + 1); // Align the item on an `alignbytes'-byte boundary. nextitem = (void*)(alignptr + (uintptr_t)alignbytes - (alignptr % (uintptr_t)alignbytes)); // There are lots of unallocated items left in this block. unallocateditems = itemsperblock; // The stack of deallocated items is empty. deaditemstack = (void*)NULL; } /////////////////////////////////////////////////////////////////////////////// // // // alloc() Allocate space for an item. // // // /////////////////////////////////////////////////////////////////////////////// void* tetgenmesh::memorypool::alloc() { void* newitem; void** newblock; uintptr_t alignptr; // First check the linked list of dead items. If the list is not // empty, allocate an item from the list rather than a fresh one. if (deaditemstack != (void*)NULL) { newitem = deaditemstack; // Take first item in list. deaditemstack = *(void**)deaditemstack; } else { // Check if there are any free items left in the current block. if (unallocateditems == 0) { // Check if another block must be allocated. if (*nowblock == (void*)NULL) { // Allocate a new block of items, pointed to by the previous block. newblock = (void**)malloc(itemsperblock * itembytes + sizeof(void*) + alignbytes); if (newblock == (void**)NULL) { terminatetetgen(NULL, 1); } *nowblock = (void*)newblock; // The next block pointer is NULL. *newblock = (void*)NULL; } // Move to the new block. nowblock = (void**)*nowblock; // Find the first item in the block. // Increment by the size of (void *). alignptr = (uintptr_t)(nowblock + 1); // Align the item on an `alignbytes'-byte boundary. nextitem = (void*)(alignptr + (uintptr_t)alignbytes - (alignptr % (uintptr_t)alignbytes)); // There are lots of unallocated items left in this block. unallocateditems = itemsperblock; } // Allocate a new item. newitem = nextitem; // Advance `nextitem' pointer to next free item in block. nextitem = (void*)((uintptr_t)nextitem + itembytes); unallocateditems--; maxitems++; } items++; return newitem; } /////////////////////////////////////////////////////////////////////////////// // // // dealloc() Deallocate space for an item. // // // // The deallocated space is stored in a queue for later reuse. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::memorypool::dealloc(void* dyingitem) { // Push freshly killed item onto stack. *((void**)dyingitem) = deaditemstack; deaditemstack = dyingitem; items--; } /////////////////////////////////////////////////////////////////////////////// // // // traversalinit() Prepare to traverse the entire list of items. // // // // This routine is used in conjunction with traverse(). // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::memorypool::traversalinit() { uintptr_t alignptr; // Begin the traversal in the first block. pathblock = firstblock; // Find the first item in the block. Increment by the size of (void *). alignptr = (uintptr_t)(pathblock + 1); // Align with item on an `alignbytes'-byte boundary. pathitem = (void*)(alignptr + (uintptr_t)alignbytes - (alignptr % (uintptr_t)alignbytes)); // Set the number of items left in the current block. pathitemsleft = itemsperblock; } /////////////////////////////////////////////////////////////////////////////// // // // traverse() Find the next item in the list. // // // // This routine is used in conjunction with traversalinit(). Be forewarned // // that this routine successively returns all items in the list, including // // deallocated ones on the deaditemqueue. It's up to you to figure out which // // ones are actually dead. It can usually be done more space-efficiently by // // a routine that knows something about the structure of the item. // // // /////////////////////////////////////////////////////////////////////////////// void* tetgenmesh::memorypool::traverse() { void* newitem; uintptr_t alignptr; // Stop upon exhausting the list of items. if (pathitem == nextitem) { return (void*)NULL; } // Check whether any untraversed items remain in the current block. if (pathitemsleft == 0) { // Find the next block. pathblock = (void**)*pathblock; // Find the first item in the block. Increment by the size of (void *). alignptr = (uintptr_t)(pathblock + 1); // Align with item on an `alignbytes'-byte boundary. pathitem = (void*)(alignptr + (uintptr_t)alignbytes - (alignptr % (uintptr_t)alignbytes)); // Set the number of items left in the current block. pathitemsleft = itemsperblock; } newitem = pathitem; // Find the next item in the block. pathitem = (void*)((uintptr_t)pathitem + itembytes); pathitemsleft--; return newitem; } /////////////////////////////////////////////////////////////////////////////// // // // makeindex2pointmap() Create a map from index to vertices. // // // // 'idx2verlist' returns the created map. Traverse all vertices, a pointer // // to each vertex is set into the array. The pointer to the first vertex is // // saved in 'idx2verlist[in->firstnumber]'. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::makeindex2pointmap(point*& idx2verlist) { point pointloop; int idx; if (b->verbose > 1) { printf(" Constructing mapping from indices to points.\n"); } idx2verlist = new point[points->items + 1]; points->traversalinit(); pointloop = pointtraverse(); idx = in->firstnumber; while (pointloop != (point)NULL) { idx2verlist[idx++] = pointloop; pointloop = pointtraverse(); } } /////////////////////////////////////////////////////////////////////////////// // // // makesubfacemap() Create a map from vertex to subfaces incident at it. // // // // The map is returned in two arrays 'idx2faclist' and 'facperverlist'. All // // subfaces incident at i-th vertex (i is counted from 0) are found in the // // array facperverlist[j], where idx2faclist[i] <= j < idx2faclist[i + 1]. // // Each entry in facperverlist[j] is a subface whose origin is the vertex. // // // // NOTE: These two arrays will be created inside this routine, don't forget // // to free them after using. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::makepoint2submap(memorypool* pool, int*& idx2faclist, face*& facperverlist) { face shloop; int i, j, k; if (b->verbose > 1) { printf(" Making a map from points to subfaces.\n"); } // Initialize 'idx2faclist'. idx2faclist = new int[points->items + 1]; for (i = 0; i < points->items + 1; i++) idx2faclist[i] = 0; // Loop all subfaces, counter the number of subfaces incident at a vertex. pool->traversalinit(); shloop.sh = shellfacetraverse(pool); while (shloop.sh != (shellface*)NULL) { // Increment the number of incident subfaces for each vertex. j = pointmark((point)shloop.sh[3]) - in->firstnumber; idx2faclist[j]++; j = pointmark((point)shloop.sh[4]) - in->firstnumber; idx2faclist[j]++; // Skip the third corner if it is a segment. if (shloop.sh[5] != NULL) { j = pointmark((point)shloop.sh[5]) - in->firstnumber; idx2faclist[j]++; } shloop.sh = shellfacetraverse(pool); } // Calculate the total length of array 'facperverlist'. j = idx2faclist[0]; idx2faclist[0] = 0; // Array starts from 0 element. for (i = 0; i < points->items; i++) { k = idx2faclist[i + 1]; idx2faclist[i + 1] = idx2faclist[i] + j; j = k; } // The total length is in the last unit of idx2faclist. facperverlist = new face[idx2faclist[i]]; // Loop all subfaces again, remember the subfaces at each vertex. pool->traversalinit(); shloop.sh = shellfacetraverse(pool); while (shloop.sh != (shellface*)NULL) { j = pointmark((point)shloop.sh[3]) - in->firstnumber; shloop.shver = 0; // save the origin. facperverlist[idx2faclist[j]] = shloop; idx2faclist[j]++; // Is it a subface or a subsegment? if (shloop.sh[5] != NULL) { j = pointmark((point)shloop.sh[4]) - in->firstnumber; shloop.shver = 2; // save the origin. facperverlist[idx2faclist[j]] = shloop; idx2faclist[j]++; j = pointmark((point)shloop.sh[5]) - in->firstnumber; shloop.shver = 4; // save the origin. facperverlist[idx2faclist[j]] = shloop; idx2faclist[j]++; } else { j = pointmark((point)shloop.sh[4]) - in->firstnumber; shloop.shver = 1; // save the origin. facperverlist[idx2faclist[j]] = shloop; idx2faclist[j]++; } shloop.sh = shellfacetraverse(pool); } // Contents in 'idx2faclist' are shifted, now shift them back. for (i = points->items - 1; i >= 0; i--) { idx2faclist[i + 1] = idx2faclist[i]; } idx2faclist[0] = 0; } /////////////////////////////////////////////////////////////////////////////// // // // tetrahedrondealloc() Deallocate space for a tet., marking it dead. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::tetrahedrondealloc(tetrahedron* dyingtetrahedron) { // Set tetrahedron's vertices to NULL. This makes it possible to detect // dead tetrahedra when traversing the list of all tetrahedra. dyingtetrahedron[4] = (tetrahedron)NULL; // Dealloc the space to subfaces/subsegments. if (dyingtetrahedron[8] != NULL) { tet2segpool->dealloc((shellface*)dyingtetrahedron[8]); } if (dyingtetrahedron[9] != NULL) { tet2subpool->dealloc((shellface*)dyingtetrahedron[9]); } tetrahedrons->dealloc((void*)dyingtetrahedron); } /////////////////////////////////////////////////////////////////////////////// // // // tetrahedrontraverse() Traverse the tetrahedra, skipping dead ones. // // // /////////////////////////////////////////////////////////////////////////////// tetgenmesh::tetrahedron* tetgenmesh::tetrahedrontraverse() { tetrahedron* newtetrahedron; do { newtetrahedron = (tetrahedron*)tetrahedrons->traverse(); if (newtetrahedron == (tetrahedron*)NULL) { return (tetrahedron*)NULL; } } while ((newtetrahedron[4] == (tetrahedron)NULL) || ((point)newtetrahedron[7] == dummypoint)); return newtetrahedron; } tetgenmesh::tetrahedron* tetgenmesh::alltetrahedrontraverse() { tetrahedron* newtetrahedron; do { newtetrahedron = (tetrahedron*)tetrahedrons->traverse(); if (newtetrahedron == (tetrahedron*)NULL) { return (tetrahedron*)NULL; } } while (newtetrahedron[4] == (tetrahedron)NULL); // Skip dead ones. return newtetrahedron; } /////////////////////////////////////////////////////////////////////////////// // // // shellfacedealloc() Deallocate space for a shellface, marking it dead. // // Used both for dealloc a subface and subsegment. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::shellfacedealloc(memorypool* pool, shellface* dyingsh) { // Set shellface's vertices to NULL. This makes it possible to detect dead // shellfaces when traversing the list of all shellfaces. dyingsh[3] = (shellface)NULL; pool->dealloc((void*)dyingsh); } /////////////////////////////////////////////////////////////////////////////// // // // shellfacetraverse() Traverse the subfaces, skipping dead ones. Used // // for both subfaces and subsegments pool traverse. // // // /////////////////////////////////////////////////////////////////////////////// tetgenmesh::shellface* tetgenmesh::shellfacetraverse(memorypool* pool) { shellface* newshellface; do { newshellface = (shellface*)pool->traverse(); if (newshellface == (shellface*)NULL) { return (shellface*)NULL; } } while (newshellface[3] == (shellface)NULL); // Skip dead ones. return newshellface; } /////////////////////////////////////////////////////////////////////////////// // // // pointdealloc() Deallocate space for a point, marking it dead. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::pointdealloc(point dyingpoint) { // Mark the point as dead. This makes it possible to detect dead points // when traversing the list of all points. setpointtype(dyingpoint, DEADVERTEX); points->dealloc((void*)dyingpoint); } /////////////////////////////////////////////////////////////////////////////// // // // pointtraverse() Traverse the points, skipping dead ones. // // // /////////////////////////////////////////////////////////////////////////////// tetgenmesh::point tetgenmesh::pointtraverse() { point newpoint; do { newpoint = (point)points->traverse(); if (newpoint == (point)NULL) { return (point)NULL; } } while (pointtype(newpoint) == DEADVERTEX); // Skip dead ones. return newpoint; } /////////////////////////////////////////////////////////////////////////////// // // // maketetrahedron() Create a new tetrahedron. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::maketetrahedron(triface* newtet) { newtet->tet = (tetrahedron*)tetrahedrons->alloc(); // Initialize the four adjoining tetrahedra to be "outer space". newtet->tet[0] = NULL; newtet->tet[1] = NULL; newtet->tet[2] = NULL; newtet->tet[3] = NULL; // Four NULL vertices. newtet->tet[4] = NULL; newtet->tet[5] = NULL; newtet->tet[6] = NULL; newtet->tet[7] = NULL; // No attached segments and subfaces yet. newtet->tet[8] = NULL; newtet->tet[9] = NULL; // Initialize the marker (clear all flags). setelemmarker(newtet->tet, 0); for (int i = 0; i < numelemattrib; i++) { setelemattribute(newtet->tet, i, 0.0); } if (b->varvolume) { setvolumebound(newtet->tet, -1.0); } // Initialize the version to be Zero. newtet->ver = 11; } /////////////////////////////////////////////////////////////////////////////// // // // makeshellface() Create a new shellface with version zero. Used for // // both subfaces and subsegments. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::makeshellface(memorypool* pool, face* newface) { newface->sh = (shellface*)pool->alloc(); // No adjointing subfaces. newface->sh[0] = NULL; newface->sh[1] = NULL; newface->sh[2] = NULL; // Three NULL vertices. newface->sh[3] = NULL; newface->sh[4] = NULL; newface->sh[5] = NULL; // No adjoining subsegments. newface->sh[6] = NULL; newface->sh[7] = NULL; newface->sh[8] = NULL; // No adjoining tetrahedra. newface->sh[9] = NULL; newface->sh[10] = NULL; if (checkconstraints) { // Initialize the maximum area bound. setareabound(*newface, 0.0); } // Set the boundary marker to zero. setshellmark(*newface, 0); // Clear the infection and marktest bits. ((int*)(newface->sh))[shmarkindex + 1] = 0; if (useinsertradius) { setfacetindex(*newface, 0); } newface->shver = 0; } /////////////////////////////////////////////////////////////////////////////// // // // makepoint() Create a new point. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::makepoint(point* pnewpoint, enum verttype vtype) { int i; *pnewpoint = (point)points->alloc(); // Initialize the point attributes. for (i = 0; i < numpointattrib; i++) { (*pnewpoint)[3 + i] = 0.0; } // Initialize the metric tensor. for (i = 0; i < sizeoftensor; i++) { (*pnewpoint)[pointmtrindex + i] = 0.0; } setpoint2tet(*pnewpoint, NULL); setpoint2ppt(*pnewpoint, NULL); if (b->plc || b->refine) { // Initialize the point-to-simplex field. setpoint2sh(*pnewpoint, NULL); if (b->metric && (bgm != NULL)) { setpoint2bgmtet(*pnewpoint, NULL); } } // Initialize the point marker (starting from in->firstnumber). setpointmark(*pnewpoint, (int)(points->items) - (!in->firstnumber)); // Clear all flags. ((int*)(*pnewpoint))[pointmarkindex + 1] = 0; // Initialize (set) the point type. setpointtype(*pnewpoint, vtype); } /////////////////////////////////////////////////////////////////////////////// // // // initializepools() Calculate the sizes of the point, tetrahedron, and // // subface. Initialize their memory pools. // // // // This routine also computes the indices 'pointmarkindex', 'point2simindex',// // 'point2pbcptindex', 'elemattribindex', and 'volumeboundindex'. They are // // used to find values within each point and tetrahedron, respectively. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::initializepools() { int pointsize = 0, elesize = 0, shsize = 0; int i; if (b->verbose) { printf(" Initializing memorypools.\n"); printf(" tetrahedron per block: %d.\n", b->tetrahedraperblock); } inittables(); // There are three input point lists available, which are in, addin, // and bgm->in. These point lists may have different number of // attributes. Decide the maximum number. numpointattrib = in->numberofpointattributes; if (bgm != NULL) { if (bgm->in->numberofpointattributes > numpointattrib) { numpointattrib = bgm->in->numberofpointattributes; } } if (addin != NULL) { if (addin->numberofpointattributes > numpointattrib) { numpointattrib = addin->numberofpointattributes; } } if (b->weighted || b->flipinsert) { // -w or -L. // The internal number of point attribute needs to be at least 1 // (for storing point weights). if (numpointattrib == 0) { numpointattrib = 1; } } // Default varconstraint = 0; if (in->segmentconstraintlist || in->facetconstraintlist) { checkconstraints = 1; } if (b->plc || b->refine) { // Save the insertion radius for Steiner points if boundaries // are allowed be split. if (!b->nobisect || checkconstraints) { useinsertradius = 1; } } // The index within each point at which its metric tensor is found. // Each vertex has three coordinates. if (b->psc) { // '-s' option (PSC), the u,v coordinates are provided. pointmtrindex = 5 + numpointattrib; // The index within each point at which its u, v coordinates are found. // Comment: They are saved after the list of point attributes. pointparamindex = pointmtrindex - 2; } else { pointmtrindex = 3 + numpointattrib; } // For '-m' option. A tensor field is provided (*.mtr or *.b.mtr file). if (b->metric) { // Decide the size (1, 3, or 6) of the metric tensor. if (bgm != (tetgenmesh*)NULL) { // A background mesh is allocated. It may not exist though. sizeoftensor = (bgm->in != (tetgenio*)NULL) ? bgm->in->numberofpointmtrs : in->numberofpointmtrs; } else { // No given background mesh - Itself is a background mesh. sizeoftensor = in->numberofpointmtrs; } // Make sure sizeoftensor is at least 1. sizeoftensor = (sizeoftensor > 0) ? sizeoftensor : 1; } else { // For '-q' option. Make sure to have space for saving a scalar value. sizeoftensor = b->quality ? 1 : 0; } if (useinsertradius) { // Increase a space (REAL) for saving point insertion radius, it is // saved directly after the metric. sizeoftensor++; } pointinsradiusindex = pointmtrindex + sizeoftensor - 1; // The index within each point at which an element pointer is found, where // the index is measured in pointers. Ensure the index is aligned to a // sizeof(tetrahedron)-byte address. point2simindex = ((pointmtrindex + sizeoftensor) * sizeof(REAL) + sizeof(tetrahedron) - 1) / sizeof(tetrahedron); if (b->plc || b->refine || b->voroout) { // Increase the point size by three pointers, which are: // - a pointer to a tet, read by point2tet(); // - a pointer to a parent point, read by point2ppt()). // - a pointer to a subface or segment, read by point2sh(); if (b->metric && (bgm != (tetgenmesh*)NULL)) { // Increase one pointer into the background mesh, point2bgmtet(). pointsize = (point2simindex + 4) * sizeof(tetrahedron); } else { pointsize = (point2simindex + 3) * sizeof(tetrahedron); } } else { // Increase the point size by two pointer, which are: // - a pointer to a tet, read by point2tet(); // - a pointer to a parent point, read by point2ppt()). -- Used by btree. pointsize = (point2simindex + 2) * sizeof(tetrahedron); } // The index within each point at which the boundary marker is found, // Ensure the point marker is aligned to a sizeof(int)-byte address. pointmarkindex = (pointsize + sizeof(int) - 1) / sizeof(int); // Now point size is the ints (indicated by pointmarkindex) plus: // - an integer for boundary marker; // - an integer for vertex type; // - an integer for geometry tag (optional, -s option). pointsize = (pointmarkindex + 2 + (b->psc ? 1 : 0)) * sizeof(tetrahedron); // Initialize the pool of vertices. points = new memorypool(pointsize, b->vertexperblock, sizeof(REAL), 0); if (b->verbose) { printf(" Size of a point: %d bytes.\n", points->itembytes); } // Initialize the infinite vertex. dummypoint = (point) new char[pointsize]; // Initialize all fields of this point. dummypoint[0] = 0.0; dummypoint[1] = 0.0; dummypoint[2] = 0.0; for (i = 0; i < numpointattrib; i++) { dummypoint[3 + i] = 0.0; } // Initialize the metric tensor. for (i = 0; i < sizeoftensor; i++) { dummypoint[pointmtrindex + i] = 0.0; } setpoint2tet(dummypoint, NULL); setpoint2ppt(dummypoint, NULL); if (b->plc || b->psc || b->refine) { // Initialize the point-to-simplex field. setpoint2sh(dummypoint, NULL); if (b->metric && (bgm != NULL)) { setpoint2bgmtet(dummypoint, NULL); } } // Initialize the point marker (starting from in->firstnumber). setpointmark(dummypoint, -1); // The unique marker for dummypoint. // Clear all flags. ((int*)(dummypoint))[pointmarkindex + 1] = 0; // Initialize (set) the point type. setpointtype(dummypoint, UNUSEDVERTEX); // Does not matter. // The number of bytes occupied by a tetrahedron is varying by the user- // specified options. The contents of the first 12 pointers are listed // in the following table: // [0] |__ neighbor at f0 __| // [1] |__ neighbor at f1 __| // [2] |__ neighbor at f2 __| // [3] |__ neighbor at f3 __| // [4] |_____ vertex p0 ____| // [5] |_____ vertex p1 ____| // [6] |_____ vertex p2 ____| // [7] |_____ vertex p3 ____| // [8] |__ segments array __| (used by -p) // [9] |__ subfaces array __| (used by -p) // [10] |_____ reserved _____| // [11] |___ elem marker ____| (used as an integer) elesize = 12 * sizeof(tetrahedron); // The index to find the element markers. An integer containing varies // flags and element counter. if (!(sizeof(int) <= sizeof(tetrahedron)) || ((sizeof(tetrahedron) % sizeof(int)))) { terminatetetgen(this, 2); } elemmarkerindex = (elesize - sizeof(tetrahedron)) / sizeof(int); // The actual number of element attributes. Note that if the // `b->regionattrib' flag is set, an additional attribute will be added. numelemattrib = in->numberoftetrahedronattributes + (b->regionattrib > 0); // The index within each element at which its attributes are found, where // the index is measured in REALs. elemattribindex = (elesize + sizeof(REAL) - 1) / sizeof(REAL); // The index within each element at which the maximum volume bound is // found, where the index is measured in REALs. volumeboundindex = elemattribindex + numelemattrib; // If element attributes or an constraint are needed, increase the number // of bytes occupied by an element. if (b->varvolume) { elesize = (volumeboundindex + 1) * sizeof(REAL); } else if (numelemattrib > 0) { elesize = volumeboundindex * sizeof(REAL); } // Having determined the memory size of an element, initialize the pool. tetrahedrons = new memorypool(elesize, b->tetrahedraperblock, sizeof(void*), 16); if (b->verbose) { printf(" Size of a tetrahedron: %d (%d) bytes.\n", elesize, tetrahedrons->itembytes); } if (b->plc || b->refine) { // if (b->useshelles) { // The number of bytes occupied by a subface. The list of pointers // stored in a subface are: three to other subfaces, three to corners, // three to subsegments, two to tetrahedra. shsize = 11 * sizeof(shellface); // The index within each subface at which the maximum area bound is // found, where the index is measured in REALs. areaboundindex = (shsize + sizeof(REAL) - 1) / sizeof(REAL); // If -q switch is in use, increase the number of bytes occupied by // a subface for saving maximum area bound. if (checkconstraints) { shsize = (areaboundindex + 1) * sizeof(REAL); } else { shsize = areaboundindex * sizeof(REAL); } // The index within subface at which the facet marker is found. Ensure // the marker is aligned to a sizeof(int)-byte address. shmarkindex = (shsize + sizeof(int) - 1) / sizeof(int); // Increase the number of bytes by two or three integers, one for facet // marker, one for shellface type and flags, and optionally one // for storing facet index (for mesh refinement). shsize = (shmarkindex + 2 + useinsertradius) * sizeof(shellface); // Initialize the pool of subfaces. Each subface record is eight-byte // aligned so it has room to store an edge version (from 0 to 5) in // the least three bits. subfaces = new memorypool(shsize, b->shellfaceperblock, sizeof(void*), 8); if (b->verbose) { printf(" Size of a shellface: %d (%d) bytes.\n", shsize, subfaces->itembytes); } // Initialize the pool of subsegments. The subsegment's record is same // with subface. subsegs = new memorypool(shsize, b->shellfaceperblock, sizeof(void*), 8); // Initialize the pool for tet-subseg connections. tet2segpool = new memorypool(6 * sizeof(shellface), b->shellfaceperblock, sizeof(void*), 0); // Initialize the pool for tet-subface connections. tet2subpool = new memorypool(4 * sizeof(shellface), b->shellfaceperblock, sizeof(void*), 0); // Initialize arraypools for segment & facet recovery. subsegstack = new arraypool(sizeof(face), 10); subfacstack = new arraypool(sizeof(face), 10); subvertstack = new arraypool(sizeof(point), 8); // Initialize arraypools for surface point insertion/deletion. caveshlist = new arraypool(sizeof(face), 8); caveshbdlist = new arraypool(sizeof(face), 8); cavesegshlist = new arraypool(sizeof(face), 4); cavetetshlist = new arraypool(sizeof(face), 8); cavetetseglist = new arraypool(sizeof(face), 8); caveencshlist = new arraypool(sizeof(face), 8); caveencseglist = new arraypool(sizeof(face), 8); } // Initialize the pools for flips. flippool = new memorypool(sizeof(badface), 1024, sizeof(void*), 0); unflipqueue = new arraypool(sizeof(badface), 10); // Initialize the arraypools for point insertion. cavetetlist = new arraypool(sizeof(triface), 10); cavebdrylist = new arraypool(sizeof(triface), 10); caveoldtetlist = new arraypool(sizeof(triface), 10); cavetetvertlist = new arraypool(sizeof(point), 10); } //// //// //// //// //// mempool_cxx ////////////////////////////////////////////////////////////// //// geom_cxx ///////////////////////////////////////////////////////////////// //// //// //// //// // PI is the ratio of a circle's circumference to its diameter. REAL tetgenmesh::PI = 3.14159265358979323846264338327950288419716939937510582; /////////////////////////////////////////////////////////////////////////////// // // // insphere_s() Insphere test with symbolic perturbation. // // // // Given four points pa, pb, pc, and pd, test if the point pe lies inside or // // outside the circumscribed sphere of the four points. // // // // Here we assume that the 3d orientation of the point sequence {pa, pb, pc, // // pd} is positive (NOT zero), i.e., pd lies above the plane passing through // // points pa, pb, and pc. Otherwise, the returned sign is flipped. // // // // Return a positive value (> 0) if pe lies inside, a negative value (< 0) // // if pe lies outside the sphere, the returned value will not be zero. // // // /////////////////////////////////////////////////////////////////////////////// REAL tetgenmesh::insphere_s(REAL* pa, REAL* pb, REAL* pc, REAL* pd, REAL* pe) { REAL sign; sign = insphere(pa, pb, pc, pd, pe); if (sign != 0.0) { return sign; } // Symbolic perturbation. point pt[5], swappt; REAL oriA, oriB; int swaps, count; int n, i; pt[0] = pa; pt[1] = pb; pt[2] = pc; pt[3] = pd; pt[4] = pe; // Sort the five points such that their indices are in the increasing // order. An optimized bubble sort algorithm is used, i.e., it has // the worst case O(n^2) runtime, but it is usually much faster. swaps = 0; // Record the total number of swaps. n = 5; do { count = 0; n = n - 1; for (i = 0; i < n; i++) { if (pointmark(pt[i]) > pointmark(pt[i + 1])) { swappt = pt[i]; pt[i] = pt[i + 1]; pt[i + 1] = swappt; count++; } } swaps += count; } while (count > 0); // Continue if some points are swapped. oriA = orient3d(pt[1], pt[2], pt[3], pt[4]); if (oriA != 0.0) { // Flip the sign if there are odd number of swaps. if ((swaps % 2) != 0) oriA = -oriA; return oriA; } oriB = -orient3d(pt[0], pt[2], pt[3], pt[4]); if (oriB == 0.0) { terminatetetgen(this, 2); } // Flip the sign if there are odd number of swaps. if ((swaps % 2) != 0) oriB = -oriB; return oriB; } /////////////////////////////////////////////////////////////////////////////// // // // orient4d_s() 4d orientation test with symbolic perturbation. // // // // Given four lifted points pa', pb', pc', and pd' in R^4,test if the lifted // // point pe' in R^4 lies below or above the hyperplane passing through the // // four points pa', pb', pc', and pd'. // // // // Here we assume that the 3d orientation of the point sequence {pa, pb, pc, // // pd} is positive (NOT zero), i.e., pd lies above the plane passing through // // the points pa, pb, and pc. Otherwise, the returned sign is flipped. // // // // Return a positive value (> 0) if pe' lies below, a negative value (< 0) // // if pe' lies above the hyperplane, the returned value should not be zero. // // // /////////////////////////////////////////////////////////////////////////////// REAL tetgenmesh::orient4d_s(REAL* pa, REAL* pb, REAL* pc, REAL* pd, REAL* pe, REAL aheight, REAL bheight, REAL cheight, REAL dheight, REAL eheight) { REAL sign; sign = orient4d(pa, pb, pc, pd, pe, aheight, bheight, cheight, dheight, eheight); if (sign != 0.0) { return sign; } // Symbolic perturbation. point pt[5], swappt; REAL oriA, oriB; int swaps, count; int n, i; pt[0] = pa; pt[1] = pb; pt[2] = pc; pt[3] = pd; pt[4] = pe; // Sort the five points such that their indices are in the increasing // order. An optimized bubble sort algorithm is used, i.e., it has // the worst case O(n^2) runtime, but it is usually much faster. swaps = 0; // Record the total number of swaps. n = 5; do { count = 0; n = n - 1; for (i = 0; i < n; i++) { if (pointmark(pt[i]) > pointmark(pt[i + 1])) { swappt = pt[i]; pt[i] = pt[i + 1]; pt[i + 1] = swappt; count++; } } swaps += count; } while (count > 0); // Continue if some points are swapped. oriA = orient3d(pt[1], pt[2], pt[3], pt[4]); if (oriA != 0.0) { // Flip the sign if there are odd number of swaps. if ((swaps % 2) != 0) oriA = -oriA; return oriA; } oriB = -orient3d(pt[0], pt[2], pt[3], pt[4]); if (oriB == 0.0) { terminatetetgen(this, 2); } // Flip the sign if there are odd number of swaps. if ((swaps % 2) != 0) oriB = -oriB; return oriB; } /////////////////////////////////////////////////////////////////////////////// // // // tri_edge_test() Triangle-edge intersection test. // // // // This routine takes a triangle T (with vertices A, B, C) and an edge E (P, // // Q) in 3D, and tests if they intersect each other. // // // // If the point 'R' is not NULL, it lies strictly above the plane defined by // // A, B, C. It is used in test when T and E are coplanar. // // // // If T and E intersect each other, they may intersect in different ways. If // // 'level' > 0, their intersection type will be reported 'types' and 'pos'. // // // // The return value indicates one of the following cases: // // - 0, T and E are disjoint. // // - 1, T and E intersect each other. // // - 2, T and E are not coplanar. They intersect at a single point. // // - 4, T and E are coplanar. They intersect at a single point or a line // // segment (if types[1] != DISJOINT). // // // /////////////////////////////////////////////////////////////////////////////// #define SETVECTOR3(V, a0, a1, a2) \ (V)[0] = (a0); \ (V)[1] = (a1); \ (V)[2] = (a2) #define SWAP2(a0, a1, tmp) \ (tmp) = (a0); \ (a0) = (a1); \ (a1) = (tmp) int tetgenmesh::tri_edge_2d(point A, point B, point C, point P, point Q, point R, int level, int* types, int* pos) { point U[3], V[3]; // The permuted vectors of points. int pu[3], pv[3]; // The original positions of points. REAL abovept[3]; REAL sA, sB, sC; REAL s1, s2, s3, s4; int z1; if (R == NULL) { // Calculate a lift point. if (1) { REAL n[3], len; // Calculate a lift point, saved in dummypoint. facenormal(A, B, C, n, 1, NULL); len = sqrt(dot(n, n)); if (len != 0) { n[0] /= len; n[1] /= len; n[2] /= len; len = distance(A, B); len += distance(B, C); len += distance(C, A); len /= 3.0; R = abovept; // dummypoint; R[0] = A[0] + len * n[0]; R[1] = A[1] + len * n[1]; R[2] = A[2] + len * n[2]; } else { // The triangle [A,B,C] is (nearly) degenerate, i.e., it is (close) // to a line. We need a line-line intersection test. // !!! A non-save return value.!!! return 0; // DISJOINT } } } // Test A's, B's, and C's orientations wrt plane PQR. sA = orient3d(P, Q, R, A); sB = orient3d(P, Q, R, B); sC = orient3d(P, Q, R, C); if (sA < 0) { if (sB < 0) { if (sC < 0) { // (---). return 0; } else { if (sC > 0) { // (--+). // All points are in the right positions. SETVECTOR3(U, A, B, C); // I3 SETVECTOR3(V, P, Q, R); // I2 SETVECTOR3(pu, 0, 1, 2); SETVECTOR3(pv, 0, 1, 2); z1 = 0; } else { // (--0). SETVECTOR3(U, A, B, C); // I3 SETVECTOR3(V, P, Q, R); // I2 SETVECTOR3(pu, 0, 1, 2); SETVECTOR3(pv, 0, 1, 2); z1 = 1; } } } else { if (sB > 0) { if (sC < 0) { // (-+-). SETVECTOR3(U, C, A, B); // PT = ST SETVECTOR3(V, P, Q, R); // I2 SETVECTOR3(pu, 2, 0, 1); SETVECTOR3(pv, 0, 1, 2); z1 = 0; } else { if (sC > 0) { // (-++). SETVECTOR3(U, B, C, A); // PT = ST x ST SETVECTOR3(V, Q, P, R); // PL = SL SETVECTOR3(pu, 1, 2, 0); SETVECTOR3(pv, 1, 0, 2); z1 = 0; } else { // (-+0). SETVECTOR3(U, C, A, B); // PT = ST SETVECTOR3(V, P, Q, R); // I2 SETVECTOR3(pu, 2, 0, 1); SETVECTOR3(pv, 0, 1, 2); z1 = 2; } } } else { if (sC < 0) { // (-0-). SETVECTOR3(U, C, A, B); // PT = ST SETVECTOR3(V, P, Q, R); // I2 SETVECTOR3(pu, 2, 0, 1); SETVECTOR3(pv, 0, 1, 2); z1 = 1; } else { if (sC > 0) { // (-0+). SETVECTOR3(U, B, C, A); // PT = ST x ST SETVECTOR3(V, Q, P, R); // PL = SL SETVECTOR3(pu, 1, 2, 0); SETVECTOR3(pv, 1, 0, 2); z1 = 2; } else { // (-00). SETVECTOR3(U, B, C, A); // PT = ST x ST SETVECTOR3(V, Q, P, R); // PL = SL SETVECTOR3(pu, 1, 2, 0); SETVECTOR3(pv, 1, 0, 2); z1 = 3; } } } } } else { if (sA > 0) { if (sB < 0) { if (sC < 0) { // (+--). SETVECTOR3(U, B, C, A); // PT = ST x ST SETVECTOR3(V, P, Q, R); // I2 SETVECTOR3(pu, 1, 2, 0); SETVECTOR3(pv, 0, 1, 2); z1 = 0; } else { if (sC > 0) { // (+-+). SETVECTOR3(U, C, A, B); // PT = ST SETVECTOR3(V, Q, P, R); // PL = SL SETVECTOR3(pu, 2, 0, 1); SETVECTOR3(pv, 1, 0, 2); z1 = 0; } else { // (+-0). SETVECTOR3(U, C, A, B); // PT = ST SETVECTOR3(V, Q, P, R); // PL = SL SETVECTOR3(pu, 2, 0, 1); SETVECTOR3(pv, 1, 0, 2); z1 = 2; } } } else { if (sB > 0) { if (sC < 0) { // (++-). SETVECTOR3(U, A, B, C); // I3 SETVECTOR3(V, Q, P, R); // PL = SL SETVECTOR3(pu, 0, 1, 2); SETVECTOR3(pv, 1, 0, 2); z1 = 0; } else { if (sC > 0) { // (+++). return 0; } else { // (++0). SETVECTOR3(U, A, B, C); // I3 SETVECTOR3(V, Q, P, R); // PL = SL SETVECTOR3(pu, 0, 1, 2); SETVECTOR3(pv, 1, 0, 2); z1 = 1; } } } else { // (+0#) if (sC < 0) { // (+0-). SETVECTOR3(U, B, C, A); // PT = ST x ST SETVECTOR3(V, P, Q, R); // I2 SETVECTOR3(pu, 1, 2, 0); SETVECTOR3(pv, 0, 1, 2); z1 = 2; } else { if (sC > 0) { // (+0+). SETVECTOR3(U, C, A, B); // PT = ST SETVECTOR3(V, Q, P, R); // PL = SL SETVECTOR3(pu, 2, 0, 1); SETVECTOR3(pv, 1, 0, 2); z1 = 1; } else { // (+00). SETVECTOR3(U, B, C, A); // PT = ST x ST SETVECTOR3(V, P, Q, R); // I2 SETVECTOR3(pu, 1, 2, 0); SETVECTOR3(pv, 0, 1, 2); z1 = 3; } } } } } else { if (sB < 0) { if (sC < 0) { // (0--). SETVECTOR3(U, B, C, A); // PT = ST x ST SETVECTOR3(V, P, Q, R); // I2 SETVECTOR3(pu, 1, 2, 0); SETVECTOR3(pv, 0, 1, 2); z1 = 1; } else { if (sC > 0) { // (0-+). SETVECTOR3(U, A, B, C); // I3 SETVECTOR3(V, P, Q, R); // I2 SETVECTOR3(pu, 0, 1, 2); SETVECTOR3(pv, 0, 1, 2); z1 = 2; } else { // (0-0). SETVECTOR3(U, C, A, B); // PT = ST SETVECTOR3(V, Q, P, R); // PL = SL SETVECTOR3(pu, 2, 0, 1); SETVECTOR3(pv, 1, 0, 2); z1 = 3; } } } else { if (sB > 0) { if (sC < 0) { // (0+-). SETVECTOR3(U, A, B, C); // I3 SETVECTOR3(V, Q, P, R); // PL = SL SETVECTOR3(pu, 0, 1, 2); SETVECTOR3(pv, 1, 0, 2); z1 = 2; } else { if (sC > 0) { // (0++). SETVECTOR3(U, B, C, A); // PT = ST x ST SETVECTOR3(V, Q, P, R); // PL = SL SETVECTOR3(pu, 1, 2, 0); SETVECTOR3(pv, 1, 0, 2); z1 = 1; } else { // (0+0). SETVECTOR3(U, C, A, B); // PT = ST SETVECTOR3(V, P, Q, R); // I2 SETVECTOR3(pu, 2, 0, 1); SETVECTOR3(pv, 0, 1, 2); z1 = 3; } } } else { // (00#) if (sC < 0) { // (00-). SETVECTOR3(U, A, B, C); // I3 SETVECTOR3(V, Q, P, R); // PL = SL SETVECTOR3(pu, 0, 1, 2); SETVECTOR3(pv, 1, 0, 2); z1 = 3; } else { if (sC > 0) { // (00+). SETVECTOR3(U, A, B, C); // I3 SETVECTOR3(V, P, Q, R); // I2 SETVECTOR3(pu, 0, 1, 2); SETVECTOR3(pv, 0, 1, 2); z1 = 3; } else { // (000) // Not possible unless ABC is degenerate. // Avoiding compiler warnings. SETVECTOR3(U, A, B, C); // I3 SETVECTOR3(V, P, Q, R); // I2 SETVECTOR3(pu, 0, 1, 2); SETVECTOR3(pv, 0, 1, 2); z1 = 4; } } } } } } s1 = orient3d(U[0], U[2], R, V[1]); // A, C, R, Q s2 = orient3d(U[1], U[2], R, V[0]); // B, C, R, P if (s1 > 0) { return 0; } if (s2 < 0) { return 0; } if (level == 0) { return 1; // They are intersected. } if (z1 == 1) { if (s1 == 0) { // (0###) // C = Q. types[0] = (int)SHAREVERT; pos[0] = pu[2]; // C pos[1] = pv[1]; // Q types[1] = (int)DISJOINT; } else { if (s2 == 0) { // (#0##) // C = P. types[0] = (int)SHAREVERT; pos[0] = pu[2]; // C pos[1] = pv[0]; // P types[1] = (int)DISJOINT; } else { // (-+##) // C in [P, Q]. types[0] = (int)ACROSSVERT; pos[0] = pu[2]; // C pos[1] = pv[0]; // [P, Q] types[1] = (int)DISJOINT; } } return 4; } s3 = orient3d(U[0], U[2], R, V[0]); // A, C, R, P s4 = orient3d(U[1], U[2], R, V[1]); // B, C, R, Q if (z1 == 0) { // (tritri-03) if (s1 < 0) { if (s3 > 0) { if (s4 > 0) { // [P, Q] overlaps [k, l] (-+++). types[0] = (int)ACROSSEDGE; pos[0] = pu[2]; // [C, A] pos[1] = pv[0]; // [P, Q] types[1] = (int)TOUCHFACE; pos[2] = 3; // [A, B, C] pos[3] = pv[1]; // Q } else { if (s4 == 0) { // Q = l, [P, Q] contains [k, l] (-++0). types[0] = (int)ACROSSEDGE; pos[0] = pu[2]; // [C, A] pos[1] = pv[0]; // [P, Q] types[1] = (int)TOUCHEDGE; pos[2] = pu[1]; // [B, C] pos[3] = pv[1]; // Q } else { // s4 < 0 // [P, Q] contains [k, l] (-++-). types[0] = (int)ACROSSEDGE; pos[0] = pu[2]; // [C, A] pos[1] = pv[0]; // [P, Q] types[1] = (int)ACROSSEDGE; pos[2] = pu[1]; // [B, C] pos[3] = pv[0]; // [P, Q] } } } else { if (s3 == 0) { if (s4 > 0) { // P = k, [P, Q] in [k, l] (-+0+). types[0] = (int)TOUCHEDGE; pos[0] = pu[2]; // [C, A] pos[1] = pv[0]; // P types[1] = (int)TOUCHFACE; pos[2] = 3; // [A, B, C] pos[3] = pv[1]; // Q } else { if (s4 == 0) { // [P, Q] = [k, l] (-+00). types[0] = (int)TOUCHEDGE; pos[0] = pu[2]; // [C, A] pos[1] = pv[0]; // P types[1] = (int)TOUCHEDGE; pos[2] = pu[1]; // [B, C] pos[3] = pv[1]; // Q } else { // P = k, [P, Q] contains [k, l] (-+0-). types[0] = (int)TOUCHEDGE; pos[0] = pu[2]; // [C, A] pos[1] = pv[0]; // P types[1] = (int)ACROSSEDGE; pos[2] = pu[1]; // [B, C] pos[3] = pv[0]; // [P, Q] } } } else { // s3 < 0 if (s2 > 0) { if (s4 > 0) { // [P, Q] in [k, l] (-+-+). types[0] = (int)TOUCHFACE; pos[0] = 3; // [A, B, C] pos[1] = pv[0]; // P types[1] = (int)TOUCHFACE; pos[2] = 3; // [A, B, C] pos[3] = pv[1]; // Q } else { if (s4 == 0) { // Q = l, [P, Q] in [k, l] (-+-0). types[0] = (int)TOUCHFACE; pos[0] = 3; // [A, B, C] pos[1] = pv[0]; // P types[1] = (int)TOUCHEDGE; pos[2] = pu[1]; // [B, C] pos[3] = pv[1]; // Q } else { // s4 < 0 // [P, Q] overlaps [k, l] (-+--). types[0] = (int)TOUCHFACE; pos[0] = 3; // [A, B, C] pos[1] = pv[0]; // P types[1] = (int)ACROSSEDGE; pos[2] = pu[1]; // [B, C] pos[3] = pv[0]; // [P, Q] } } } else { // s2 == 0 // P = l (#0##). types[0] = (int)TOUCHEDGE; pos[0] = pu[1]; // [B, C] pos[1] = pv[0]; // P types[1] = (int)DISJOINT; } } } } else { // s1 == 0 // Q = k (0####) types[0] = (int)TOUCHEDGE; pos[0] = pu[2]; // [C, A] pos[1] = pv[1]; // Q types[1] = (int)DISJOINT; } } else if (z1 == 2) { // (tritri-23) if (s1 < 0) { if (s3 > 0) { if (s4 > 0) { // [P, Q] overlaps [A, l] (-+++). types[0] = (int)ACROSSVERT; pos[0] = pu[0]; // A pos[1] = pv[0]; // [P, Q] types[1] = (int)TOUCHFACE; pos[2] = 3; // [A, B, C] pos[3] = pv[1]; // Q } else { if (s4 == 0) { // Q = l, [P, Q] contains [A, l] (-++0). types[0] = (int)ACROSSVERT; pos[0] = pu[0]; // A pos[1] = pv[0]; // [P, Q] types[1] = (int)TOUCHEDGE; pos[2] = pu[1]; // [B, C] pos[3] = pv[1]; // Q } else { // s4 < 0 // [P, Q] contains [A, l] (-++-). types[0] = (int)ACROSSVERT; pos[0] = pu[0]; // A pos[1] = pv[0]; // [P, Q] types[1] = (int)ACROSSEDGE; pos[2] = pu[1]; // [B, C] pos[3] = pv[0]; // [P, Q] } } } else { if (s3 == 0) { if (s4 > 0) { // P = A, [P, Q] in [A, l] (-+0+). types[0] = (int)SHAREVERT; pos[0] = pu[0]; // A pos[1] = pv[0]; // P types[1] = (int)TOUCHFACE; pos[2] = 3; // [A, B, C] pos[3] = pv[1]; // Q } else { if (s4 == 0) { // [P, Q] = [A, l] (-+00). types[0] = (int)SHAREVERT; pos[0] = pu[0]; // A pos[1] = pv[0]; // P types[1] = (int)TOUCHEDGE; pos[2] = pu[1]; // [B, C] pos[3] = pv[1]; // Q } else { // s4 < 0 // Q = l, [P, Q] in [A, l] (-+0-). types[0] = (int)SHAREVERT; pos[0] = pu[0]; // A pos[1] = pv[0]; // P types[1] = (int)ACROSSEDGE; pos[2] = pu[1]; // [B, C] pos[3] = pv[0]; // [P, Q] } } } else { // s3 < 0 if (s2 > 0) { if (s4 > 0) { // [P, Q] in [A, l] (-+-+). types[0] = (int)TOUCHFACE; pos[0] = 3; // [A, B, C] pos[1] = pv[0]; // P types[0] = (int)TOUCHFACE; pos[0] = 3; // [A, B, C] pos[1] = pv[1]; // Q } else { if (s4 == 0) { // Q = l, [P, Q] in [A, l] (-+-0). types[0] = (int)TOUCHFACE; pos[0] = 3; // [A, B, C] pos[1] = pv[0]; // P types[0] = (int)TOUCHEDGE; pos[0] = pu[1]; // [B, C] pos[1] = pv[1]; // Q } else { // s4 < 0 // [P, Q] overlaps [A, l] (-+--). types[0] = (int)TOUCHFACE; pos[0] = 3; // [A, B, C] pos[1] = pv[0]; // P types[0] = (int)ACROSSEDGE; pos[0] = pu[1]; // [B, C] pos[1] = pv[0]; // [P, Q] } } } else { // s2 == 0 // P = l (#0##). types[0] = (int)TOUCHEDGE; pos[0] = pu[1]; // [B, C] pos[1] = pv[0]; // P types[1] = (int)DISJOINT; } } } } else { // s1 == 0 // Q = A (0###). types[0] = (int)SHAREVERT; pos[0] = pu[0]; // A pos[1] = pv[1]; // Q types[1] = (int)DISJOINT; } } else if (z1 == 3) { // (tritri-33) if (s1 < 0) { if (s3 > 0) { if (s4 > 0) { // [P, Q] overlaps [A, B] (-+++). types[0] = (int)ACROSSVERT; pos[0] = pu[0]; // A pos[1] = pv[0]; // [P, Q] types[1] = (int)TOUCHEDGE; pos[2] = pu[0]; // [A, B] pos[3] = pv[1]; // Q } else { if (s4 == 0) { // Q = B, [P, Q] contains [A, B] (-++0). types[0] = (int)ACROSSVERT; pos[0] = pu[0]; // A pos[1] = pv[0]; // [P, Q] types[1] = (int)SHAREVERT; pos[2] = pu[1]; // B pos[3] = pv[1]; // Q } else { // s4 < 0 // [P, Q] contains [A, B] (-++-). types[0] = (int)ACROSSVERT; pos[0] = pu[0]; // A pos[1] = pv[0]; // [P, Q] types[1] = (int)ACROSSVERT; pos[2] = pu[1]; // B pos[3] = pv[0]; // [P, Q] } } } else { if (s3 == 0) { if (s4 > 0) { // P = A, [P, Q] in [A, B] (-+0+). types[0] = (int)SHAREVERT; pos[0] = pu[0]; // A pos[1] = pv[0]; // P types[1] = (int)TOUCHEDGE; pos[2] = pu[0]; // [A, B] pos[3] = pv[1]; // Q } else { if (s4 == 0) { // [P, Q] = [A, B] (-+00). types[0] = (int)SHAREEDGE; pos[0] = pu[0]; // [A, B] pos[1] = pv[0]; // [P, Q] types[1] = (int)DISJOINT; } else { // s4 < 0 // P= A, [P, Q] in [A, B] (-+0-). types[0] = (int)SHAREVERT; pos[0] = pu[0]; // A pos[1] = pv[0]; // P types[1] = (int)ACROSSVERT; pos[2] = pu[1]; // B pos[3] = pv[0]; // [P, Q] } } } else { // s3 < 0 if (s2 > 0) { if (s4 > 0) { // [P, Q] in [A, B] (-+-+). types[0] = (int)TOUCHEDGE; pos[0] = pu[0]; // [A, B] pos[1] = pv[0]; // P types[1] = (int)TOUCHEDGE; pos[2] = pu[0]; // [A, B] pos[3] = pv[1]; // Q } else { if (s4 == 0) { // Q = B, [P, Q] in [A, B] (-+-0). types[0] = (int)TOUCHEDGE; pos[0] = pu[0]; // [A, B] pos[1] = pv[0]; // P types[1] = (int)SHAREVERT; pos[2] = pu[1]; // B pos[3] = pv[1]; // Q } else { // s4 < 0 // [P, Q] overlaps [A, B] (-+--). types[0] = (int)TOUCHEDGE; pos[0] = pu[0]; // [A, B] pos[1] = pv[0]; // P types[1] = (int)ACROSSVERT; pos[2] = pu[1]; // B pos[3] = pv[0]; // [P, Q] } } } else { // s2 == 0 // P = B (#0##). types[0] = (int)SHAREVERT; pos[0] = pu[1]; // B pos[1] = pv[0]; // P types[1] = (int)DISJOINT; } } } } else { // s1 == 0 // Q = A (0###). types[0] = (int)SHAREVERT; pos[0] = pu[0]; // A pos[1] = pv[1]; // Q types[1] = (int)DISJOINT; } } return 4; } int tetgenmesh::tri_edge_tail(point A, point B, point C, point P, point Q, point R, REAL sP, REAL sQ, int level, int* types, int* pos) { point U[3], V[3]; //, Ptmp; int pu[3], pv[3]; //, itmp; REAL s1, s2, s3; int z1; if (sP < 0) { if (sQ < 0) { // (--) disjoint return 0; } else { if (sQ > 0) { // (-+) SETVECTOR3(U, A, B, C); SETVECTOR3(V, P, Q, R); SETVECTOR3(pu, 0, 1, 2); SETVECTOR3(pv, 0, 1, 2); z1 = 0; } else { // (-0) SETVECTOR3(U, A, B, C); SETVECTOR3(V, P, Q, R); SETVECTOR3(pu, 0, 1, 2); SETVECTOR3(pv, 0, 1, 2); z1 = 1; } } } else { if (sP > 0) { // (+-) if (sQ < 0) { SETVECTOR3(U, A, B, C); SETVECTOR3(V, Q, P, R); // P and Q are flipped. SETVECTOR3(pu, 0, 1, 2); SETVECTOR3(pv, 1, 0, 2); z1 = 0; } else { if (sQ > 0) { // (++) disjoint return 0; } else { // (+0) SETVECTOR3(U, B, A, C); // A and B are flipped. SETVECTOR3(V, P, Q, R); SETVECTOR3(pu, 1, 0, 2); SETVECTOR3(pv, 0, 1, 2); z1 = 1; } } } else { // sP == 0 if (sQ < 0) { // (0-) SETVECTOR3(U, A, B, C); SETVECTOR3(V, Q, P, R); // P and Q are flipped. SETVECTOR3(pu, 0, 1, 2); SETVECTOR3(pv, 1, 0, 2); z1 = 1; } else { if (sQ > 0) { // (0+) SETVECTOR3(U, B, A, C); // A and B are flipped. SETVECTOR3(V, Q, P, R); // P and Q are flipped. SETVECTOR3(pu, 1, 0, 2); SETVECTOR3(pv, 1, 0, 2); z1 = 1; } else { // (00) // A, B, C, P, and Q are coplanar. z1 = 2; } } } } if (z1 == 2) { // The triangle and the edge are coplanar. return tri_edge_2d(A, B, C, P, Q, R, level, types, pos); } s1 = orient3d(U[0], U[1], V[0], V[1]); if (s1 < 0) { return 0; } s2 = orient3d(U[1], U[2], V[0], V[1]); if (s2 < 0) { return 0; } s3 = orient3d(U[2], U[0], V[0], V[1]); if (s3 < 0) { return 0; } if (level == 0) { return 1; // The are intersected. } types[1] = (int)DISJOINT; // No second intersection point. if (z1 == 0) { if (s1 > 0) { if (s2 > 0) { if (s3 > 0) { // (+++) // [P, Q] passes interior of [A, B, C]. types[0] = (int)ACROSSFACE; pos[0] = 3; // interior of [A, B, C] pos[1] = 0; // [P, Q] } else { // s3 == 0 (++0) // [P, Q] intersects [C, A]. types[0] = (int)ACROSSEDGE; pos[0] = pu[2]; // [C, A] pos[1] = 0; // [P, Q] } } else { // s2 == 0 if (s3 > 0) { // (+0+) // [P, Q] intersects [B, C]. types[0] = (int)ACROSSEDGE; pos[0] = pu[1]; // [B, C] pos[1] = 0; // [P, Q] } else { // s3 == 0 (+00) // [P, Q] passes C. types[0] = (int)ACROSSVERT; pos[0] = pu[2]; // C pos[1] = 0; // [P, Q] } } } else { // s1 == 0 if (s2 > 0) { if (s3 > 0) { // (0++) // [P, Q] intersects [A, B]. types[0] = (int)ACROSSEDGE; pos[0] = pu[0]; // [A, B] pos[1] = 0; // [P, Q] } else { // s3 == 0 (0+0) // [P, Q] passes A. types[0] = (int)ACROSSVERT; pos[0] = pu[0]; // A pos[1] = 0; // [P, Q] } } else { // s2 == 0 if (s3 > 0) { // (00+) // [P, Q] passes B. types[0] = (int)ACROSSVERT; pos[0] = pu[1]; // B pos[1] = 0; // [P, Q] } } } } else { // z1 == 1 if (s1 > 0) { if (s2 > 0) { if (s3 > 0) { // (+++) // Q lies in [A, B, C]. types[0] = (int)TOUCHFACE; pos[0] = 0; // [A, B, C] pos[1] = pv[1]; // Q } else { // s3 == 0 (++0) // Q lies on [C, A]. types[0] = (int)TOUCHEDGE; pos[0] = pu[2]; // [C, A] pos[1] = pv[1]; // Q } } else { // s2 == 0 if (s3 > 0) { // (+0+) // Q lies on [B, C]. types[0] = (int)TOUCHEDGE; pos[0] = pu[1]; // [B, C] pos[1] = pv[1]; // Q } else { // s3 == 0 (+00) // Q = C. types[0] = (int)SHAREVERT; pos[0] = pu[2]; // C pos[1] = pv[1]; // Q } } } else { // s1 == 0 if (s2 > 0) { if (s3 > 0) { // (0++) // Q lies on [A, B]. types[0] = (int)TOUCHEDGE; pos[0] = pu[0]; // [A, B] pos[1] = pv[1]; // Q } else { // s3 == 0 (0+0) // Q = A. types[0] = (int)SHAREVERT; pos[0] = pu[0]; // A pos[1] = pv[1]; // Q } } else { // s2 == 0 if (s3 > 0) { // (00+) // Q = B. types[0] = (int)SHAREVERT; pos[0] = pu[1]; // B pos[1] = pv[1]; // Q } } } } // T and E intersect in a single point. return 2; } int tetgenmesh::tri_edge_test(point A, point B, point C, point P, point Q, point R, int level, int* types, int* pos) { REAL sP, sQ; // Test the locations of P and Q with respect to ABC. sP = orient3d(A, B, C, P); sQ = orient3d(A, B, C, Q); return tri_edge_tail(A, B, C, P, Q, R, sP, sQ, level, types, pos); } /////////////////////////////////////////////////////////////////////////////// // // // tri_tri_inter() Test whether two triangle (abc) and (opq) are // // intersecting or not. // // // // Return 0 if they are disjoint. Otherwise, return 1. 'type' returns one of // // the four cases: SHAREVERTEX, SHAREEDGE, SHAREFACE, and INTERSECT. // // // /////////////////////////////////////////////////////////////////////////////// int tetgenmesh::tri_edge_inter_tail(REAL* A, REAL* B, REAL* C, REAL* P, REAL* Q, REAL s_p, REAL s_q) { int types[2], pos[4]; int ni; // =0, 2, 4 ni = tri_edge_tail(A, B, C, P, Q, NULL, s_p, s_q, 1, types, pos); if (ni > 0) { if (ni == 2) { // Get the intersection type. if (types[0] == (int)SHAREVERT) { return (int)SHAREVERT; } else { return (int)INTERSECT; } } else if (ni == 4) { // There may be two intersections. if (types[0] == (int)SHAREVERT) { if (types[1] == (int)DISJOINT) { return (int)SHAREVERT; } else { return (int)INTERSECT; } } else { if (types[0] == (int)SHAREEDGE) { return (int)SHAREEDGE; } else { return (int)INTERSECT; } } } } return (int)DISJOINT; } int tetgenmesh::tri_tri_inter(REAL* A, REAL* B, REAL* C, REAL* O, REAL* P, REAL* Q) { REAL s_o, s_p, s_q; REAL s_a, s_b, s_c; s_o = orient3d(A, B, C, O); s_p = orient3d(A, B, C, P); s_q = orient3d(A, B, C, Q); if ((s_o * s_p > 0.0) && (s_o * s_q > 0.0)) { // o, p, q are all in the same halfspace of ABC. return 0; // DISJOINT; } s_a = orient3d(O, P, Q, A); s_b = orient3d(O, P, Q, B); s_c = orient3d(O, P, Q, C); if ((s_a * s_b > 0.0) && (s_a * s_c > 0.0)) { // a, b, c are all in the same halfspace of OPQ. return 0; // DISJOINT; } int abcop, abcpq, abcqo; int shareedge = 0; abcop = tri_edge_inter_tail(A, B, C, O, P, s_o, s_p); if (abcop == (int)INTERSECT) { return (int)INTERSECT; } else if (abcop == (int)SHAREEDGE) { shareedge++; } abcpq = tri_edge_inter_tail(A, B, C, P, Q, s_p, s_q); if (abcpq == (int)INTERSECT) { return (int)INTERSECT; } else if (abcpq == (int)SHAREEDGE) { shareedge++; } abcqo = tri_edge_inter_tail(A, B, C, Q, O, s_q, s_o); if (abcqo == (int)INTERSECT) { return (int)INTERSECT; } else if (abcqo == (int)SHAREEDGE) { shareedge++; } if (shareedge == 3) { // opq are coincident with abc. return (int)SHAREFACE; } // Continue to detect whether opq and abc are intersecting or not. int opqab, opqbc, opqca; opqab = tri_edge_inter_tail(O, P, Q, A, B, s_a, s_b); if (opqab == (int)INTERSECT) { return (int)INTERSECT; } opqbc = tri_edge_inter_tail(O, P, Q, B, C, s_b, s_c); if (opqbc == (int)INTERSECT) { return (int)INTERSECT; } opqca = tri_edge_inter_tail(O, P, Q, C, A, s_c, s_a); if (opqca == (int)INTERSECT) { return (int)INTERSECT; } // At this point, two triangles are not intersecting and not coincident. // They may be share an edge, or share a vertex, or disjoint. if (abcop == (int)SHAREEDGE) { // op is coincident with an edge of abc. return (int)SHAREEDGE; } if (abcpq == (int)SHAREEDGE) { // pq is coincident with an edge of abc. return (int)SHAREEDGE; } if (abcqo == (int)SHAREEDGE) { // qo is coincident with an edge of abc. return (int)SHAREEDGE; } // They may share a vertex or disjoint. if (abcop == (int)SHAREVERT) { return (int)SHAREVERT; } if (abcpq == (int)SHAREVERT) { // q is the coincident vertex. return (int)SHAREVERT; } // They are disjoint. return (int)DISJOINT; } /////////////////////////////////////////////////////////////////////////////// // // // lu_decmp() Compute the LU decomposition of a matrix. // // // // Compute the LU decomposition of a (non-singular) square matrix A using // // partial pivoting and implicit row exchanges. The result is: // // A = P * L * U, // // where P is a permutation matrix, L is unit lower triangular, and U is // // upper triangular. The factored form of A is used in combination with // // 'lu_solve()' to solve linear equations: Ax = b, or invert a matrix. // // // // The inputs are a square matrix 'lu[N..n+N-1][N..n+N-1]', it's size is 'n'.// // On output, 'lu' is replaced by the LU decomposition of a rowwise permuta- // // tion of itself, 'ps[N..n+N-1]' is an output vector that records the row // // permutation effected by the partial pivoting, effectively, 'ps' array // // tells the user what the permutation matrix P is; 'd' is output as +1/-1 // // depending on whether the number of row interchanges was even or odd, // // respectively. // // // // Return true if the LU decomposition is successfully computed, otherwise, // // return false in case that A is a singular matrix. // // // /////////////////////////////////////////////////////////////////////////////// bool tetgenmesh::lu_decmp(REAL lu[4][4], int n, int* ps, REAL* d, int N) { REAL scales[4]; REAL pivot, biggest, mult, tempf; int pivotindex = 0; int i, j, k; *d = 1.0; // No row interchanges yet. for (i = N; i < n + N; i++) { // For each row. // Find the largest element in each row for row equilibration biggest = 0.0; for (j = N; j < n + N; j++) if (biggest < (tempf = fabs(lu[i][j]))) biggest = tempf; if (biggest != 0.0) scales[i] = 1.0 / biggest; else { scales[i] = 0.0; return false; // Zero row: singular matrix. } ps[i] = i; // Initialize pivot sequence. } for (k = N; k < n + N - 1; k++) { // For each column. // Find the largest element in each column to pivot around. biggest = 0.0; for (i = k; i < n + N; i++) { if (biggest < (tempf = fabs(lu[ps[i]][k]) * scales[ps[i]])) { biggest = tempf; pivotindex = i; } } if (biggest == 0.0) { return false; // Zero column: singular matrix. } if (pivotindex != k) { // Update pivot sequence. j = ps[k]; ps[k] = ps[pivotindex]; ps[pivotindex] = j; *d = -(*d); // ...and change the parity of d. } // Pivot, eliminating an extra variable each time pivot = lu[ps[k]][k]; for (i = k + 1; i < n + N; i++) { lu[ps[i]][k] = mult = lu[ps[i]][k] / pivot; if (mult != 0.0) { for (j = k + 1; j < n + N; j++) lu[ps[i]][j] -= mult * lu[ps[k]][j]; } } } // (lu[ps[n + N - 1]][n + N - 1] == 0.0) ==> A is singular. return lu[ps[n + N - 1]][n + N - 1] != 0.0; } /////////////////////////////////////////////////////////////////////////////// // // // lu_solve() Solves the linear equation: Ax = b, after the matrix A // // has been decomposed into the lower and upper triangular // // matrices L and U, where A = LU. // // // // 'lu[N..n+N-1][N..n+N-1]' is input, not as the matrix 'A' but rather as // // its LU decomposition, computed by the routine 'lu_decmp'; 'ps[N..n+N-1]' // // is input as the permutation vector returned by 'lu_decmp'; 'b[N..n+N-1]' // // is input as the right-hand side vector, and returns with the solution // // vector. 'lu', 'n', and 'ps' are not modified by this routine and can be // // left in place for successive calls with different right-hand sides 'b'. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::lu_solve(REAL lu[4][4], int n, int* ps, REAL* b, int N) { int i, j; REAL X[4], dot; for (i = N; i < n + N; i++) X[i] = 0.0; // Vector reduction using U triangular matrix. for (i = N; i < n + N; i++) { dot = 0.0; for (j = N; j < i + N; j++) dot += lu[ps[i]][j] * X[j]; X[i] = b[ps[i]] - dot; } // Back substitution, in L triangular matrix. for (i = n + N - 1; i >= N; i--) { dot = 0.0; for (j = i + 1; j < n + N; j++) dot += lu[ps[i]][j] * X[j]; X[i] = (X[i] - dot) / lu[ps[i]][i]; } for (i = N; i < n + N; i++) b[i] = X[i]; } /////////////////////////////////////////////////////////////////////////////// // // // incircle3d() 3D in-circle test. // // // // Return a negative value if pd is inside the circumcircle of the triangle // // pa, pb, and pc. // // // // IMPORTANT: It assumes that [a,b] is the common edge, i.e., the two input // // triangles are [a,b,c] and [b,a,d]. // // // /////////////////////////////////////////////////////////////////////////////// REAL tetgenmesh::incircle3d(point pa, point pb, point pc, point pd) { REAL area2[2], n1[3], n2[3], c[3]; REAL sign, r, d; // Calculate the areas of the two triangles [a, b, c] and [b, a, d]. facenormal(pa, pb, pc, n1, 1, NULL); area2[0] = dot(n1, n1); facenormal(pb, pa, pd, n2, 1, NULL); area2[1] = dot(n2, n2); if (area2[0] > area2[1]) { // Choose [a, b, c] as the base triangle. circumsphere(pa, pb, pc, NULL, c, &r); d = distance(c, pd); } else { // Choose [b, a, d] as the base triangle. if (area2[1] > 0) { circumsphere(pb, pa, pd, NULL, c, &r); d = distance(c, pc); } else { // The four points are collinear. This case only happens on the boundary. return 0; // Return "not inside". } } sign = d - r; if (fabs(sign) / r < b->epsilon) { sign = 0; } return sign; } /////////////////////////////////////////////////////////////////////////////// // // // facenormal() Calculate the normal of the face. // // // // The normal of the face abc can be calculated by the cross product of 2 of // // its 3 edge vectors. A better choice of two edge vectors will reduce the // // numerical error during the calculation. Burdakov proved that the optimal // // basis problem is equivalent to the minimum spanning tree problem with the // // edge length be the functional, see Burdakov, "A greedy algorithm for the // // optimal basis problem", BIT 37:3 (1997), 591-599. If 'pivot' > 0, the two // // short edges in abc are chosen for the calculation. // // // // If 'lav' is not NULL and if 'pivot' is set, the average edge length of // // the edges of the face [a,b,c] is returned. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::facenormal(point pa, point pb, point pc, REAL* n, int pivot, REAL* lav) { REAL v1[3], v2[3], v3[3], *pv1, *pv2; REAL L1, L2, L3; v1[0] = pb[0] - pa[0]; // edge vector v1: a->b v1[1] = pb[1] - pa[1]; v1[2] = pb[2] - pa[2]; v2[0] = pa[0] - pc[0]; // edge vector v2: c->a v2[1] = pa[1] - pc[1]; v2[2] = pa[2] - pc[2]; // Default, normal is calculated by: v1 x (-v2) (see Fig. fnormal). if (pivot > 0) { // Choose edge vectors by Burdakov's algorithm. v3[0] = pc[0] - pb[0]; // edge vector v3: b->c v3[1] = pc[1] - pb[1]; v3[2] = pc[2] - pb[2]; L1 = dot(v1, v1); L2 = dot(v2, v2); L3 = dot(v3, v3); // Sort the three edge lengths. if (L1 < L2) { if (L2 < L3) { pv1 = v1; pv2 = v2; // n = v1 x (-v2). } else { pv1 = v3; pv2 = v1; // n = v3 x (-v1). } } else { if (L1 < L3) { pv1 = v1; pv2 = v2; // n = v1 x (-v2). } else { pv1 = v2; pv2 = v3; // n = v2 x (-v3). } } if (lav) { // return the average edge length. *lav = (sqrt(L1) + sqrt(L2) + sqrt(L3)) / 3.0; } } else { pv1 = v1; pv2 = v2; // n = v1 x (-v2). } // Calculate the face normal. cross(pv1, pv2, n); // Inverse the direction; n[0] = -n[0]; n[1] = -n[1]; n[2] = -n[2]; } /////////////////////////////////////////////////////////////////////////////// // // // shortdistance() Returns the shortest distance from point p to a line // // defined by two points e1 and e2. // // // // First compute the projection length l_p of the vector v1 = p - e1 along // // the vector v2 = e2 - e1. Then Pythagoras' Theorem is used to compute the // // shortest distance. // // // // This routine allows that p is collinear with the line. In this case, the // // return value is zero. The two points e1 and e2 should not be identical. // // // /////////////////////////////////////////////////////////////////////////////// REAL tetgenmesh::shortdistance(REAL* p, REAL* e1, REAL* e2) { REAL v1[3], v2[3]; REAL len, l_p; v1[0] = e2[0] - e1[0]; v1[1] = e2[1] - e1[1]; v1[2] = e2[2] - e1[2]; v2[0] = p[0] - e1[0]; v2[1] = p[1] - e1[1]; v2[2] = p[2] - e1[2]; len = sqrt(dot(v1, v1)); v1[0] /= len; v1[1] /= len; v1[2] /= len; l_p = dot(v1, v2); return sqrt(dot(v2, v2) - l_p * l_p); } /////////////////////////////////////////////////////////////////////////////// // // // triarea() Return the area of a triangle. // // // /////////////////////////////////////////////////////////////////////////////// REAL tetgenmesh::triarea(REAL* pa, REAL* pb, REAL* pc) { REAL A[4][4]; // Compute the coefficient matrix A (3x3). A[0][0] = pb[0] - pa[0]; A[0][1] = pb[1] - pa[1]; A[0][2] = pb[2] - pa[2]; // vector V1 (pa->pb) A[1][0] = pc[0] - pa[0]; A[1][1] = pc[1] - pa[1]; A[1][2] = pc[2] - pa[2]; // vector V2 (pa->pc) cross(A[0], A[1], A[2]); // vector V3 (V1 X V2) return 0.5 * sqrt(dot(A[2], A[2])); // The area of [a,b,c]. } REAL tetgenmesh::orient3dfast(REAL* pa, REAL* pb, REAL* pc, REAL* pd) { REAL adx, bdx, cdx; REAL ady, bdy, cdy; REAL adz, bdz, cdz; adx = pa[0] - pd[0]; bdx = pb[0] - pd[0]; cdx = pc[0] - pd[0]; ady = pa[1] - pd[1]; bdy = pb[1] - pd[1]; cdy = pc[1] - pd[1]; adz = pa[2] - pd[2]; bdz = pb[2] - pd[2]; cdz = pc[2] - pd[2]; return adx * (bdy * cdz - bdz * cdy) + bdx * (cdy * adz - cdz * ady) + cdx * (ady * bdz - adz * bdy); } /////////////////////////////////////////////////////////////////////////////// // // // interiorangle() Return the interior angle (0 - 2 * PI) between vectors // // o->p1 and o->p2. // // // // 'n' is the normal of the plane containing face (o, p1, p2). The interior // // angle is the total angle rotating from o->p1 around n to o->p2. Exchange // // the position of p1 and p2 will get the complement angle of the other one. // // i.e., interiorangle(o, p1, p2) = 2 * PI - interiorangle(o, p2, p1). Set // // 'n' be NULL if you only want the interior angle between 0 - PI. // // // /////////////////////////////////////////////////////////////////////////////// REAL tetgenmesh::interiorangle(REAL* o, REAL* p1, REAL* p2, REAL* n) { REAL v1[3], v2[3], np[3]; REAL theta, costheta, lenlen; REAL ori, len1, len2; // Get the interior angle (0 - PI) between o->p1, and o->p2. v1[0] = p1[0] - o[0]; v1[1] = p1[1] - o[1]; v1[2] = p1[2] - o[2]; v2[0] = p2[0] - o[0]; v2[1] = p2[1] - o[1]; v2[2] = p2[2] - o[2]; len1 = sqrt(dot(v1, v1)); len2 = sqrt(dot(v2, v2)); lenlen = len1 * len2; costheta = dot(v1, v2) / lenlen; if (costheta > 1.0) { costheta = 1.0; // Roundoff. } else if (costheta < -1.0) { costheta = -1.0; // Roundoff. } theta = acos(costheta); if (n != NULL) { // Get a point above the face (o, p1, p2); np[0] = o[0] + n[0]; np[1] = o[1] + n[1]; np[2] = o[2] + n[2]; // Adjust theta (0 - 2 * PI). ori = orient3d(p1, o, np, p2); if (ori > 0.0) { theta = 2 * PI - theta; } } return theta; } /////////////////////////////////////////////////////////////////////////////// // // // projpt2edge() Return the projection point from a point to an edge. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::projpt2edge(REAL* p, REAL* e1, REAL* e2, REAL* prj) { REAL v1[3], v2[3]; REAL len, l_p; v1[0] = e2[0] - e1[0]; v1[1] = e2[1] - e1[1]; v1[2] = e2[2] - e1[2]; v2[0] = p[0] - e1[0]; v2[1] = p[1] - e1[1]; v2[2] = p[2] - e1[2]; len = sqrt(dot(v1, v1)); v1[0] /= len; v1[1] /= len; v1[2] /= len; l_p = dot(v1, v2); prj[0] = e1[0] + l_p * v1[0]; prj[1] = e1[1] + l_p * v1[1]; prj[2] = e1[2] + l_p * v1[2]; } /////////////////////////////////////////////////////////////////////////////// // // // projpt2face() Return the projection point from a point to a face. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::projpt2face(REAL* p, REAL* f1, REAL* f2, REAL* f3, REAL* prj) { REAL fnormal[3], v1[3]; REAL len, dist; // Get the unit face normal. facenormal(f1, f2, f3, fnormal, 1, NULL); len = sqrt(fnormal[0] * fnormal[0] + fnormal[1] * fnormal[1] + fnormal[2] * fnormal[2]); fnormal[0] /= len; fnormal[1] /= len; fnormal[2] /= len; // Get the vector v1 = |p - f1|. v1[0] = p[0] - f1[0]; v1[1] = p[1] - f1[1]; v1[2] = p[2] - f1[2]; // Get the project distance. dist = dot(fnormal, v1); // Get the project point. prj[0] = p[0] - dist * fnormal[0]; prj[1] = p[1] - dist * fnormal[1]; prj[2] = p[2] - dist * fnormal[2]; } /////////////////////////////////////////////////////////////////////////////// // // // tetalldihedral() Get all (six) dihedral angles of a tet. // // // // If 'cosdd' is not NULL, it returns the cosines of the 6 dihedral angles, // // the edge indices are given in the global array 'edge2ver'. If 'cosmaxd' // // (or 'cosmind') is not NULL, it returns the cosine of the maximal (or // // minimal) dihedral angle. // // // /////////////////////////////////////////////////////////////////////////////// bool tetgenmesh::tetalldihedral(point pa, point pb, point pc, point pd, REAL* cosdd, REAL* cosmaxd, REAL* cosmind) { REAL N[4][3], vol, cosd, len; int f1 = 0, f2 = 0, i, j; vol = 0; // Check if the tet is valid or not. // Get four normals of faces of the tet. tetallnormal(pa, pb, pc, pd, N, &vol); if (vol > 0) { // Normalize the normals. for (i = 0; i < 4; i++) { len = sqrt(dot(N[i], N[i])); if (len != 0.0) { for (j = 0; j < 3; j++) N[i][j] /= len; } else { // There are degeneracies, such as duplicated vertices. vol = 0; // assert(0); } } } if (vol <= 0) { // if (vol == 0.0) { // A degenerated tet or an inverted tet. facenormal(pc, pb, pd, N[0], 1, NULL); facenormal(pa, pc, pd, N[1], 1, NULL); facenormal(pb, pa, pd, N[2], 1, NULL); facenormal(pa, pb, pc, N[3], 1, NULL); // Normalize the normals. for (i = 0; i < 4; i++) { len = sqrt(dot(N[i], N[i])); if (len != 0.0) { for (j = 0; j < 3; j++) N[i][j] /= len; } else { // There are degeneracies, such as duplicated vertices. break; // Not a valid normal. } } if (i < 4) { // Do not calculate dihedral angles. // Set all angles be 0 degree. There will be no quality optimization for // this tet! Use volume optimization to correct it. if (cosdd != NULL) { for (i = 0; i < 6; i++) { cosdd[i] = -1.0; // 180 degree. } } // This tet has zero volume. if (cosmaxd != NULL) { *cosmaxd = -1.0; // 180 degree. } if (cosmind != NULL) { *cosmind = -1.0; // 180 degree. } return false; } } // Calculate the cosine of the dihedral angles of the edges. for (i = 0; i < 6; i++) { switch (i) { case 0: f1 = 0; f2 = 1; break; // [c,d]. case 1: f1 = 1; f2 = 2; break; // [a,d]. case 2: f1 = 2; f2 = 3; break; // [a,b]. case 3: f1 = 0; f2 = 3; break; // [b,c]. case 4: f1 = 2; f2 = 0; break; // [b,d]. case 5: f1 = 1; f2 = 3; break; // [a,c]. } cosd = -dot(N[f1], N[f2]); if (cosd < -1.0) cosd = -1.0; // Rounding. if (cosd > 1.0) cosd = 1.0; // Rounding. if (cosdd) cosdd[i] = cosd; if (cosmaxd || cosmind) { if (i == 0) { if (cosmaxd) *cosmaxd = cosd; if (cosmind) *cosmind = cosd; } else { if (cosmaxd) *cosmaxd = cosd < *cosmaxd ? cosd : *cosmaxd; if (cosmind) *cosmind = cosd > *cosmind ? cosd : *cosmind; } } } return true; } /////////////////////////////////////////////////////////////////////////////// // // // tetallnormal() Get the in-normals of the four faces of a given tet. // // // // Let tet be abcd. N[4][3] returns the four normals, which are: N[0] cbd, // // N[1] acd, N[2] bad, N[3] abc (exactly corresponding to the face indices // // of the mesh data structure). These normals are unnormalized. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::tetallnormal(point pa, point pb, point pc, point pd, REAL N[4][3], REAL* volume) { REAL A[4][4], rhs[4], D; int indx[4]; int i, j; // get the entries of A[3][3]. for (i = 0; i < 3; i++) A[0][i] = pa[i] - pd[i]; // d->a vec for (i = 0; i < 3; i++) A[1][i] = pb[i] - pd[i]; // d->b vec for (i = 0; i < 3; i++) A[2][i] = pc[i] - pd[i]; // d->c vec // Compute the inverse of matrix A, to get 3 normals of the 4 faces. if (lu_decmp(A, 3, indx, &D, 0)) { // Decompose the matrix just once. if (volume != NULL) { // Get the volume of the tet. *volume = fabs((A[indx[0]][0] * A[indx[1]][1] * A[indx[2]][2])) / 6.0; } for (j = 0; j < 3; j++) { for (i = 0; i < 3; i++) rhs[i] = 0.0; rhs[j] = 1.0; // Positive means the inside direction lu_solve(A, 3, indx, rhs, 0); for (i = 0; i < 3; i++) N[j][i] = rhs[i]; } // Get the fourth normal by summing up the first three. for (i = 0; i < 3; i++) N[3][i] = -N[0][i] - N[1][i] - N[2][i]; } else { // The tet is degenerated. if (volume != NULL) { *volume = 0; } } } /////////////////////////////////////////////////////////////////////////////// // // // tetaspectratio() Calculate the aspect ratio of the tetrahedron. // // // // The aspect ratio of a tet is L/h, where L is the longest edge length, and // // h is the shortest height of the tet. // // // /////////////////////////////////////////////////////////////////////////////// REAL tetgenmesh::tetaspectratio(point pa, point pb, point pc, point pd) { REAL V[6][3], edgelength[6], longlen; REAL vda[3], vdb[3], vdc[3]; REAL N[4][3], A[4][4], rhs[4], D; REAL H[4], volume, minheightinv; int indx[4]; int i, j; // Set the edge vectors: V[0], ..., V[5] for (i = 0; i < 3; i++) V[0][i] = pa[i] - pd[i]; for (i = 0; i < 3; i++) V[1][i] = pb[i] - pd[i]; for (i = 0; i < 3; i++) V[2][i] = pc[i] - pd[i]; for (i = 0; i < 3; i++) V[3][i] = pb[i] - pa[i]; for (i = 0; i < 3; i++) V[4][i] = pc[i] - pb[i]; for (i = 0; i < 3; i++) V[5][i] = pa[i] - pc[i]; // Get the squares of the edge lengths. for (i = 0; i < 6; i++) edgelength[i] = dot(V[i], V[i]); // Calculate the longest and shortest edge length. longlen = edgelength[0]; for (i = 1; i < 6; i++) { longlen = edgelength[i] > longlen ? edgelength[i] : longlen; } // Set the matrix A = [vda, vdb, vdc]^T. for (i = 0; i < 3; i++) A[0][i] = vda[i] = pa[i] - pd[i]; for (i = 0; i < 3; i++) A[1][i] = vdb[i] = pb[i] - pd[i]; for (i = 0; i < 3; i++) A[2][i] = vdc[i] = pc[i] - pd[i]; // Lu-decompose the matrix A. lu_decmp(A, 3, indx, &D, 0); // Get the volume of abcd. volume = (A[indx[0]][0] * A[indx[1]][1] * A[indx[2]][2]) / 6.0; // Check if it is zero. if (volume == 0.0) return 1.0e+200; // A degenerate tet. // Compute the 4 face normals (N[0], ..., N[3]). for (j = 0; j < 3; j++) { for (i = 0; i < 3; i++) rhs[i] = 0.0; rhs[j] = 1.0; // Positive means the inside direction lu_solve(A, 3, indx, rhs, 0); for (i = 0; i < 3; i++) N[j][i] = rhs[i]; } // Get the fourth normal by summing up the first three. for (i = 0; i < 3; i++) N[3][i] = -N[0][i] - N[1][i] - N[2][i]; // Normalized the normals. for (i = 0; i < 4; i++) { // H[i] is the inverse of the height of its corresponding face. H[i] = sqrt(dot(N[i], N[i])); // if (H[i] > 0.0) { // for (j = 0; j < 3; j++) N[i][j] /= H[i]; // } } // Get the radius of the inscribed sphere. // insradius = 1.0 / (H[0] + H[1] + H[2] + H[3]); // Get the biggest H[i] (corresponding to the smallest height). minheightinv = H[0]; for (i = 1; i < 4; i++) { if (H[i] > minheightinv) minheightinv = H[i]; } return sqrt(longlen) * minheightinv; } /////////////////////////////////////////////////////////////////////////////// // // // circumsphere() Calculate the smallest circumsphere (center and radius) // // of the given three or four points. // // // // The circumsphere of four points (a tetrahedron) is unique if they are not // // degenerate. If 'pd = NULL', the smallest circumsphere of three points is // // the diametral sphere of the triangle if they are not degenerate. // // // // Return TRUE if the input points are not degenerate and the circumcenter // // and circumradius are returned in 'cent' and 'radius' respectively if they // // are not NULLs. Otherwise, return FALSE, the four points are co-planar. // // // /////////////////////////////////////////////////////////////////////////////// bool tetgenmesh::circumsphere(REAL* pa, REAL* pb, REAL* pc, REAL* pd, REAL* cent, REAL* radius) { REAL A[4][4], rhs[4], D; int indx[4]; // Compute the coefficient matrix A (3x3). A[0][0] = pb[0] - pa[0]; A[0][1] = pb[1] - pa[1]; A[0][2] = pb[2] - pa[2]; A[1][0] = pc[0] - pa[0]; A[1][1] = pc[1] - pa[1]; A[1][2] = pc[2] - pa[2]; if (pd != NULL) { A[2][0] = pd[0] - pa[0]; A[2][1] = pd[1] - pa[1]; A[2][2] = pd[2] - pa[2]; } else { cross(A[0], A[1], A[2]); } // Compute the right hand side vector b (3x1). rhs[0] = 0.5 * dot(A[0], A[0]); rhs[1] = 0.5 * dot(A[1], A[1]); if (pd != NULL) { rhs[2] = 0.5 * dot(A[2], A[2]); } else { rhs[2] = 0.0; } // Solve the 3 by 3 equations use LU decomposition with partial pivoting // and backward and forward substitute.. if (!lu_decmp(A, 3, indx, &D, 0)) { if (radius != (REAL*)NULL) *radius = 0.0; return false; } lu_solve(A, 3, indx, rhs, 0); if (cent != (REAL*)NULL) { cent[0] = pa[0] + rhs[0]; cent[1] = pa[1] + rhs[1]; cent[2] = pa[2] + rhs[2]; } if (radius != (REAL*)NULL) { *radius = sqrt(rhs[0] * rhs[0] + rhs[1] * rhs[1] + rhs[2] * rhs[2]); } return true; } /////////////////////////////////////////////////////////////////////////////// // // // orthosphere() Calulcate the orthosphere of four weighted points. // // // // A weighted point (p, P^2) can be interpreted as a sphere centered at the // // point 'p' with a radius 'P'. The 'height' of 'p' is pheight = p[0]^2 + // // p[1]^2 + p[2]^2 - P^2. // // // /////////////////////////////////////////////////////////////////////////////// bool tetgenmesh::orthosphere(REAL* pa, REAL* pb, REAL* pc, REAL* pd, REAL aheight, REAL bheight, REAL cheight, REAL dheight, REAL* orthocent, REAL* radius) { REAL A[4][4], rhs[4], D; int indx[4]; // Set the coefficient matrix A (4 x 4). A[0][0] = 1.0; A[0][1] = pa[0]; A[0][2] = pa[1]; A[0][3] = pa[2]; A[1][0] = 1.0; A[1][1] = pb[0]; A[1][2] = pb[1]; A[1][3] = pb[2]; A[2][0] = 1.0; A[2][1] = pc[0]; A[2][2] = pc[1]; A[2][3] = pc[2]; A[3][0] = 1.0; A[3][1] = pd[0]; A[3][2] = pd[1]; A[3][3] = pd[2]; // Set the right hand side vector (4 x 1). rhs[0] = 0.5 * aheight; rhs[1] = 0.5 * bheight; rhs[2] = 0.5 * cheight; rhs[3] = 0.5 * dheight; // Solve the 4 by 4 equations use LU decomposition with partial pivoting // and backward and forward substitute.. if (!lu_decmp(A, 4, indx, &D, 0)) { if (radius != (REAL*)NULL) *radius = 0.0; return false; } lu_solve(A, 4, indx, rhs, 0); if (orthocent != (REAL*)NULL) { orthocent[0] = rhs[1]; orthocent[1] = rhs[2]; orthocent[2] = rhs[3]; } if (radius != (REAL*)NULL) { // rhs[0] = - rheight / 2; // rheight = - 2 * rhs[0]; // = r[0]^2 + r[1]^2 + r[2]^2 - radius^2 // radius^2 = r[0]^2 + r[1]^2 + r[2]^2 -rheight // = r[0]^2 + r[1]^2 + r[2]^2 + 2 * rhs[0] *radius = sqrt(rhs[1] * rhs[1] + rhs[2] * rhs[2] + rhs[3] * rhs[3] + 2.0 * rhs[0]); } return true; } void tetgenmesh::tetcircumcenter(point tetorg, point tetdest, point tetfapex, point tettapex, REAL* circumcenter, REAL* radius) { REAL xot, yot, zot, xdt, ydt, zdt, xft, yft, zft; REAL otlength, dtlength, ftlength; REAL xcrossdf, ycrossdf, zcrossdf; REAL xcrossfo, ycrossfo, zcrossfo; REAL xcrossod, ycrossod, zcrossod; REAL denominator; REAL xct, yct, zct; // tetcircumcentercount++; /* Use coordinates relative to the apex of the tetrahedron. */ xot = tetorg[0] - tettapex[0]; yot = tetorg[1] - tettapex[1]; zot = tetorg[2] - tettapex[2]; xdt = tetdest[0] - tettapex[0]; ydt = tetdest[1] - tettapex[1]; zdt = tetdest[2] - tettapex[2]; xft = tetfapex[0] - tettapex[0]; yft = tetfapex[1] - tettapex[1]; zft = tetfapex[2] - tettapex[2]; /* Squares of lengths of the origin, destination, and face apex edges. */ otlength = xot * xot + yot * yot + zot * zot; dtlength = xdt * xdt + ydt * ydt + zdt * zdt; ftlength = xft * xft + yft * yft + zft * zft; /* Cross products of the origin, destination, and face apex vectors. */ xcrossdf = ydt * zft - yft * zdt; ycrossdf = zdt * xft - zft * xdt; zcrossdf = xdt * yft - xft * ydt; xcrossfo = yft * zot - yot * zft; ycrossfo = zft * xot - zot * xft; zcrossfo = xft * yot - xot * yft; xcrossod = yot * zdt - ydt * zot; ycrossod = zot * xdt - zdt * xot; zcrossod = xot * ydt - xdt * yot; /* Calculate the denominator of all the formulae. */ // if (noexact) { // denominator = 0.5 / (xot * xcrossdf + yot * ycrossdf + zot * zcrossdf); //} else { /* Use the orient3d() routine to ensure a positive (and */ /* reasonably accurate) result, avoiding any possibility */ /* of division by zero. */ denominator = 0.5 / orient3d(tetorg, tetdest, tetfapex, tettapex); /* Don't count the above as an orientation test. */ // orientcount--; //} /* Calculate offset (from apex) of circumcenter. */ xct = (otlength * xcrossdf + dtlength * xcrossfo + ftlength * xcrossod) * denominator; yct = (otlength * ycrossdf + dtlength * ycrossfo + ftlength * ycrossod) * denominator; zct = (otlength * zcrossdf + dtlength * zcrossfo + ftlength * zcrossod) * denominator; circumcenter[0] = xct + tettapex[0]; circumcenter[1] = yct + tettapex[1]; circumcenter[2] = zct + tettapex[2]; if (radius != NULL) { *radius = sqrt(xct * xct + yct * yct + zct * zct); } } /////////////////////////////////////////////////////////////////////////////// // // // planelineint() Calculate the intersection of a line and a plane. // // // // The equation of a plane (points P are on the plane with normal N and P3 // // on the plane) can be written as: N dot (P - P3) = 0. The equation of the // // line (points P on the line passing through P1 and P2) can be written as: // // P = P1 + u (P2 - P1). The intersection of these two occurs when: // // N dot (P1 + u (P2 - P1)) = N dot P3. // // Solving for u gives: // // N dot (P3 - P1) // // u = ------------------. // // N dot (P2 - P1) // // If the denominator is 0 then N (the normal to the plane) is perpendicular // // to the line. Thus the line is either parallel to the plane and there are // // no solutions or the line is on the plane in which case there are an infi- // // nite number of solutions. // // // // The plane is given by three points pa, pb, and pc, e1 and e2 defines the // // line. If u is non-zero, The intersection point (if exists) returns in ip. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::planelineint(REAL* pa, REAL* pb, REAL* pc, REAL* e1, REAL* e2, REAL* ip, REAL* u) { REAL n[3], det, det1; // Calculate N. facenormal(pa, pb, pc, n, 1, NULL); // Calculate N dot (e2 - e1). det = n[0] * (e2[0] - e1[0]) + n[1] * (e2[1] - e1[1]) + n[2] * (e2[2] - e1[2]); if (det != 0.0) { // Calculate N dot (pa - e1) det1 = n[0] * (pa[0] - e1[0]) + n[1] * (pa[1] - e1[1]) + n[2] * (pa[2] - e1[2]); *u = det1 / det; ip[0] = e1[0] + *u * (e2[0] - e1[0]); ip[1] = e1[1] + *u * (e2[1] - e1[1]); ip[2] = e1[2] + *u * (e2[2] - e1[2]); } else { *u = 0.0; } } /////////////////////////////////////////////////////////////////////////////// // // // linelineint() Calculate the intersection(s) of two line segments. // // // // Calculate the line segment [P, Q] that is the shortest route between two // // lines from A to B and C to D. Calculate also the values of tp and tq // // where: P = A + tp (B - A), and Q = C + tq (D - C). // // // // Return 1 if the line segment exists. Otherwise, return 0. // // // /////////////////////////////////////////////////////////////////////////////// int tetgenmesh::linelineint(REAL* A, REAL* B, REAL* C, REAL* D, REAL* P, REAL* Q, REAL* tp, REAL* tq) { REAL vab[3], vcd[3], vca[3]; REAL vab_vab, vcd_vcd, vab_vcd; REAL vca_vab, vca_vcd; REAL det, eps; int i; for (i = 0; i < 3; i++) { vab[i] = B[i] - A[i]; vcd[i] = D[i] - C[i]; vca[i] = A[i] - C[i]; } vab_vab = dot(vab, vab); vcd_vcd = dot(vcd, vcd); vab_vcd = dot(vab, vcd); det = vab_vab * vcd_vcd - vab_vcd * vab_vcd; // Round the result. eps = det / (fabs(vab_vab * vcd_vcd) + fabs(vab_vcd * vab_vcd)); if (eps < b->epsilon) { return 0; } vca_vab = dot(vca, vab); vca_vcd = dot(vca, vcd); *tp = (vcd_vcd * (-vca_vab) + vab_vcd * vca_vcd) / det; *tq = (vab_vcd * (-vca_vab) + vab_vab * vca_vcd) / det; for (i = 0; i < 3; i++) P[i] = A[i] + (*tp) * vab[i]; for (i = 0; i < 3; i++) Q[i] = C[i] + (*tq) * vcd[i]; return 1; } /////////////////////////////////////////////////////////////////////////////// // // // tetprismvol() Calculate the volume of a tetrahedral prism in 4D. // // // // A tetrahedral prism is a convex uniform polychoron (four dimensional poly-// // tope). It has 6 polyhedral cells: 2 tetrahedra connected by 4 triangular // // prisms. It has 14 faces: 8 triangular and 6 square. It has 16 edges and 8 // // vertices. (Wikipedia). // // // // Let 'p0', ..., 'p3' be four affinely independent points in R^3. They form // // the lower tetrahedral facet of the prism. The top tetrahedral facet is // // formed by four vertices, 'p4', ..., 'p7' in R^4, which is obtained by // // lifting each vertex of the lower facet into R^4 by a weight (height). A // // canonical choice of the weights is the square of Euclidean norm of of the // // points (vectors). // // // // // // The return value is (4!) 24 times of the volume of the tetrahedral prism. // // // /////////////////////////////////////////////////////////////////////////////// REAL tetgenmesh::tetprismvol(REAL* p0, REAL* p1, REAL* p2, REAL* p3) { REAL *p4, *p5, *p6, *p7; REAL w4, w5, w6, w7; REAL vol[4]; p4 = p0; p5 = p1; p6 = p2; p7 = p3; // TO DO: these weights can be pre-calculated! w4 = dot(p0, p0); w5 = dot(p1, p1); w6 = dot(p2, p2); w7 = dot(p3, p3); // Calculate the volume of the tet-prism. vol[0] = orient4d(p5, p6, p4, p3, p7, w5, w6, w4, 0, w7); vol[1] = orient4d(p3, p6, p2, p0, p1, 0, w6, 0, 0, 0); vol[2] = orient4d(p4, p6, p3, p0, p1, w4, w6, 0, 0, 0); vol[3] = orient4d(p6, p5, p4, p3, p1, w6, w5, w4, 0, 0); return fabs(vol[0]) + fabs(vol[1]) + fabs(vol[2]) + fabs(vol[3]); } /////////////////////////////////////////////////////////////////////////////// // // // calculateabovepoint() Calculate a point above a facet in 'dummypoint'. // // // /////////////////////////////////////////////////////////////////////////////// bool tetgenmesh::calculateabovepoint(arraypool* facpoints, point* ppa, point* ppb, point* ppc) { point *ppt, pa, pb, pc; REAL v1[3], v2[3], n[3]; REAL lab, len, A, area; REAL x, y, z; int i; ppt = (point*)fastlookup(facpoints, 0); pa = *ppt; // a is the first point. pb = pc = NULL; // Avoid compiler warnings. // Get a point b s.t. the length of [a, b] is maximal. lab = 0; for (i = 1; i < facpoints->objects; i++) { ppt = (point*)fastlookup(facpoints, i); x = (*ppt)[0] - pa[0]; y = (*ppt)[1] - pa[1]; z = (*ppt)[2] - pa[2]; len = x * x + y * y + z * z; if (len > lab) { lab = len; pb = *ppt; } } lab = sqrt(lab); if (lab == 0) { if (!b->quiet) { printf("Warning: All points of a facet are coincident with %d.\n", pointmark(pa)); } return false; } // Get a point c s.t. the area of [a, b, c] is maximal. v1[0] = pb[0] - pa[0]; v1[1] = pb[1] - pa[1]; v1[2] = pb[2] - pa[2]; A = 0; for (i = 1; i < facpoints->objects; i++) { ppt = (point*)fastlookup(facpoints, i); v2[0] = (*ppt)[0] - pa[0]; v2[1] = (*ppt)[1] - pa[1]; v2[2] = (*ppt)[2] - pa[2]; cross(v1, v2, n); area = dot(n, n); if (area > A) { A = area; pc = *ppt; } } if (A == 0) { // All points are collinear. No above point. if (!b->quiet) { printf("Warning: All points of a facet are collinaer with [%d, %d].\n", pointmark(pa), pointmark(pb)); } return false; } // Calculate an above point of this facet. facenormal(pa, pb, pc, n, 1, NULL); len = sqrt(dot(n, n)); n[0] /= len; n[1] /= len; n[2] /= len; lab /= 2.0; // Half the maximal length. dummypoint[0] = pa[0] + lab * n[0]; dummypoint[1] = pa[1] + lab * n[1]; dummypoint[2] = pa[2] + lab * n[2]; if (ppa != NULL) { // Return the three points. *ppa = pa; *ppb = pb; *ppc = pc; } return true; } /////////////////////////////////////////////////////////////////////////////// // // // Calculate an above point. It lies above the plane containing the subface // // [a,b,c], and save it in dummypoint. Moreover, the vector pa->dummypoint // // is the normal of the plane. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::calculateabovepoint4(point pa, point pb, point pc, point pd) { REAL n1[3], n2[3], *norm; REAL len, len1, len2; // Select a base. facenormal(pa, pb, pc, n1, 1, NULL); len1 = sqrt(dot(n1, n1)); facenormal(pa, pb, pd, n2, 1, NULL); len2 = sqrt(dot(n2, n2)); if (len1 > len2) { norm = n1; len = len1; } else { norm = n2; len = len2; } norm[0] /= len; norm[1] /= len; norm[2] /= len; len = distance(pa, pb); dummypoint[0] = pa[0] + len * norm[0]; dummypoint[1] = pa[1] + len * norm[1]; dummypoint[2] = pa[2] + len * norm[2]; } /////////////////////////////////////////////////////////////////////////////// // // // report_overlapping_facets() Report two overlapping facets. // // // // Two subfaces, f1 [a, b, c] and f2 [a, b, d], share the same edge [a, b]. // // 'dihedang' is the dihedral angle between these two facets. It must less // // than the variable 'b->facet_overlap_angle_tol'. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::report_overlapping_facets(face* f1, face* f2, REAL dihedang) { point pa, pb, pc, pd; pa = sorg(*f1); pb = sdest(*f1); pc = sapex(*f1); pd = sapex(*f2); if (pc != pd) { printf("Found two %s self-intersecting facets.\n", dihedang > 0 ? "nearly" : "exactly"); printf(" 1st: [%d, %d, %d] #%d\n", pointmark(pa), pointmark(pb), pointmark(pc), shellmark(*f1)); printf(" 2nd: [%d, %d, %d] #%d\n", pointmark(pa), pointmark(pb), pointmark(pd), shellmark(*f2)); if (dihedang > 0) { printf("The dihedral angle between them is %g degree.\n", dihedang / PI * 180.0); printf("Hint: You may use -p/# to decrease the dihedral angle"); printf(" tolerance %g (degree).\n", b->facet_overlap_ang_tol); } } else { if (shellmark(*f1) != shellmark(*f2)) { // Two identical faces from two different facet. printf("Found two overlapping facets.\n"); } else { printf("Found two duplicated facets.\n"); } printf(" 1st: [%d, %d, %d] #%d\n", pointmark(pa), pointmark(pb), pointmark(pc), shellmark(*f1)); printf(" 2nd: [%d, %d, %d] #%d\n", pointmark(pa), pointmark(pb), pointmark(pd), shellmark(*f2)); } // Return the information sevent.e_type = 6; sevent.f_marker1 = shellmark(*f1); sevent.f_vertices1[0] = pointmark(pa); sevent.f_vertices1[1] = pointmark(pb); sevent.f_vertices1[2] = pointmark(pc); sevent.f_marker2 = shellmark(*f2); sevent.f_vertices2[0] = pointmark(pa); sevent.f_vertices2[1] = pointmark(pb); sevent.f_vertices2[2] = pointmark(pd); terminatetetgen(this, 3); } /////////////////////////////////////////////////////////////////////////////// // // // report_selfint_edge() Report a self-intersection at an edge. // // // // The edge 'e1'->'e2' and the tetrahedron 'itet' intersect. 'dir' indicates // // that the edge intersects the tet at its origin vertex (ACROSSVERTEX), or // // its current face (ACROSSFACE), or its current edge (ACROSSEDGE). // // If 'iedge' is not NULL, it is either a segment or a subface that contains // // the edge 'e1'->'e2'. It is used to report the geometry entity. // // // // Since it is a self-intersection, the vertex, edge or face of 'itet' that // // is intersecting with this edge must be an input vertex, a segment, or a // // subface, respectively. // // // /////////////////////////////////////////////////////////////////////////////// int tetgenmesh::report_selfint_edge(point e1, point e2, face* iedge, triface* itet, enum interresult dir) { point forg = NULL, fdest = NULL, fapex = NULL; int etype = 0, geomtag = 0, facemark = 0; if (iedge != NULL) { if (iedge->sh[5] != NULL) { etype = 2; // A subface forg = e1; fdest = e2; fapex = sapex(*iedge); facemark = shellmark(*iedge); } else { etype = 1; // A segment forg = farsorg(*iedge); fdest = farsdest(*iedge); // Get a facet containing this segment. face parentsh; spivot(*iedge, parentsh); if (parentsh.sh != NULL) { facemark = shellmark(parentsh); } } geomtag = shellmark(*iedge); } if (dir == SHAREEDGE) { // Two edges (segments) are coincide. face colseg; tsspivot1(*itet, colseg); if (etype == 1) { if (colseg.sh != iedge->sh) { face parentsh; spivot(colseg, parentsh); printf("PLC Error: Two segments are overlapping.\n"); printf(" Segment 1: [%d, %d] #%d (%d)\n", pointmark(sorg(colseg)), pointmark(sdest(colseg)), shellmark(colseg), parentsh.sh ? shellmark(parentsh) : 0); printf(" Segment 2: [%d, %d] #%d (%d)\n", pointmark(forg), pointmark(fdest), geomtag, facemark); sevent.e_type = 4; sevent.f_marker1 = (parentsh.sh ? shellmark(parentsh) : 0); sevent.s_marker1 = shellmark(colseg); sevent.f_vertices1[0] = pointmark(sorg(colseg)); sevent.f_vertices1[1] = pointmark(sdest(colseg)); sevent.f_vertices1[2] = 0; sevent.f_marker2 = facemark; sevent.s_marker2 = geomtag; sevent.f_vertices2[0] = pointmark(forg); sevent.f_vertices2[1] = pointmark(fdest); sevent.f_vertices2[2] = 0; } else { // Two identical segments. Why report it? terminatetetgen(this, 2); } } else if (etype == 2) { printf("PLC Error: A segment lies in a facet.\n"); printf(" Segment: [%d, %d] #%d\n", pointmark(sorg(colseg)), pointmark(sdest(colseg)), shellmark(colseg)); printf(" Facet: [%d,%d,%d] #%d\n", pointmark(forg), pointmark(fdest), pointmark(fapex), geomtag); sevent.e_type = 5; sevent.f_marker1 = 0; sevent.s_marker1 = shellmark(colseg); sevent.f_vertices1[0] = pointmark(sorg(colseg)); sevent.f_vertices1[1] = pointmark(sdest(colseg)); sevent.f_vertices1[2] = 0; sevent.f_marker2 = geomtag; sevent.s_marker2 = 0; sevent.f_vertices2[0] = pointmark(forg); sevent.f_vertices2[1] = pointmark(fdest); sevent.f_vertices2[2] = pointmark(fapex); } } else if (dir == SHAREFACE) { // Two triangles (subfaces) are coincide. face colface; tspivot(*itet, colface); if (etype == 2) { if (colface.sh != iedge->sh) { printf("PLC Error: Two facets are overlapping.\n"); printf(" Facet 1: [%d,%d,%d] #%d\n", pointmark(forg), pointmark(fdest), pointmark(fapex), geomtag); printf(" Facet 2: [%d,%d,%d] #%d\n", pointmark(sorg(colface)), pointmark(sdest(colface)), pointmark(sapex(colface)), shellmark(colface)); sevent.e_type = 6; sevent.f_marker1 = geomtag; sevent.s_marker1 = 0; sevent.f_vertices1[0] = pointmark(forg); sevent.f_vertices1[1] = pointmark(fdest); sevent.f_vertices1[2] = pointmark(fapex); sevent.f_marker2 = shellmark(colface); sevent.s_marker2 = 0; sevent.f_vertices2[0] = pointmark(sorg(colface)); sevent.f_vertices2[1] = pointmark(sdest(colface)); sevent.f_vertices2[2] = pointmark(sapex(colface)); } else { // Two identical subfaces. Why report it? terminatetetgen(this, 2); } } else { terminatetetgen(this, 2); } } else if (dir == ACROSSVERT) { point pp = dest(*itet); if ((pointtype(pp) == RIDGEVERTEX) || (pointtype(pp) == FACETVERTEX) || (pointtype(pp) == VOLVERTEX)) { if (etype == 1) { printf("PLC Error: A vertex lies in a segment.\n"); printf(" Vertex: [%d] (%g,%g,%g).\n", pointmark(pp), pp[0], pp[1], pp[2]); printf(" Segment: [%d, %d] #%d (%d)\n", pointmark(forg), pointmark(fdest), geomtag, facemark); sevent.e_type = 7; sevent.f_marker1 = 0; sevent.s_marker1 = 0; sevent.f_vertices1[0] = pointmark(pp); sevent.f_vertices1[1] = 0; sevent.f_vertices1[2] = 0; sevent.f_marker2 = facemark; sevent.s_marker2 = geomtag; sevent.f_vertices2[0] = pointmark(forg); sevent.f_vertices2[1] = pointmark(fdest); sevent.f_vertices2[2] = 0; sevent.int_point[0] = pp[0]; sevent.int_point[1] = pp[1]; sevent.int_point[2] = pp[2]; } else if (etype == 2) { printf("PLC Error: A vertex lies in a facet.\n"); printf(" Vertex: [%d] (%g,%g,%g).\n", pointmark(pp), pp[0], pp[1], pp[2]); printf(" Facet: [%d,%d,%d] #%d\n", pointmark(forg), pointmark(fdest), pointmark(fapex), geomtag); sevent.e_type = 8; sevent.f_marker1 = 0; sevent.s_marker1 = 0; sevent.f_vertices1[0] = pointmark(pp); sevent.f_vertices1[1] = 0; sevent.f_vertices1[2] = 0; sevent.f_marker2 = geomtag; sevent.s_marker2 = 0; sevent.f_vertices2[0] = pointmark(forg); sevent.f_vertices2[1] = pointmark(fdest); sevent.f_vertices2[2] = pointmark(fapex); sevent.int_point[0] = pp[0]; sevent.int_point[1] = pp[1]; sevent.int_point[2] = pp[2]; } } else if (pointtype(pp) == FREESEGVERTEX) { face parentseg, parentsh; sdecode(point2sh(pp), parentseg); spivot(parentseg, parentsh); if (parentseg.sh != NULL) { point p1 = farsorg(parentseg); point p2 = farsdest(parentseg); if (etype == 1) { printf("PLC Error: Two segments intersect at point (%g,%g,%g).\n", pp[0], pp[1], pp[2]); printf(" Segment 1: [%d, %d], #%d (%d)\n", pointmark(forg), pointmark(fdest), geomtag, facemark); printf(" Segment 2: [%d, %d], #%d (%d)\n", pointmark(p1), pointmark(p2), shellmark(parentseg), parentsh.sh ? shellmark(parentsh) : 0); sevent.e_type = 1; sevent.f_marker1 = facemark; sevent.s_marker1 = geomtag; sevent.f_vertices1[0] = pointmark(forg); sevent.f_vertices1[1] = pointmark(fdest); sevent.f_vertices1[2] = 0; sevent.f_marker2 = (parentsh.sh ? shellmark(parentsh) : 0); sevent.s_marker2 = shellmark(parentseg); sevent.f_vertices2[0] = pointmark(p1); sevent.f_vertices2[1] = pointmark(p2); sevent.f_vertices2[2] = 0; sevent.int_point[0] = pp[0]; sevent.int_point[1] = pp[1]; sevent.int_point[2] = pp[2]; } else if (etype == 2) { printf("PLC Error: A segment and a facet intersect at point"); printf(" (%g,%g,%g).\n", pp[0], pp[1], pp[2]); printf(" Segment: [%d, %d], #%d (%d)\n", pointmark(p1), pointmark(p2), shellmark(parentseg), parentsh.sh ? shellmark(parentsh) : 0); printf(" Facet: [%d,%d,%d] #%d\n", pointmark(forg), pointmark(fdest), pointmark(fapex), geomtag); sevent.e_type = 2; sevent.f_marker1 = (parentsh.sh ? shellmark(parentsh) : 0); sevent.s_marker1 = shellmark(parentseg); sevent.f_vertices1[0] = pointmark(p1); sevent.f_vertices1[1] = pointmark(p2); sevent.f_vertices1[2] = 0; sevent.f_marker2 = geomtag; sevent.s_marker2 = 0; sevent.f_vertices2[0] = pointmark(forg); sevent.f_vertices2[1] = pointmark(fdest); sevent.f_vertices2[2] = pointmark(fapex); sevent.int_point[0] = pp[0]; sevent.int_point[1] = pp[1]; sevent.int_point[2] = pp[2]; } } else { terminatetetgen(this, 2); // Report a bug. } } else if (pointtype(pp) == FREEFACETVERTEX) { face parentsh; sdecode(point2sh(pp), parentsh); if (parentsh.sh != NULL) { point p1 = sorg(parentsh); point p2 = sdest(parentsh); point p3 = sapex(parentsh); if (etype == 1) { printf("PLC Error: A segment and a facet intersect at point"); printf(" (%g,%g,%g).\n", pp[0], pp[1], pp[2]); printf(" Segment : [%d, %d], #%d (%d)\n", pointmark(forg), pointmark(fdest), geomtag, facemark); printf(" Facet : [%d, %d, %d] #%d.\n", pointmark(p1), pointmark(p2), pointmark(p3), shellmark(parentsh)); sevent.e_type = 2; sevent.f_marker1 = facemark; sevent.s_marker1 = geomtag; sevent.f_vertices1[0] = pointmark(forg); sevent.f_vertices1[1] = pointmark(fdest); sevent.f_vertices1[2] = 0; sevent.f_marker2 = shellmark(parentsh); sevent.s_marker2 = 0; sevent.f_vertices2[0] = pointmark(p1); sevent.f_vertices2[1] = pointmark(p2); sevent.f_vertices2[2] = pointmark(p3); sevent.int_point[0] = pp[0]; sevent.int_point[1] = pp[1]; sevent.int_point[2] = pp[2]; } else if (etype == 2) { printf("PLC Error: Two facets intersect at point (%g,%g,%g).\n", pp[0], pp[1], pp[2]); printf(" Facet 1: [%d, %d, %d] #%d.\n", pointmark(forg), pointmark(fdest), pointmark(fapex), geomtag); printf(" Facet 2: [%d, %d, %d] #%d.\n", pointmark(p1), pointmark(p2), pointmark(p3), shellmark(parentsh)); sevent.e_type = 3; sevent.f_marker1 = geomtag; sevent.s_marker1 = 0; sevent.f_vertices1[0] = pointmark(forg); sevent.f_vertices1[1] = pointmark(fdest); sevent.f_vertices1[2] = pointmark(fapex); sevent.f_marker2 = shellmark(parentsh); sevent.s_marker2 = 0; sevent.f_vertices2[0] = pointmark(p1); sevent.f_vertices2[1] = pointmark(p2); sevent.f_vertices2[2] = pointmark(p3); sevent.int_point[0] = pp[0]; sevent.int_point[1] = pp[1]; sevent.int_point[2] = pp[2]; } } else { terminatetetgen(this, 2); // Report a bug. } } else if (pointtype(pp) == FREEVOLVERTEX) { // This is not a PLC error. // We should shift the vertex. // not down yet. terminatetetgen(this, 2); // Report a bug. } else { terminatetetgen(this, 2); // Report a bug. } terminatetetgen(this, 3); } else if (dir == ACROSSEDGE) { if (issubseg(*itet)) { face checkseg; tsspivot1(*itet, checkseg); face parentsh; spivot(checkseg, parentsh); // Calulcate the intersecting point. point p1 = sorg(checkseg); point p2 = sdest(checkseg); REAL P[3], Q[3], tp = 0, tq = 0; linelineint(e1, e2, p1, p2, P, Q, &tp, &tq); if (etype == 1) { printf("PLC Error: Two segments intersect at point (%g,%g,%g).\n", P[0], P[1], P[2]); printf(" Segment 1: [%d, %d] #%d (%d)\n", pointmark(forg), pointmark(fdest), geomtag, facemark); printf(" Segment 2: [%d, %d] #%d (%d)\n", pointmark(p1), pointmark(p2), shellmark(checkseg), parentsh.sh ? shellmark(parentsh) : 0); sevent.e_type = 1; sevent.f_marker1 = facemark; sevent.s_marker1 = geomtag; sevent.f_vertices1[0] = pointmark(forg); sevent.f_vertices1[1] = pointmark(fdest); sevent.f_vertices1[2] = 0; sevent.f_marker2 = (parentsh.sh ? shellmark(parentsh) : 0); sevent.s_marker2 = shellmark(checkseg); sevent.f_vertices2[0] = pointmark(p1); sevent.f_vertices2[1] = pointmark(p2); sevent.f_vertices2[2] = 0; sevent.int_point[0] = P[0]; sevent.int_point[1] = P[1]; sevent.int_point[2] = P[2]; } else if (etype == 2) { printf("PLC Error: A segment and a facet intersect at point"); printf(" (%g,%g,%g).\n", P[0], P[1], P[2]); printf(" Segment: [%d, %d] #%d (%d)\n", pointmark(p1), pointmark(p2), shellmark(checkseg), parentsh.sh ? shellmark(parentsh) : 0); printf(" Facet: [%d, %d, %d] #%d.\n", pointmark(forg), pointmark(fdest), pointmark(fapex), geomtag); sevent.e_type = 2; sevent.f_marker1 = (parentsh.sh ? shellmark(parentsh) : 0); sevent.s_marker1 = shellmark(checkseg); sevent.f_vertices1[0] = pointmark(p1); sevent.f_vertices1[1] = pointmark(p2); sevent.f_vertices1[2] = 0; sevent.f_marker2 = geomtag; sevent.s_marker2 = 0; sevent.f_vertices2[0] = pointmark(forg); sevent.f_vertices2[1] = pointmark(fdest); sevent.f_vertices2[2] = pointmark(fapex); sevent.int_point[0] = P[0]; sevent.int_point[1] = P[1]; sevent.int_point[2] = P[2]; } terminatetetgen(this, 3); } } else if (dir == ACROSSFACE) { if (issubface(*itet)) { face checksh; tspivot(*itet, checksh); point p1 = sorg(checksh); point p2 = sdest(checksh); point p3 = sapex(checksh); REAL ip[3], u = 0; planelineint(p1, p2, p3, e1, e2, ip, &u); if (etype == 1) { printf("PLC Error: A segment and a facet intersect at point"); printf(" (%g,%g,%g).\n", ip[0], ip[1], ip[2]); printf(" Segment: [%d, %d] #%d (%d)\n", pointmark(forg), pointmark(fdest), geomtag, facemark); printf(" Facet: [%d, %d, %d] #%d.\n", pointmark(p1), pointmark(p2), pointmark(p3), shellmark(checksh)); sevent.e_type = 2; sevent.f_marker1 = facemark; sevent.s_marker1 = geomtag; sevent.f_vertices1[0] = pointmark(forg); sevent.f_vertices1[1] = pointmark(fdest); sevent.f_vertices1[2] = 0; sevent.f_marker2 = shellmark(checksh); sevent.s_marker2 = 0; sevent.f_vertices2[0] = pointmark(p1); sevent.f_vertices2[1] = pointmark(p2); sevent.f_vertices2[2] = pointmark(p3); sevent.int_point[0] = ip[0]; sevent.int_point[1] = ip[1]; sevent.int_point[2] = ip[2]; } else if (etype == 2) { printf("PLC Error: Two facets intersect at point (%g,%g,%g).\n", ip[0], ip[1], ip[2]); printf(" Facet 1: [%d, %d, %d] #%d.\n", pointmark(forg), pointmark(fdest), pointmark(fapex), geomtag); printf(" Facet 2: [%d, %d, %d] #%d.\n", pointmark(p1), pointmark(p2), pointmark(p3), shellmark(checksh)); sevent.e_type = 3; sevent.f_marker1 = geomtag; sevent.s_marker1 = 0; sevent.f_vertices1[0] = pointmark(forg); sevent.f_vertices1[1] = pointmark(fdest); sevent.f_vertices1[2] = pointmark(fapex); sevent.f_marker2 = shellmark(checksh); sevent.s_marker2 = 0; sevent.f_vertices2[0] = pointmark(p1); sevent.f_vertices2[1] = pointmark(p2); sevent.f_vertices2[2] = pointmark(p3); sevent.int_point[0] = ip[0]; sevent.int_point[1] = ip[1]; sevent.int_point[2] = ip[2]; } terminatetetgen(this, 3); } } else { // An unknown 'dir'. terminatetetgen(this, 2); } return 0; } /////////////////////////////////////////////////////////////////////////////// // // // report_selfint_face() Report a self-intersection at a facet. // // // // The triangle with vertices 'p1', 'p2', and 'p3' intersects with the edge // // of the tetrahedra 'iedge'. The intersection type is reported by 'intflag',// // 'types', and 'poss'. // // // // This routine ASSUMES (1) the triangle (p1,p2,p3) must belong to a facet, // // 'sface' is a subface of the same facet; and (2) 'iedge' must be either a // // segment or an edge of another facet. // // // /////////////////////////////////////////////////////////////////////////////// int tetgenmesh::report_selfint_face(point p1, point p2, point p3, face* sface, triface* iedge, int intflag, int* types, int* poss) { face iface; point e1 = NULL, e2 = NULL, e3 = NULL; int etype = 0, geomtag = 0, facemark = 0; geomtag = shellmark(*sface); if (issubface(*iedge)) { tspivot(*iedge, iface); e1 = sorg(iface); e2 = sdest(iface); e3 = sapex(iface); etype = 2; facemark = geomtag; } else if (issubseg(*iedge)) { tsspivot1(*iedge, iface); e1 = farsorg(iface); e2 = farsdest(iface); etype = 1; face parentsh; spivot(iface, parentsh); facemark = shellmark(parentsh); } else { terminatetetgen(this, 2); } if (intflag == 2) { // The triangle and the edge intersect only at one point. REAL ip[3], u = 0; planelineint(p1, p2, p3, e1, e2, ip, &u); if ((types[0] == (int)ACROSSFACE) || (types[0] == (int)ACROSSEDGE)) { // The triangle and the edge intersect in their interiors. if (etype == 1) { printf("PLC Error: A segment and a facet intersect at point"); printf(" (%g,%g,%g).\n", ip[0], ip[1], ip[2]); printf(" Segment: [%d,%d] #%d (%d)\n", pointmark(e1), pointmark(e2), shellmark(iface), facemark); printf(" Facet: [%d,%d,%d] #%d\n", pointmark(p1), pointmark(p2), pointmark(p3), geomtag); sevent.e_type = 2; sevent.f_marker1 = facemark; sevent.s_marker1 = shellmark(iface); sevent.f_vertices1[0] = pointmark(e1); sevent.f_vertices1[1] = pointmark(e2); sevent.f_vertices1[2] = 0; sevent.f_marker2 = geomtag; sevent.s_marker2 = 0; sevent.f_vertices2[0] = pointmark(p1); sevent.f_vertices2[1] = pointmark(p2); sevent.f_vertices2[2] = pointmark(p3); sevent.int_point[0] = ip[0]; sevent.int_point[1] = ip[1]; sevent.int_point[2] = ip[2]; } else { printf("PLC Error: Two facets intersect at point"); printf(" (%g,%g,%g).\n", ip[0], ip[1], ip[2]); printf(" Facet 1: [%d,%d,%d] #%d\n", pointmark(e1), pointmark(e2), pointmark(sorg(iface)), shellmark(iface)); printf(" Facet 2: [%d,%d,%d] #%d\n", pointmark(p1), pointmark(p2), pointmark(p3), geomtag); sevent.e_type = 3; sevent.f_marker1 = shellmark(iface); sevent.s_marker1 = 0; sevent.f_vertices1[0] = pointmark(e1); sevent.f_vertices1[1] = pointmark(e2); sevent.f_vertices1[2] = pointmark(sorg(iface)); sevent.f_marker2 = geomtag; sevent.s_marker2 = 0; sevent.f_vertices2[0] = pointmark(p1); sevent.f_vertices2[1] = pointmark(p2); sevent.f_vertices2[2] = pointmark(p3); sevent.int_point[0] = ip[0]; sevent.int_point[1] = ip[1]; sevent.int_point[2] = ip[2]; } } else if (types[0] == (int)ACROSSVERT) { // A vertex of the triangle and the edge intersect. point crosspt = NULL; if (poss[0] == 0) { crosspt = p1; } else if (poss[0] == 1) { crosspt = p2; } else if (poss[0] == 2) { crosspt = p3; } else { terminatetetgen(this, 2); } if (!issteinerpoint(crosspt)) { if (etype == 1) { printf("PLC Error: A vertex and a segment intersect at (%g,%g,%g)\n", crosspt[0], crosspt[1], crosspt[2]); printf(" Vertex: #%d\n", pointmark(crosspt)); printf(" Segment: [%d,%d] #%d (%d)\n", pointmark(e1), pointmark(e2), shellmark(iface), facemark); sevent.e_type = 7; sevent.f_marker1 = 0; sevent.s_marker1 = 0; sevent.f_vertices1[0] = pointmark(crosspt); sevent.f_vertices1[1] = 0; sevent.f_vertices1[2] = 0; sevent.f_marker2 = facemark; sevent.s_marker2 = shellmark(iface); sevent.f_vertices2[0] = pointmark(e1); sevent.f_vertices2[1] = pointmark(e2); sevent.f_vertices2[2] = 0; sevent.int_point[0] = crosspt[0]; sevent.int_point[1] = crosspt[1]; sevent.int_point[2] = crosspt[2]; } else { printf("PLC Error: A vertex and a facet intersect at (%g,%g,%g)\n", crosspt[0], crosspt[1], crosspt[2]); printf(" Vertex: #%d\n", pointmark(crosspt)); printf(" Facet: [%d,%d,%d] #%d\n", pointmark(p1), pointmark(p2), pointmark(p3), geomtag); sevent.e_type = 8; sevent.f_marker1 = 0; sevent.s_marker1 = 0; sevent.f_vertices1[0] = pointmark(crosspt); sevent.f_vertices1[1] = 0; sevent.f_vertices1[2] = 0; sevent.f_marker2 = geomtag; sevent.s_marker2 = 0; sevent.f_vertices2[0] = pointmark(p1); sevent.f_vertices2[1] = pointmark(p2); sevent.f_vertices2[2] = pointmark(p3); sevent.int_point[0] = crosspt[0]; sevent.int_point[1] = crosspt[1]; sevent.int_point[2] = crosspt[2]; } } else { // It is a Steiner point. To be processed. terminatetetgen(this, 2); } } else if ((types[0] == (int)TOUCHFACE) || (types[0] == (int)TOUCHEDGE)) { // The triangle and a vertex of the edge intersect. point touchpt = NULL; if (poss[1] == 0) { touchpt = org(*iedge); } else if (poss[1] == 1) { touchpt = dest(*iedge); } else { terminatetetgen(this, 2); } if (!issteinerpoint(touchpt)) { printf("PLC Error: A vertex and a facet intersect at (%g,%g,%g)\n", touchpt[0], touchpt[1], touchpt[2]); printf(" Vertex: #%d\n", pointmark(touchpt)); printf(" Facet: [%d,%d,%d] #%d\n", pointmark(p1), pointmark(p2), pointmark(p3), geomtag); sevent.e_type = 8; sevent.f_marker1 = 0; sevent.s_marker1 = 0; sevent.f_vertices1[0] = pointmark(touchpt); sevent.f_vertices1[1] = 0; sevent.f_vertices1[2] = 0; sevent.f_marker2 = geomtag; sevent.s_marker2 = 0; sevent.f_vertices2[0] = pointmark(p1); sevent.f_vertices2[1] = pointmark(p2); sevent.f_vertices2[2] = pointmark(p3); sevent.int_point[0] = touchpt[0]; sevent.int_point[1] = touchpt[1]; sevent.int_point[2] = touchpt[2]; } else { // It is a Steiner point. To be processed. terminatetetgen(this, 2); } } else if (types[0] == (int)SHAREVERT) { terminatetetgen(this, 2); } else { terminatetetgen(this, 2); } } else if (intflag == 4) { if (types[0] == (int)SHAREFACE) { printf("PLC Error: Two facets are overlapping.\n"); printf(" Facet 1: [%d,%d,%d] #%d\n", pointmark(e1), pointmark(e2), pointmark(e3), facemark); printf(" Facet 2: [%d,%d,%d] #%d\n", pointmark(p1), pointmark(p2), pointmark(p3), geomtag); sevent.e_type = 6; sevent.f_marker1 = facemark; sevent.s_marker1 = 0; sevent.f_vertices1[0] = pointmark(e1); sevent.f_vertices1[1] = pointmark(e2); sevent.f_vertices1[2] = pointmark(e3); sevent.f_marker2 = geomtag; sevent.s_marker2 = 0; sevent.f_vertices2[0] = pointmark(p1); sevent.f_vertices2[1] = pointmark(p2); sevent.f_vertices2[2] = pointmark(p3); } else { terminatetetgen(this, 2); } } else { terminatetetgen(this, 2); } terminatetetgen(this, 3); return 0; } //// //// //// //// //// geom_cxx ///////////////////////////////////////////////////////////////// //// flip_cxx ///////////////////////////////////////////////////////////////// //// //// //// //// /////////////////////////////////////////////////////////////////////////////// // // // flip23() Perform a 2-to-3 flip (face-to-edge flip). // // // // 'fliptets' is an array of three tets (handles), where the [0] and [1] are // // [a,b,c,d] and [b,a,c,e]. The three new tets: [e,d,a,b], [e,d,b,c], and // // [e,d,c,a] are returned in [0], [1], and [2] of 'fliptets'. As a result, // // The face [a,b,c] is removed, and the edge [d,e] is created. // // // // If 'hullflag' > 0, hull tets may be involved in this flip, i.e., one of // // the five vertices may be 'dummypoint'. There are two canonical cases: // // (1) d is 'dummypoint', then all three new tets are hull tets. If e is // // 'dummypoint', we reconfigure e to d, i.e., turn it up-side down. // // (2) c is 'dummypoint', then two new tets: [e,d,b,c] and [e,d,c,a], are // // hull tets. If a or b is 'dummypoint', we reconfigure it to c, i.e., // // rotate the three input tets counterclockwisely (right-hand rule) // // until a or b is in c's position. // // // // If 'fc->enqflag' is set, convex hull faces will be queued for flipping. // // In particular, if 'fc->enqflag' is 1, it is called by incrementalflip() // // after the insertion of a new point. It is assumed that 'd' is the new // // point. IN this case, only link faces of 'd' are queued. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::flip23(triface* fliptets, int hullflag, flipconstraints* fc) { triface topcastets[3], botcastets[3]; triface newface, casface; point pa, pb, pc, pd, pe; REAL attrib, volume; int dummyflag = 0; // range = {-1, 0, 1, 2}. int i; if (hullflag > 0) { // Check if e is dummypoint. if (oppo(fliptets[1]) == dummypoint) { // Swap the two old tets. newface = fliptets[0]; fliptets[0] = fliptets[1]; fliptets[1] = newface; dummyflag = -1; // d is dummypoint. } else { // Check if either a or b is dummypoint. if (org(fliptets[0]) == dummypoint) { dummyflag = 1; // a is dummypoint. enextself(fliptets[0]); eprevself(fliptets[1]); } else if (dest(fliptets[0]) == dummypoint) { dummyflag = 2; // b is dummypoint. eprevself(fliptets[0]); enextself(fliptets[1]); } else { dummyflag = 0; // either c or d may be dummypoint. } } } pa = org(fliptets[0]); pb = dest(fliptets[0]); pc = apex(fliptets[0]); pd = oppo(fliptets[0]); pe = oppo(fliptets[1]); flip23count++; // Get the outer boundary faces. for (i = 0; i < 3; i++) { fnext(fliptets[0], topcastets[i]); enextself(fliptets[0]); } for (i = 0; i < 3; i++) { fnext(fliptets[1], botcastets[i]); eprevself(fliptets[1]); } // Re-use fliptets[0] and fliptets[1]. fliptets[0].ver = 11; fliptets[1].ver = 11; setelemmarker(fliptets[0].tet, 0); // Clear all flags. setelemmarker(fliptets[1].tet, 0); // NOTE: the element attributes and volume constraint remain unchanged. if (checksubsegflag) { // Dealloc the space to subsegments. if (fliptets[0].tet[8] != NULL) { tet2segpool->dealloc((shellface*)fliptets[0].tet[8]); fliptets[0].tet[8] = NULL; } if (fliptets[1].tet[8] != NULL) { tet2segpool->dealloc((shellface*)fliptets[1].tet[8]); fliptets[1].tet[8] = NULL; } } if (checksubfaceflag) { // Dealloc the space to subfaces. if (fliptets[0].tet[9] != NULL) { tet2subpool->dealloc((shellface*)fliptets[0].tet[9]); fliptets[0].tet[9] = NULL; } if (fliptets[1].tet[9] != NULL) { tet2subpool->dealloc((shellface*)fliptets[1].tet[9]); fliptets[1].tet[9] = NULL; } } // Create a new tet. maketetrahedron(&(fliptets[2])); // The new tet have the same attributes from the old tet. for (i = 0; i < numelemattrib; i++) { attrib = elemattribute(fliptets[0].tet, i); setelemattribute(fliptets[2].tet, i, attrib); } if (b->varvolume) { volume = volumebound(fliptets[0].tet); setvolumebound(fliptets[2].tet, volume); } if (hullflag > 0) { // Check if d is dummytet. if (pd != dummypoint) { setvertices(fliptets[0], pe, pd, pa, pb); // [e,d,a,b] * setvertices(fliptets[1], pe, pd, pb, pc); // [e,d,b,c] * // Check if c is dummypoint. if (pc != dummypoint) { setvertices(fliptets[2], pe, pd, pc, pa); // [e,d,c,a] * } else { setvertices(fliptets[2], pd, pe, pa, pc); // [d,e,a,c] esymself(fliptets[2]); // [e,d,c,a] * } // The hullsize does not change. } else { // d is dummypoint. setvertices(fliptets[0], pa, pb, pe, pd); // [a,b,e,d] setvertices(fliptets[1], pb, pc, pe, pd); // [b,c,e,d] setvertices(fliptets[2], pc, pa, pe, pd); // [c,a,e,d] // Adjust the faces to [e,d,a,b], [e,d,b,c], [e,d,c,a] * for (i = 0; i < 3; i++) { eprevesymself(fliptets[i]); enextself(fliptets[i]); } // We deleted one hull tet, and created three hull tets. hullsize += 2; } } else { setvertices(fliptets[0], pe, pd, pa, pb); // [e,d,a,b] * setvertices(fliptets[1], pe, pd, pb, pc); // [e,d,b,c] * setvertices(fliptets[2], pe, pd, pc, pa); // [e,d,c,a] * } if (fc->remove_ndelaunay_edge) { // calc_tetprism_vol REAL volneg[2], volpos[3], vol_diff; if (pd != dummypoint) { if (pc != dummypoint) { volpos[0] = tetprismvol(pe, pd, pa, pb); volpos[1] = tetprismvol(pe, pd, pb, pc); volpos[2] = tetprismvol(pe, pd, pc, pa); volneg[0] = tetprismvol(pa, pb, pc, pd); volneg[1] = tetprismvol(pb, pa, pc, pe); } else { // pc == dummypoint volpos[0] = tetprismvol(pe, pd, pa, pb); volpos[1] = 0.; volpos[2] = 0.; volneg[0] = 0.; volneg[1] = 0.; } } else { // pd == dummypoint. volpos[0] = 0.; volpos[1] = 0.; volpos[2] = 0.; volneg[0] = 0.; volneg[1] = tetprismvol(pb, pa, pc, pe); } vol_diff = volpos[0] + volpos[1] + volpos[2] - volneg[0] - volneg[1]; fc->tetprism_vol_sum += vol_diff; // Update the total sum. } // Bond three new tets together. for (i = 0; i < 3; i++) { esym(fliptets[i], newface); bond(newface, fliptets[(i + 1) % 3]); } // Bond to top outer boundary faces (at [a,b,c,d]). for (i = 0; i < 3; i++) { eorgoppo(fliptets[i], newface); // At edges [b,a], [c,b], [a,c]. bond(newface, topcastets[i]); } // Bond bottom outer boundary faces (at [b,a,c,e]). for (i = 0; i < 3; i++) { edestoppo(fliptets[i], newface); // At edges [a,b], [b,c], [c,a]. bond(newface, botcastets[i]); } if (checksubsegflag) { // Bond subsegments if there are. // Each new tet has 5 edges to be checked (except the edge [e,d]). face checkseg; // The middle three: [a,b], [b,c], [c,a]. for (i = 0; i < 3; i++) { if (issubseg(topcastets[i])) { tsspivot1(topcastets[i], checkseg); eorgoppo(fliptets[i], newface); tssbond1(newface, checkseg); sstbond1(checkseg, newface); if (fc->chkencflag & 1) { enqueuesubface(badsubsegs, &checkseg); } } } // The top three: [d,a], [d,b], [d,c]. Two tets per edge. for (i = 0; i < 3; i++) { eprev(topcastets[i], casface); if (issubseg(casface)) { tsspivot1(casface, checkseg); enext(fliptets[i], newface); tssbond1(newface, checkseg); sstbond1(checkseg, newface); esym(fliptets[(i + 2) % 3], newface); eprevself(newface); tssbond1(newface, checkseg); sstbond1(checkseg, newface); if (fc->chkencflag & 1) { enqueuesubface(badsubsegs, &checkseg); } } } // The bot three: [a,e], [b,e], [c,e]. Two tets per edge. for (i = 0; i < 3; i++) { enext(botcastets[i], casface); if (issubseg(casface)) { tsspivot1(casface, checkseg); eprev(fliptets[i], newface); tssbond1(newface, checkseg); sstbond1(checkseg, newface); esym(fliptets[(i + 2) % 3], newface); enextself(newface); tssbond1(newface, checkseg); sstbond1(checkseg, newface); if (fc->chkencflag & 1) { enqueuesubface(badsubsegs, &checkseg); } } } } // if (checksubsegflag) if (checksubfaceflag) { // Bond 6 subfaces if there are. face checksh; for (i = 0; i < 3; i++) { if (issubface(topcastets[i])) { tspivot(topcastets[i], checksh); eorgoppo(fliptets[i], newface); sesymself(checksh); tsbond(newface, checksh); if (fc->chkencflag & 2) { enqueuesubface(badsubfacs, &checksh); } } } for (i = 0; i < 3; i++) { if (issubface(botcastets[i])) { tspivot(botcastets[i], checksh); edestoppo(fliptets[i], newface); sesymself(checksh); tsbond(newface, checksh); if (fc->chkencflag & 2) { enqueuesubface(badsubfacs, &checksh); } } } } // if (checksubfaceflag) if (fc->chkencflag & 4) { // Put three new tets into check list. for (i = 0; i < 3; i++) { enqueuetetrahedron(&(fliptets[i])); } } // Update the point-to-tet map. setpoint2tet(pa, (tetrahedron)fliptets[0].tet); setpoint2tet(pb, (tetrahedron)fliptets[0].tet); setpoint2tet(pc, (tetrahedron)fliptets[1].tet); setpoint2tet(pd, (tetrahedron)fliptets[0].tet); setpoint2tet(pe, (tetrahedron)fliptets[0].tet); if (hullflag > 0) { if (dummyflag != 0) { // Restore the original position of the points (for flipnm()). if (dummyflag == -1) { // Reverse the edge. for (i = 0; i < 3; i++) { esymself(fliptets[i]); } // Swap the last two new tets. newface = fliptets[1]; fliptets[1] = fliptets[2]; fliptets[2] = newface; } else { // either a or b were swapped. if (dummyflag == 1) { // a is dummypoint. newface = fliptets[0]; fliptets[0] = fliptets[2]; fliptets[2] = fliptets[1]; fliptets[1] = newface; } else { // dummyflag == 2 // b is dummypoint. newface = fliptets[0]; fliptets[0] = fliptets[1]; fliptets[1] = fliptets[2]; fliptets[2] = newface; } } } } if (fc->enqflag > 0) { // Queue faces which may be locally non-Delaunay. for (i = 0; i < 3; i++) { eprevesym(fliptets[i], newface); flippush(flipstack, &newface); } if (fc->enqflag > 1) { for (i = 0; i < 3; i++) { enextesym(fliptets[i], newface); flippush(flipstack, &newface); } } } recenttet = fliptets[0]; } /////////////////////////////////////////////////////////////////////////////// // // // flip32() Perform a 3-to-2 flip (edge-to-face flip). // // // // 'fliptets' is an array of three tets (handles), which are [e,d,a,b], // // [e,d,b,c], and [e,d,c,a]. The two new tets: [a,b,c,d] and [b,a,c,e] are // // returned in [0] and [1] of 'fliptets'. As a result, the edge [e,d] is // // replaced by the face [a,b,c]. // // // // If 'hullflag' > 0, hull tets may be involved in this flip, i.e., one of // // the five vertices may be 'dummypoint'. There are two canonical cases: // // (1) d is 'dummypoint', then [a,b,c,d] is hull tet. If e is 'dummypoint',// // we reconfigure e to d, i.e., turnover it. // // (2) c is 'dummypoint' then both [a,b,c,d] and [b,a,c,e] are hull tets. // // If a or b is 'dummypoint', we reconfigure it to c, i.e., rotate the // // three old tets counterclockwisely (right-hand rule) until a or b // // is in c's position. // // // // If 'fc->enqflag' is set, convex hull faces will be queued for flipping. // // In particular, if 'fc->enqflag' is 1, it is called by incrementalflip() // // after the insertion of a new point. It is assumed that 'a' is the new // // point. In this case, only link faces of 'a' are queued. // // // // If 'checksubfaceflag' is on (global variable), and assume [e,d] is not a // // segment. There may be two (interior) subfaces sharing at [e,d], which are // // [e,d,p] and [e,d,q], where the pair (p,q) may be either (a,b), or (b,c), // // or (c,a) In such case, a 2-to-2 flip is performed on these two subfaces // // and two new subfaces [p,q,e] and [p,q,d] are created. They are inserted // // back into the tetrahedralization. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::flip32(triface* fliptets, int hullflag, flipconstraints* fc) { triface topcastets[3], botcastets[3]; triface newface, casface; face flipshs[3]; face checkseg; point pa, pb, pc, pd, pe; REAL attrib, volume; int dummyflag = 0; // Rangle = {-1, 0, 1, 2} int spivot = -1, scount = 0; // for flip22() int t1ver; int i, j; if (hullflag > 0) { // Check if e is 'dummypoint'. if (org(fliptets[0]) == dummypoint) { // Reverse the edge. for (i = 0; i < 3; i++) { esymself(fliptets[i]); } // Swap the last two tets. newface = fliptets[1]; fliptets[1] = fliptets[2]; fliptets[2] = newface; dummyflag = -1; // e is dummypoint. } else { // Check if a or b is the 'dummypoint'. if (apex(fliptets[0]) == dummypoint) { dummyflag = 1; // a is dummypoint. newface = fliptets[0]; fliptets[0] = fliptets[1]; fliptets[1] = fliptets[2]; fliptets[2] = newface; } else if (apex(fliptets[1]) == dummypoint) { dummyflag = 2; // b is dummypoint. newface = fliptets[0]; fliptets[0] = fliptets[2]; fliptets[2] = fliptets[1]; fliptets[1] = newface; } else { dummyflag = 0; // either c or d may be dummypoint. } } } pa = apex(fliptets[0]); pb = apex(fliptets[1]); pc = apex(fliptets[2]); pd = dest(fliptets[0]); pe = org(fliptets[0]); flip32count++; // Get the outer boundary faces. for (i = 0; i < 3; i++) { eorgoppo(fliptets[i], casface); fsym(casface, topcastets[i]); } for (i = 0; i < 3; i++) { edestoppo(fliptets[i], casface); fsym(casface, botcastets[i]); } if (checksubfaceflag) { // Check if there are interior subfaces at the edge [e,d]. for (i = 0; i < 3; i++) { tspivot(fliptets[i], flipshs[i]); if (flipshs[i].sh != NULL) { // Found an interior subface. stdissolve(flipshs[i]); // Disconnect the sub-tet bond. scount++; } else { spivot = i; } } } // Re-use fliptets[0] and fliptets[1]. fliptets[0].ver = 11; fliptets[1].ver = 11; setelemmarker(fliptets[0].tet, 0); // Clear all flags. setelemmarker(fliptets[1].tet, 0); if (checksubsegflag) { // Dealloc the space to subsegments. if (fliptets[0].tet[8] != NULL) { tet2segpool->dealloc((shellface*)fliptets[0].tet[8]); fliptets[0].tet[8] = NULL; } if (fliptets[1].tet[8] != NULL) { tet2segpool->dealloc((shellface*)fliptets[1].tet[8]); fliptets[1].tet[8] = NULL; } } if (checksubfaceflag) { // Dealloc the space to subfaces. if (fliptets[0].tet[9] != NULL) { tet2subpool->dealloc((shellface*)fliptets[0].tet[9]); fliptets[0].tet[9] = NULL; } if (fliptets[1].tet[9] != NULL) { tet2subpool->dealloc((shellface*)fliptets[1].tet[9]); fliptets[1].tet[9] = NULL; } } if (checksubfaceflag) { if (scount > 0) { // The element attributes and volume constraint must be set correctly. // There are two subfaces involved in this flip. The three tets are // separated into two different regions, one may be exterior. The // first region has two tets, and the second region has only one. // The two created tets must be in the same region as the first region. // The element attributes and volume constraint must be set correctly. // assert(spivot != -1); // The tet fliptets[spivot] is in the first region. for (j = 0; j < 2; j++) { for (i = 0; i < numelemattrib; i++) { attrib = elemattribute(fliptets[spivot].tet, i); setelemattribute(fliptets[j].tet, i, attrib); } if (b->varvolume) { volume = volumebound(fliptets[spivot].tet); setvolumebound(fliptets[j].tet, volume); } } } } // Delete an old tet. tetrahedrondealloc(fliptets[2].tet); if (hullflag > 0) { // Check if c is dummypointc. if (pc != dummypoint) { // Check if d is dummypoint. if (pd != dummypoint) { // No hull tet is involved. } else { // We deleted three hull tets, and created one hull tet. hullsize -= 2; } setvertices(fliptets[0], pa, pb, pc, pd); setvertices(fliptets[1], pb, pa, pc, pe); } else { // c is dummypoint. The two new tets are hull tets. setvertices(fliptets[0], pb, pa, pd, pc); setvertices(fliptets[1], pa, pb, pe, pc); // Adjust badc -> abcd. esymself(fliptets[0]); // Adjust abec -> bace. esymself(fliptets[1]); // The hullsize does not change. } } else { setvertices(fliptets[0], pa, pb, pc, pd); setvertices(fliptets[1], pb, pa, pc, pe); } if (fc->remove_ndelaunay_edge) { // calc_tetprism_vol REAL volneg[3], volpos[2], vol_diff; if (pc != dummypoint) { if (pd != dummypoint) { volneg[0] = tetprismvol(pe, pd, pa, pb); volneg[1] = tetprismvol(pe, pd, pb, pc); volneg[2] = tetprismvol(pe, pd, pc, pa); volpos[0] = tetprismvol(pa, pb, pc, pd); volpos[1] = tetprismvol(pb, pa, pc, pe); } else { // pd == dummypoint volneg[0] = 0.; volneg[1] = 0.; volneg[2] = 0.; volpos[0] = 0.; volpos[1] = tetprismvol(pb, pa, pc, pe); } } else { // pc == dummypoint. volneg[0] = tetprismvol(pe, pd, pa, pb); volneg[1] = 0.; volneg[2] = 0.; volpos[0] = 0.; volpos[1] = 0.; } vol_diff = volpos[0] + volpos[1] - volneg[0] - volneg[1] - volneg[2]; fc->tetprism_vol_sum += vol_diff; // Update the total sum. } // Bond abcd <==> bace. bond(fliptets[0], fliptets[1]); // Bond new faces to top outer boundary faces (at abcd). for (i = 0; i < 3; i++) { esym(fliptets[0], newface); bond(newface, topcastets[i]); enextself(fliptets[0]); } // Bond new faces to bottom outer boundary faces (at bace). for (i = 0; i < 3; i++) { esym(fliptets[1], newface); bond(newface, botcastets[i]); eprevself(fliptets[1]); } if (checksubsegflag) { // Bond 9 segments to new (flipped) tets. for (i = 0; i < 3; i++) { // edges a->b, b->c, c->a. if (issubseg(topcastets[i])) { tsspivot1(topcastets[i], checkseg); tssbond1(fliptets[0], checkseg); sstbond1(checkseg, fliptets[0]); tssbond1(fliptets[1], checkseg); sstbond1(checkseg, fliptets[1]); if (fc->chkencflag & 1) { enqueuesubface(badsubsegs, &checkseg); } } enextself(fliptets[0]); eprevself(fliptets[1]); } // The three top edges. for (i = 0; i < 3; i++) { // edges b->d, c->d, a->d. esym(fliptets[0], newface); eprevself(newface); enext(topcastets[i], casface); if (issubseg(casface)) { tsspivot1(casface, checkseg); tssbond1(newface, checkseg); sstbond1(checkseg, newface); if (fc->chkencflag & 1) { enqueuesubface(badsubsegs, &checkseg); } } enextself(fliptets[0]); } // The three bot edges. for (i = 0; i < 3; i++) { // edges b<-e, c<-e, a<-e. esym(fliptets[1], newface); enextself(newface); eprev(botcastets[i], casface); if (issubseg(casface)) { tsspivot1(casface, checkseg); tssbond1(newface, checkseg); sstbond1(checkseg, newface); if (fc->chkencflag & 1) { enqueuesubface(badsubsegs, &checkseg); } } eprevself(fliptets[1]); } } // if (checksubsegflag) if (checksubfaceflag) { face checksh; // Bond the top three casing subfaces. for (i = 0; i < 3; i++) { // At edges [b,a], [c,b], [a,c] if (issubface(topcastets[i])) { tspivot(topcastets[i], checksh); esym(fliptets[0], newface); sesymself(checksh); tsbond(newface, checksh); if (fc->chkencflag & 2) { enqueuesubface(badsubfacs, &checksh); } } enextself(fliptets[0]); } // Bond the bottom three casing subfaces. for (i = 0; i < 3; i++) { // At edges [a,b], [b,c], [c,a] if (issubface(botcastets[i])) { tspivot(botcastets[i], checksh); esym(fliptets[1], newface); sesymself(checksh); tsbond(newface, checksh); if (fc->chkencflag & 2) { enqueuesubface(badsubfacs, &checksh); } } eprevself(fliptets[1]); } if (scount > 0) { face flipfaces[2]; // Perform a 2-to-2 flip in subfaces. flipfaces[0] = flipshs[(spivot + 1) % 3]; flipfaces[1] = flipshs[(spivot + 2) % 3]; sesymself(flipfaces[1]); flip22(flipfaces, 0, fc->chkencflag); // Connect the flipped subfaces to flipped tets. // First go to the corresponding flipping edge. // Re-use top- and botcastets[0]. topcastets[0] = fliptets[0]; botcastets[0] = fliptets[1]; for (i = 0; i < ((spivot + 1) % 3); i++) { enextself(topcastets[0]); eprevself(botcastets[0]); } // Connect the top subface to the top tets. esymself(topcastets[0]); sesymself(flipfaces[0]); // Check if there already exists a subface. tspivot(topcastets[0], checksh); if (checksh.sh == NULL) { tsbond(topcastets[0], flipfaces[0]); fsymself(topcastets[0]); sesymself(flipfaces[0]); tsbond(topcastets[0], flipfaces[0]); } else { // An invalid 2-to-2 flip. Report a bug. terminatetetgen(this, 2); } // Connect the bot subface to the bottom tets. esymself(botcastets[0]); sesymself(flipfaces[1]); // Check if there already exists a subface. tspivot(botcastets[0], checksh); if (checksh.sh == NULL) { tsbond(botcastets[0], flipfaces[1]); fsymself(botcastets[0]); sesymself(flipfaces[1]); tsbond(botcastets[0], flipfaces[1]); } else { // An invalid 2-to-2 flip. Report a bug. terminatetetgen(this, 2); } } // if (scount > 0) } // if (checksubfaceflag) if (fc->chkencflag & 4) { // Put two new tets into check list. for (i = 0; i < 2; i++) { enqueuetetrahedron(&(fliptets[i])); } } setpoint2tet(pa, (tetrahedron)fliptets[0].tet); setpoint2tet(pb, (tetrahedron)fliptets[0].tet); setpoint2tet(pc, (tetrahedron)fliptets[0].tet); setpoint2tet(pd, (tetrahedron)fliptets[0].tet); setpoint2tet(pe, (tetrahedron)fliptets[1].tet); if (hullflag > 0) { if (dummyflag != 0) { // Restore the original position of the points (for flipnm()). if (dummyflag == -1) { // e were dummypoint. Swap the two new tets. newface = fliptets[0]; fliptets[0] = fliptets[1]; fliptets[1] = newface; } else { // a or b was dummypoint. if (dummyflag == 1) { eprevself(fliptets[0]); enextself(fliptets[1]); } else { // dummyflag == 2 enextself(fliptets[0]); eprevself(fliptets[1]); } } } } if (fc->enqflag > 0) { // Queue faces which may be locally non-Delaunay. // pa = org(fliptets[0]); // 'a' may be a new vertex. enextesym(fliptets[0], newface); flippush(flipstack, &newface); eprevesym(fliptets[1], newface); flippush(flipstack, &newface); if (fc->enqflag > 1) { // pb = dest(fliptets[0]); eprevesym(fliptets[0], newface); flippush(flipstack, &newface); enextesym(fliptets[1], newface); flippush(flipstack, &newface); // pc = apex(fliptets[0]); esym(fliptets[0], newface); flippush(flipstack, &newface); esym(fliptets[1], newface); flippush(flipstack, &newface); } } recenttet = fliptets[0]; } /////////////////////////////////////////////////////////////////////////////// // // // flip41() Perform a 4-to-1 flip (Remove a vertex). // // // // 'fliptets' is an array of four tetrahedra in the star of the removing // // vertex 'p'. Let the four vertices in the star of p be a, b, c, and d. The // // four tets in 'fliptets' are: [p,d,a,b], [p,d,b,c], [p,d,c,a], and [a,b,c, // // p]. On return, 'fliptets[0]' is the new tet [a,b,c,d]. // // // // If 'hullflag' is set (> 0), one of the five vertices may be 'dummypoint'. // // The 'hullsize' may be changed. Note that p may be dummypoint. In this // // case, four hull tets are replaced by one real tet. // // // // If 'checksubface' flag is set (>0), it is possible that there are three // // interior subfaces connecting at p. If so, a 3-to-1 flip is performed to // // to remove p from the surface triangulation. // // // // If it is called by the routine incrementalflip(), we assume that d is the // // newly inserted vertex. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::flip41(triface* fliptets, int hullflag, flipconstraints* fc) { triface topcastets[3], botcastet; triface newface, neightet; face flipshs[4]; point pa, pb, pc, pd, pp; int dummyflag = 0; // in {0, 1, 2, 3, 4} int spivot = -1, scount = 0; int t1ver; int i; pa = org(fliptets[3]); pb = dest(fliptets[3]); pc = apex(fliptets[3]); pd = dest(fliptets[0]); pp = org(fliptets[0]); // The removing vertex. flip41count++; // Get the outer boundary faces. for (i = 0; i < 3; i++) { enext(fliptets[i], topcastets[i]); fnextself(topcastets[i]); // [d,a,b,#], [d,b,c,#], [d,c,a,#] enextself(topcastets[i]); // [a,b,d,#], [b,c,d,#], [c,a,d,#] } fsym(fliptets[3], botcastet); // [b,a,c,#] if (checksubfaceflag) { // Check if there are three subfaces at 'p'. // Re-use 'newface'. for (i = 0; i < 3; i++) { fnext(fliptets[3], newface); // [a,b,p,d],[b,c,p,d],[c,a,p,d]. tspivot(newface, flipshs[i]); if (flipshs[i].sh != NULL) { spivot = i; // Remember this subface. scount++; } enextself(fliptets[3]); } if (scount > 0) { // There are three subfaces connecting at p. if (scount < 3) { // The new subface is one of {[a,b,d], [b,c,d], [c,a,d]}. // Go to the tet containing the three subfaces. fsym(topcastets[spivot], neightet); // Get the three subfaces connecting at p. for (i = 0; i < 3; i++) { esym(neightet, newface); tspivot(newface, flipshs[i]); eprevself(neightet); } } else { spivot = 3; // The new subface is [a,b,c]. } } } // if (checksubfaceflag) // Re-use fliptets[0] for [a,b,c,d]. fliptets[0].ver = 11; setelemmarker(fliptets[0].tet, 0); // Clean all flags. // NOTE: the element attributes and volume constraint remain unchanged. if (checksubsegflag) { // Dealloc the space to subsegments. if (fliptets[0].tet[8] != NULL) { tet2segpool->dealloc((shellface*)fliptets[0].tet[8]); fliptets[0].tet[8] = NULL; } } if (checksubfaceflag) { // Dealloc the space to subfaces. if (fliptets[0].tet[9] != NULL) { tet2subpool->dealloc((shellface*)fliptets[0].tet[9]); fliptets[0].tet[9] = NULL; } } // Delete the other three tets. for (i = 1; i < 4; i++) { tetrahedrondealloc(fliptets[i].tet); } if (pp != dummypoint) { // Mark the point pp as unused. setpointtype(pp, UNUSEDVERTEX); unuverts++; } // Create the new tet [a,b,c,d]. if (hullflag > 0) { // One of the five vertices may be 'dummypoint'. if (pa == dummypoint) { // pa is dummypoint. setvertices(fliptets[0], pc, pb, pd, pa); esymself(fliptets[0]); // [b,c,a,d] eprevself(fliptets[0]); // [a,b,c,d] dummyflag = 1; } else if (pb == dummypoint) { setvertices(fliptets[0], pa, pc, pd, pb); esymself(fliptets[0]); // [c,a,b,d] enextself(fliptets[0]); // [a,b,c,d] dummyflag = 2; } else if (pc == dummypoint) { setvertices(fliptets[0], pb, pa, pd, pc); esymself(fliptets[0]); // [a,b,c,d] dummyflag = 3; } else if (pd == dummypoint) { setvertices(fliptets[0], pa, pb, pc, pd); dummyflag = 4; } else { setvertices(fliptets[0], pa, pb, pc, pd); if (pp == dummypoint) { dummyflag = -1; } else { dummyflag = 0; } } if (dummyflag > 0) { // We deleted 3 hull tets, and create 1 hull tet. hullsize -= 2; } else if (dummyflag < 0) { // We deleted 4 hull tets. hullsize -= 4; // meshedges does not change. } } else { setvertices(fliptets[0], pa, pb, pc, pd); } if (fc->remove_ndelaunay_edge) { // calc_tetprism_vol REAL volneg[4], volpos[1], vol_diff; if (dummyflag > 0) { if (pa == dummypoint) { volneg[0] = 0.; volneg[1] = tetprismvol(pp, pd, pb, pc); volneg[2] = 0.; volneg[3] = 0.; } else if (pb == dummypoint) { volneg[0] = 0.; volneg[1] = 0.; volneg[2] = tetprismvol(pp, pd, pc, pa); volneg[3] = 0.; } else if (pc == dummypoint) { volneg[0] = tetprismvol(pp, pd, pa, pb); volneg[1] = 0.; volneg[2] = 0.; volneg[3] = 0.; } else { // pd == dummypoint volneg[0] = 0.; volneg[1] = 0.; volneg[2] = 0.; volneg[3] = tetprismvol(pa, pb, pc, pp); } volpos[0] = 0.; } else if (dummyflag < 0) { volneg[0] = 0.; volneg[1] = 0.; volneg[2] = 0.; volneg[3] = 0.; volpos[0] = tetprismvol(pa, pb, pc, pd); } else { volneg[0] = tetprismvol(pp, pd, pa, pb); volneg[1] = tetprismvol(pp, pd, pb, pc); volneg[2] = tetprismvol(pp, pd, pc, pa); volneg[3] = tetprismvol(pa, pb, pc, pp); volpos[0] = tetprismvol(pa, pb, pc, pd); } vol_diff = volpos[0] - volneg[0] - volneg[1] - volneg[2] - volneg[3]; fc->tetprism_vol_sum += vol_diff; // Update the total sum. } // Bond the new tet to adjacent tets. for (i = 0; i < 3; i++) { esym(fliptets[0], newface); // At faces [b,a,d], [c,b,d], [a,c,d]. bond(newface, topcastets[i]); enextself(fliptets[0]); } bond(fliptets[0], botcastet); if (checksubsegflag) { face checkseg; // Bond 6 segments (at edges of [a,b,c,d]) if there there are. for (i = 0; i < 3; i++) { eprev(topcastets[i], newface); // At edges [d,a],[d,b],[d,c]. if (issubseg(newface)) { tsspivot1(newface, checkseg); esym(fliptets[0], newface); enextself(newface); // At edges [a,d], [b,d], [c,d]. tssbond1(newface, checkseg); sstbond1(checkseg, newface); if (fc->chkencflag & 1) { enqueuesubface(badsubsegs, &checkseg); } } enextself(fliptets[0]); } for (i = 0; i < 3; i++) { if (issubseg(topcastets[i])) { tsspivot1(topcastets[i], checkseg); // At edges [a,b],[b,c],[c,a]. tssbond1(fliptets[0], checkseg); sstbond1(checkseg, fliptets[0]); if (fc->chkencflag & 1) { enqueuesubface(badsubsegs, &checkseg); } } enextself(fliptets[0]); } } if (checksubfaceflag) { face checksh; // Bond 4 subfaces (at faces of [a,b,c,d]) if there are. for (i = 0; i < 3; i++) { if (issubface(topcastets[i])) { tspivot(topcastets[i], checksh); // At faces [a,b,d],[b,c,d],[c,a,d] esym(fliptets[0], newface); // At faces [b,a,d],[c,b,d],[a,c,d] sesymself(checksh); tsbond(newface, checksh); if (fc->chkencflag & 2) { enqueuesubface(badsubfacs, &checksh); } } enextself(fliptets[0]); } if (issubface(botcastet)) { tspivot(botcastet, checksh); // At face [b,a,c] sesymself(checksh); tsbond(fliptets[0], checksh); if (fc->chkencflag & 2) { enqueuesubface(badsubfacs, &checksh); } } if (spivot >= 0) { // Perform a 3-to-1 flip in surface triangulation. // Depending on the value of 'spivot', the three subfaces are: // - 0: [a,b,p], [b,d,p], [d,a,p] // - 1: [b,c,p], [c,d,p], [d,b,p] // - 2: [c,a,p], [a,d,p], [d,c,p] // - 3: [a,b,p], [b,c,p], [c,a,p] // Adjust the three subfaces such that their origins are p, i.e., // - 3: [p,a,b], [p,b,c], [p,c,a]. (Required by the flip31()). for (i = 0; i < 3; i++) { senext2self(flipshs[i]); } flip31(flipshs, 0); // Delete the three old subfaces. for (i = 0; i < 3; i++) { shellfacedealloc(subfaces, flipshs[i].sh); } if (spivot < 3) { // // Bond the new subface to the new tet [a,b,c,d]. tsbond(topcastets[spivot], flipshs[3]); fsym(topcastets[spivot], newface); sesym(flipshs[3], checksh); tsbond(newface, checksh); } else { // Bound the new subface [a,b,c] to the new tet [a,b,c,d]. tsbond(fliptets[0], flipshs[3]); fsym(fliptets[0], newface); sesym(flipshs[3], checksh); tsbond(newface, checksh); } } // if (spivot > 0) } // if (checksubfaceflag) if (fc->chkencflag & 4) { enqueuetetrahedron(&(fliptets[0])); } // Update the point-to-tet map. setpoint2tet(pa, (tetrahedron)fliptets[0].tet); setpoint2tet(pb, (tetrahedron)fliptets[0].tet); setpoint2tet(pc, (tetrahedron)fliptets[0].tet); setpoint2tet(pd, (tetrahedron)fliptets[0].tet); if (fc->enqflag > 0) { // Queue faces which may be locally non-Delaunay. flippush(flipstack, &(fliptets[0])); // [a,b,c] (opposite to new point). if (fc->enqflag > 1) { for (i = 0; i < 3; i++) { esym(fliptets[0], newface); flippush(flipstack, &newface); enextself(fliptets[0]); } } } recenttet = fliptets[0]; } /////////////////////////////////////////////////////////////////////////////// // // // flipnm() Flip an edge through a sequence of elementary flips. // // // // 'abtets' is an array of 'n' tets in the star of edge [a,b].These tets are // // ordered in a counterclockwise cycle with respect to the vector a->b, i.e.,// // use the right-hand rule. // // // // 'level' (>= 0) indicates the current link level. If 'level > 0', we are // // flipping a link edge of an edge [a',b'], and 'abedgepivot' indicates // // which link edge, i.e., [c',b'] or [a',c'], is [a,b] These two parameters // // allow us to determine the new tets after a 3-to-2 flip, i.e., tets that // // do not inside the reduced star of edge [a',b']. // // // // If the flag 'fc->unflip' is set, this routine un-does the flips performed // // in flipnm([a,b]) so that the mesh is returned to its original state // // before doing the flipnm([a,b]) operation. // // // // The return value is an integer nn, where nn <= n. If nn is 2, then the // // edge is flipped. The first and the second tets in 'abtets' are new tets. // // Otherwise, nn > 2, the edge is not flipped, and nn is the number of tets // // in the current star of [a,b]. // // // // ASSUMPTIONS: // // - Neither a nor b is 'dummypoint'. // // - [a,b] must not be a segment. // // // /////////////////////////////////////////////////////////////////////////////// int tetgenmesh::flipnm(triface* abtets, int n, int level, int abedgepivot, flipconstraints* fc) { triface fliptets[3], spintet, flipedge; triface *tmpabtets, *parytet; point pa, pb, pc, pd, pe, pf; REAL ori; int hullflag, hulledgeflag; int reducflag, rejflag; int reflexlinkedgecount; int edgepivot; int n1, nn; int t1ver; int i, j; pa = org(abtets[0]); pb = dest(abtets[0]); if (n > 3) { // Try to reduce the size of the Star(ab) by flipping a face in it. reflexlinkedgecount = 0; for (i = 0; i < n; i++) { // Let the face of 'abtets[i]' be [a,b,c]. if (checksubfaceflag) { if (issubface(abtets[i])) { continue; // Skip a subface. } } // Do not flip this face if it is involved in two Stars. if ((elemcounter(abtets[i]) > 1) || (elemcounter(abtets[(i - 1 + n) % n]) > 1)) { continue; } pc = apex(abtets[i]); pd = apex(abtets[(i + 1) % n]); pe = apex(abtets[(i - 1 + n) % n]); if ((pd == dummypoint) || (pe == dummypoint)) { continue; // [a,b,c] is a hull face. } // Decide whether [a,b,c] is flippable or not. reducflag = 0; hullflag = (pc == dummypoint); // pc may be dummypoint. hulledgeflag = 0; if (hullflag == 0) { ori = orient3d(pb, pc, pd, pe); // Is [b,c] locally convex? if (ori > 0) { ori = orient3d(pc, pa, pd, pe); // Is [c,a] locally convex? if (ori > 0) { // Test if [a,b] is locally convex OR flat. ori = orient3d(pa, pb, pd, pe); if (ori > 0) { // Found a 2-to-3 flip: [a,b,c] => [e,d] reducflag = 1; } else if (ori == 0) { // [a,b] is flat. if (n == 4) { // The "flat" tet can be removed immediately by a 3-to-2 flip. reducflag = 1; // Check if [e,d] is a hull edge. pf = apex(abtets[(i + 2) % n]); hulledgeflag = (pf == dummypoint); } } } } if (!reducflag) { reflexlinkedgecount++; } } else { // 'c' is dummypoint. if (n == 4) { // Let the vertex opposite to 'c' is 'f'. // A 4-to-4 flip is possible if the two tets [d,e,f,a] and [e,d,f,b] // are valid tets. // Note: When the mesh is not convex, it is possible that [a,b] is // locally non-convex (at hull faces [a,b,e] and [b,a,d]). // In this case, an edge flip [a,b] to [e,d] is still possible. pf = apex(abtets[(i + 2) % n]); ori = orient3d(pd, pe, pf, pa); if (ori < 0) { ori = orient3d(pe, pd, pf, pb); if (ori < 0) { // Found a 4-to-4 flip: [a,b] => [e,d] reducflag = 1; ori = 0; // Signal as a 4-to-4 flip (like a co-planar case). hulledgeflag = 1; // [e,d] is a hull edge. } } } } // if (hullflag) if (reducflag) { if (nonconvex && hulledgeflag) { // We will create a hull edge [e,d]. Make sure it does not exist. if (getedge(pe, pd, &spintet)) { // The 2-to-3 flip is not a topological valid flip. reducflag = 0; } } } if (reducflag) { // [a,b,c] could be removed by a 2-to-3 flip. rejflag = 0; if (fc->checkflipeligibility) { // Check if the flip can be performed. rejflag = checkflipeligibility(1, pa, pb, pc, pd, pe, level, abedgepivot, fc); } if (!rejflag) { // Do flip: [a,b,c] => [e,d]. fliptets[0] = abtets[i]; fsym(fliptets[0], fliptets[1]); // abtets[i-1]. flip23(fliptets, hullflag, fc); // Shrink the array 'abtets', maintain the original order. // Two tets 'abtets[i-1] ([a,b,e,c])' and 'abtets[i] ([a,b,c,d])' // are flipped, i.e., they do not in Star(ab) anymore. // 'fliptets[0]' ([e,d,a,b]) is in Star(ab), it is saved in // 'abtets[i-1]' (adjust it to be [a,b,e,d]), see below: // // before after // [0] |___________| [0] |___________| // ... |___________| ... |___________| // [i-1] |_[a,b,e,c]_| [i-1] |_[a,b,e,d]_| // [i] |_[a,b,c,d]_| --> [i] |_[a,b,d,#]_| // [i+1] |_[a,b,d,#]_| [i+1] |_[a,b,#,*]_| // ... |___________| ... |___________| // [n-2] |___________| [n-2] |___________| // [n-1] |___________| [n-1] |_[i]_2-t-3_| // edestoppoself(fliptets[0]); // [a,b,e,d] // Increase the counter of this new tet (it is in Star(ab)). increaseelemcounter(fliptets[0]); abtets[(i - 1 + n) % n] = fliptets[0]; for (j = i; j < n - 1; j++) { abtets[j] = abtets[j + 1]; // Upshift } // The last entry 'abtets[n-1]' is empty. It is used in two ways: // (i) it remembers the vertex 'c' (in 'abtets[n-1].tet'), and // (ii) it remembers the position [i] where this flip took place. // These information let us to either undo this flip or recover // the original edge link (for collecting new created tets). abtets[n - 1].tet = (tetrahedron*)pc; abtets[n - 1].ver = 0; // Clear it. // 'abtets[n - 1].ver' is in range [0,11] -- only uses 4 bits. // Use the 5th bit in 'abtets[n - 1].ver' to signal a 2-to-3 flip. abtets[n - 1].ver |= (1 << 4); // The poisition [i] of this flip is saved above the 7th bit. abtets[n - 1].ver |= (i << 6); if (fc->collectnewtets) { // Push the two new tets [e,d,b,c] and [e,d,c,a] into a stack. // Re-use the global array 'cavetetlist'. for (j = 1; j < 3; j++) { cavetetlist->newindex((void**)&parytet); *parytet = fliptets[j]; // fliptets[1], fliptets[2]. } } // Star(ab) is reduced. Try to flip the edge [a,b]. nn = flipnm(abtets, n - 1, level, abedgepivot, fc); if (nn == 2) { // The edge has been flipped. return nn; } else { // if (nn > 2) // The edge is not flipped. if (fc->unflip || (ori == 0)) { // Undo the previous 2-to-3 flip, i.e., do a 3-to-2 flip to // transform [e,d] => [a,b,c]. // 'ori == 0' means that the previous flip created a degenerated // tet. It must be removed. // Remember that 'abtets[i-1]' is [a,b,e,d]. We can use it to // find another two tets [e,d,b,c] and [e,d,c,a]. fliptets[0] = abtets[(i - 1 + (n - 1)) % (n - 1)]; // [a,b,e,d] edestoppoself(fliptets[0]); // [e,d,a,b] fnext(fliptets[0], fliptets[1]); // [1] is [e,d,b,c] fnext(fliptets[1], fliptets[2]); // [2] is [e,d,c,a] // Restore the two original tets in Star(ab). flip32(fliptets, hullflag, fc); // Marktest the two restored tets in Star(ab). for (j = 0; j < 2; j++) { increaseelemcounter(fliptets[j]); } // Expand the array 'abtets', maintain the original order. for (j = n - 2; j >= i; j--) { abtets[j + 1] = abtets[j]; // Downshift } // Insert the two new tets 'fliptets[0]' [a,b,c,d] and // 'fliptets[1]' [b,a,c,e] into the (i-1)-th and i-th entries, // respectively. esym(fliptets[1], abtets[(i - 1 + n) % n]); // [a,b,e,c] abtets[i] = fliptets[0]; // [a,b,c,d] nn++; if (fc->collectnewtets) { // Pop two (flipped) tets from the stack. cavetetlist->objects -= 2; } } // if (unflip || (ori == 0)) } // if (nn > 2) if (!fc->unflip) { // The flips are not reversed. The current Star(ab) can not be // further reduced. Return its current size (# of tets). return nn; } // unflip is set. // Continue the search for flips. } } // if (reducflag) } // i // The Star(ab) is not reduced. if (reflexlinkedgecount > 0) { // There are reflex edges in the Link(ab). if (((b->fliplinklevel < 0) && (level < autofliplinklevel)) || ((b->fliplinklevel >= 0) && (level < b->fliplinklevel))) { // Try to reduce the Star(ab) by flipping a reflex edge in Link(ab). for (i = 0; i < n; i++) { // Do not flip this face [a,b,c] if there are two Stars involved. if ((elemcounter(abtets[i]) > 1) || (elemcounter(abtets[(i - 1 + n) % n]) > 1)) { continue; } pc = apex(abtets[i]); if (pc == dummypoint) { continue; // [a,b] is a hull edge. } pd = apex(abtets[(i + 1) % n]); pe = apex(abtets[(i - 1 + n) % n]); if ((pd == dummypoint) || (pe == dummypoint)) { continue; // [a,b,c] is a hull face. } edgepivot = 0; // No edge is selected yet. // Test if [b,c] is locally convex or flat. ori = orient3d(pb, pc, pd, pe); if (ori <= 0) { // Select the edge [c,b]. enext(abtets[i], flipedge); // [b,c,a,d] edgepivot = 1; } if (!edgepivot) { // Test if [c,a] is locally convex or flat. ori = orient3d(pc, pa, pd, pe); if (ori <= 0) { // Select the edge [a,c]. eprev(abtets[i], flipedge); // [c,a,b,d]. edgepivot = 2; } } if (!edgepivot) continue; // An edge is selected. if (checksubsegflag) { // Do not flip it if it is a segment. if (issubseg(flipedge)) { if (fc->collectencsegflag) { face checkseg, *paryseg; tsspivot1(flipedge, checkseg); if (!sinfected(checkseg)) { // Queue this segment in list. sinfect(checkseg); caveencseglist->newindex((void**)&paryseg); *paryseg = checkseg; } } continue; } } // Try to flip the selected edge ([c,b] or [a,c]). esymself(flipedge); // Count the number of tets at the edge. n1 = 0; j = 0; // Sum of the star counters. spintet = flipedge; while (1) { n1++; j += (elemcounter(spintet)); fnextself(spintet); if (spintet.tet == flipedge.tet) break; } if (n1 < 3) { // This is only possible when the mesh contains inverted // elements. Reprot a bug. terminatetetgen(this, 2); } if (j > 2) { // The Star(flipedge) overlaps other Stars. continue; // Do not flip this edge. } if ((b->flipstarsize > 0) && (n1 > b->flipstarsize)) { // The star size exceeds the given limit. continue; // Do not flip it. } // Allocate spaces for Star(flipedge). tmpabtets = new triface[n1]; // Form the Star(flipedge). j = 0; spintet = flipedge; while (1) { tmpabtets[j] = spintet; // Increase the star counter of this tet. increaseelemcounter(tmpabtets[j]); j++; fnextself(spintet); if (spintet.tet == flipedge.tet) break; } // Try to flip the selected edge away. nn = flipnm(tmpabtets, n1, level + 1, edgepivot, fc); if (nn == 2) { // The edge is flipped. Star(ab) is reduced. // Shrink the array 'abtets', maintain the original order. if (edgepivot == 1) { // 'tmpabtets[0]' is [d,a,e,b] => contains [a,b]. spintet = tmpabtets[0]; // [d,a,e,b] enextself(spintet); esymself(spintet); enextself(spintet); // [a,b,e,d] } else { // 'tmpabtets[1]' is [b,d,e,a] => contains [a,b]. spintet = tmpabtets[1]; // [b,d,e,a] eprevself(spintet); esymself(spintet); eprevself(spintet); // [a,b,e,d] } // edgepivot == 2 increaseelemcounter(spintet); // It is in Star(ab). // Put the new tet at [i-1]-th entry. abtets[(i - 1 + n) % n] = spintet; for (j = i; j < n - 1; j++) { abtets[j] = abtets[j + 1]; // Upshift } // Remember the flips in the last entry of the array 'abtets'. // They can be used to recover the flipped edge. abtets[n - 1].tet = (tetrahedron*)tmpabtets; // The star(fedge). abtets[n - 1].ver = 0; // Clear it. // Use the 1st and 2nd bit to save 'edgepivot' (1 or 2). abtets[n - 1].ver |= edgepivot; // Use the 6th bit to signal this n1-to-m1 flip. abtets[n - 1].ver |= (1 << 5); // The poisition [i] of this flip is saved from 7th to 19th bit. abtets[n - 1].ver |= (i << 6); // The size of the star 'n1' is saved from 20th bit. abtets[n - 1].ver |= (n1 << 19); // Remember the flipped link vertex 'c'. It can be used to recover // the original edge link of [a,b], and to collect new tets. tmpabtets[0].tet = (tetrahedron*)pc; tmpabtets[0].ver = (1 << 5); // Flag it as a vertex handle. // Continue to flip the edge [a,b]. nn = flipnm(abtets, n - 1, level, abedgepivot, fc); if (nn == 2) { // The edge has been flipped. return nn; } else { // if (nn > 2) { // The edge is not flipped. if (fc->unflip) { // Recover the flipped edge ([c,b] or [a,c]). // The sequence of flips are saved in 'tmpabtets'. // abtets[(i-1) % (n-1)] is [a,b,e,d], i.e., the tet created by // the flipping of edge [c,b] or [a,c].It must still exist in // Star(ab). It is the start tet to recover the flipped edge. if (edgepivot == 1) { // The flip edge is [c,b]. tmpabtets[0] = abtets[((i - 1) + (n - 1)) % (n - 1)]; // [a,b,e,d] eprevself(tmpabtets[0]); esymself(tmpabtets[0]); eprevself(tmpabtets[0]); // [d,a,e,b] fsym(tmpabtets[0], tmpabtets[1]); // [a,d,e,c] } else { // The flip edge is [a,c]. tmpabtets[1] = abtets[((i - 1) + (n - 1)) % (n - 1)]; // [a,b,e,d] enextself(tmpabtets[1]); esymself(tmpabtets[1]); enextself(tmpabtets[1]); // [b,d,e,a] fsym(tmpabtets[1], tmpabtets[0]); // [d,b,e,c] } // if (edgepivot == 2) // Recover the flipped edge ([c,b] or [a,c]). flipnm_post(tmpabtets, n1, 2, edgepivot, fc); // Insert the two recovered tets into Star(ab). for (j = n - 2; j >= i; j--) { abtets[j + 1] = abtets[j]; // Downshift } if (edgepivot == 1) { // tmpabtets[0] is [c,b,d,a] ==> contains [a,b] // tmpabtets[1] is [c,b,a,e] ==> contains [a,b] // tmpabtets[2] is [c,b,e,d] fliptets[0] = tmpabtets[1]; enextself(fliptets[0]); esymself(fliptets[0]); // [a,b,e,c] fliptets[1] = tmpabtets[0]; esymself(fliptets[1]); eprevself(fliptets[1]); // [a,b,c,d] } else { // tmpabtets[0] is [a,c,d,b] ==> contains [a,b] // tmpabtets[1] is [a,c,b,e] ==> contains [a,b] // tmpabtets[2] is [a,c,e,d] fliptets[0] = tmpabtets[1]; eprevself(fliptets[0]); esymself(fliptets[0]); // [a,b,e,c] fliptets[1] = tmpabtets[0]; esymself(fliptets[1]); enextself(fliptets[1]); // [a,b,c,d] } // edgepivot == 2 for (j = 0; j < 2; j++) { increaseelemcounter(fliptets[j]); } // Insert the two recovered tets into Star(ab). abtets[(i - 1 + n) % n] = fliptets[0]; abtets[i] = fliptets[1]; nn++; // Release the allocated spaces. delete[] tmpabtets; } // if (unflip) } // if (nn > 2) if (!fc->unflip) { // The flips are not reversed. The current Star(ab) can not be // further reduced. Return its size (# of tets). return nn; } // unflip is set. // Continue the search for flips. } else { // The selected edge is not flipped. if (!fc->unflip) { // Release the memory used in this attempted flip. flipnm_post(tmpabtets, n1, nn, edgepivot, fc); } // Decrease the star counters of tets in Star(flipedge). for (j = 0; j < nn; j++) { decreaseelemcounter(tmpabtets[j]); } // Release the allocated spaces. delete[] tmpabtets; } } // i } // if (level...) } // if (reflexlinkedgecount > 0) } else { // Check if a 3-to-2 flip is possible. // Let the three apexes be c, d,and e. Hull tets may be involved. If so, // we rearrange them such that the vertex e is dummypoint. hullflag = 0; if (apex(abtets[0]) == dummypoint) { pc = apex(abtets[1]); pd = apex(abtets[2]); pe = apex(abtets[0]); hullflag = 1; } else if (apex(abtets[1]) == dummypoint) { pc = apex(abtets[2]); pd = apex(abtets[0]); pe = apex(abtets[1]); hullflag = 2; } else { pc = apex(abtets[0]); pd = apex(abtets[1]); pe = apex(abtets[2]); hullflag = (pe == dummypoint) ? 3 : 0; } reducflag = 0; rejflag = 0; if (hullflag == 0) { // Make sure that no inverted tet will be created, i.e. the new tets // [d,c,e,a] and [c,d,e,b] must be valid tets. ori = orient3d(pd, pc, pe, pa); if (ori < 0) { ori = orient3d(pc, pd, pe, pb); if (ori < 0) { reducflag = 1; } } } else { // [a,b] is a hull edge. // Note: This can happen when it is in the middle of a 4-to-4 flip. // Note: [a,b] may even be a non-convex hull edge. if (!nonconvex) { // The mesh is convex, only do flip if it is a coplanar hull edge. ori = orient3d(pa, pb, pc, pd); if (ori == 0) { reducflag = 1; } } else { // nonconvex reducflag = 1; } if (reducflag == 1) { // [a,b], [a,b,c] and [a,b,d] are on the convex hull. // Make sure that no inverted tet will be created. point searchpt = NULL, chkpt; REAL bigvol = 0.0, ori1, ori2; // Search an interior vertex which is an apex of edge [c,d]. // In principle, it can be arbitrary interior vertex. To avoid // numerical issue, we choose the vertex which belongs to a tet // 't' at edge [c,d] and 't' has the biggest volume. fliptets[0] = abtets[hullflag % 3]; // [a,b,c,d]. eorgoppoself(fliptets[0]); // [d,c,b,a] spintet = fliptets[0]; while (1) { fnextself(spintet); chkpt = oppo(spintet); if (chkpt == pb) break; if ((chkpt != dummypoint) && (apex(spintet) != dummypoint)) { ori = -orient3d(pd, pc, apex(spintet), chkpt); if (ori > bigvol) { bigvol = ori; searchpt = chkpt; } } } if (searchpt != NULL) { // Now valid the configuration. ori1 = orient3d(pd, pc, searchpt, pa); ori2 = orient3d(pd, pc, searchpt, pb); if (ori1 * ori2 >= 0.0) { reducflag = 0; // Not valid. } else { ori1 = orient3d(pa, pb, searchpt, pc); ori2 = orient3d(pa, pb, searchpt, pd); if (ori1 * ori2 >= 0.0) { reducflag = 0; // Not valid. } } } else { // No valid searchpt is found. reducflag = 0; // Do not flip it. } } // if (reducflag == 1) } // if (hullflag == 1) if (reducflag) { // A 3-to-2 flip is possible. if (checksubfaceflag) { // This edge (must not be a segment) can be flipped ONLY IF it belongs // to either 0 or 2 subfaces. In the latter case, a 2-to-2 flip in // the surface mesh will be automatically performed within the // 3-to-2 flip. nn = 0; edgepivot = -1; // Re-use it. for (j = 0; j < 3; j++) { if (issubface(abtets[j])) { nn++; // Found a subface. } else { edgepivot = j; } } if (nn == 1) { // Found only 1 subface containing this edge. This can happen in // the boundary recovery phase. The neighbor subface is not yet // recovered. This edge should not be flipped at this moment. rejflag = 1; } else if (nn == 2) { // Found two subfaces. A 2-to-2 flip is possible. Validate it. // Below we check if the two faces [p,q,a] and [p,q,b] are subfaces. eorgoppo(abtets[(edgepivot + 1) % 3], spintet); // [q,p,b,a] if (issubface(spintet)) { rejflag = 1; // Conflict to a 2-to-2 flip. } else { esymself(spintet); if (issubface(spintet)) { rejflag = 1; // Conflict to a 2-to-2 flip. } } } else if (nn == 3) { // Report a bug. terminatetetgen(this, 2); } } if (!rejflag && fc->checkflipeligibility) { // Here we must exchange 'a' and 'b'. Since in the check... function, // we assume the following point sequence, 'a,b,c,d,e', where // the face [a,b,c] will be flipped and the edge [e,d] will be // created. The two new tets are [a,b,c,d] and [b,a,c,e]. rejflag = checkflipeligibility(2, pc, pd, pe, pb, pa, level, abedgepivot, fc); } if (!rejflag) { // Do flip: [a,b] => [c,d,e] flip32(abtets, hullflag, fc); if (fc->remove_ndelaunay_edge) { if (level == 0) { // It is the desired removing edge. Check if we have improved // the objective function. if ((fc->tetprism_vol_sum >= 0.0) || (fabs(fc->tetprism_vol_sum) < fc->bak_tetprism_vol)) { // No improvement! flip back: [c,d,e] => [a,b]. flip23(abtets, hullflag, fc); // Increase the element counter -- They are in cavity. for (j = 0; j < 3; j++) { increaseelemcounter(abtets[j]); } return 3; } } // if (level == 0) } if (fc->collectnewtets) { // Collect new tets. if (level == 0) { // Push the two new tets into stack. for (j = 0; j < 2; j++) { cavetetlist->newindex((void**)&parytet); *parytet = abtets[j]; } } else { // Only one of the new tets is collected. The other one is inside // the reduced edge star. 'abedgepivot' is either '1' or '2'. cavetetlist->newindex((void**)&parytet); if (abedgepivot == 1) { // [c,b] *parytet = abtets[1]; } else { *parytet = abtets[0]; } } } // if (fc->collectnewtets) return 2; } } // if (reducflag) } // if (n == 3) // The current (reduced) Star size. return n; } /////////////////////////////////////////////////////////////////////////////// // // // flipnm_post() Post process a n-to-m flip. // // // // IMPORTANT: This routine only works when there is no other flip operation // // is done after flipnm([a,b]) which attempts to remove an edge [a,b]. // // // // 'abtets' is an array of 'n' (>= 3) tets which are in the original star of // // [a,b] before flipnm([a,b]). 'nn' (< n) is the value returned by flipnm. // // If 'nn == 2', the edge [a,b] has been flipped. 'abtets[0]' and 'abtets[1]'// // are [c,d,e,b] and [d,c,e,a], i.e., a 2-to-3 flip can recover the edge [a, // // b] and its initial Star([a,b]). If 'nn >= 3' edge [a,b] still exists in // // current mesh and 'nn' is the current number of tets in Star([a,b]). // // // // Each 'abtets[i]', where nn <= i < n, saves either a 2-to-3 flip or a // // flipnm([p1,p2]) operation ([p1,p2] != [a,b]) which created the tet // // 'abtets[t-1]', where '0 <= t <= i'. These information can be used to // // undo the flips performed in flipnm([a,b]) or to collect new tets created // // by the flipnm([a,b]) operation. // // // // Default, this routine only walks through the flips and frees the spaces // // allocated during the flipnm([a,b]) operation. // // // // If the flag 'fc->unflip' is set, this routine un-does the flips performed // // in flipnm([a,b]) so that the mesh is returned to its original state // // before doing the flipnm([a,b]) operation. // // // // // /////////////////////////////////////////////////////////////////////////////// int tetgenmesh::flipnm_post(triface* abtets, int n, int nn, int abedgepivot, flipconstraints* fc) { triface fliptets[3], flipface; triface* tmpabtets; int fliptype; int edgepivot; int t, n1; int i, j; if (nn == 2) { // The edge [a,b] has been flipped. // 'abtets[0]' is [c,d,e,b] or [#,#,#,b]. // 'abtets[1]' is [d,c,e,a] or [#,#,#,a]. if (fc->unflip) { // Do a 2-to-3 flip to recover the edge [a,b]. There may be hull tets. flip23(abtets, 1, fc); if (fc->collectnewtets) { // Pop up new (flipped) tets from the stack. if (abedgepivot == 0) { // Two new tets were collected. cavetetlist->objects -= 2; } else { // Only one of the two new tets was collected. cavetetlist->objects -= 1; } } } // The initial size of Star(ab) is 3. nn++; } // Walk through the performed flips. for (i = nn; i < n; i++) { // At the beginning of each step 'i', the size of the Star([a,b]) is 'i'. // At the end of this step, the size of the Star([a,b]) is 'i+1'. // The sizes of the Link([a,b]) are the same. fliptype = ((abtets[i].ver >> 4) & 3); // 0, 1, or 2. if (fliptype == 1) { // It was a 2-to-3 flip: [a,b,c]->[e,d]. t = (abtets[i].ver >> 6); if (fc->unflip) { if (b->verbose > 2) { printf(" Recover a 2-to-3 flip at f[%d].\n", t); } // 'abtets[(t-1)%i]' is the tet [a,b,e,d] in current Star(ab), i.e., // it is created by a 2-to-3 flip [a,b,c] => [e,d]. fliptets[0] = abtets[((t - 1) + i) % i]; // [a,b,e,d] eprevself(fliptets[0]); esymself(fliptets[0]); enextself(fliptets[0]); // [e,d,a,b] fnext(fliptets[0], fliptets[1]); // [e,d,b,c] fnext(fliptets[1], fliptets[2]); // [e,d,c,a] // Do a 3-to-2 flip: [e,d] => [a,b,c]. // NOTE: hull tets may be invloved. flip32(fliptets, 1, fc); // Expand the array 'abtets', maintain the original order. // The new array length is (i+1). for (j = i - 1; j >= t; j--) { abtets[j + 1] = abtets[j]; // Downshift } // The tet abtets[(t-1)%i] is deleted. Insert the two new tets // 'fliptets[0]' [a,b,c,d] and 'fliptets[1]' [b,a,c,e] into // the (t-1)-th and t-th entries, respectively. esym(fliptets[1], abtets[((t - 1) + (i + 1)) % (i + 1)]); // [a,b,e,c] abtets[t] = fliptets[0]; // [a,b,c,d] if (fc->collectnewtets) { // Pop up two (flipped) tets from the stack. cavetetlist->objects -= 2; } } } else if (fliptype == 2) { tmpabtets = (triface*)(abtets[i].tet); n1 = ((abtets[i].ver >> 19) & 8191); // \sum_{i=0^12}{2^i} = 8191 edgepivot = (abtets[i].ver & 3); t = ((abtets[i].ver >> 6) & 8191); if (fc->unflip) { if (b->verbose > 2) { printf(" Recover a %d-to-m flip at e[%d] of f[%d].\n", n1, edgepivot, t); } // Recover the flipped edge ([c,b] or [a,c]). // abtets[(t - 1 + i) % i] is [a,b,e,d], i.e., the tet created by // the flipping of edge [c,b] or [a,c]. It must still exist in // Star(ab). Use it to recover the flipped edge. if (edgepivot == 1) { // The flip edge is [c,b]. tmpabtets[0] = abtets[(t - 1 + i) % i]; // [a,b,e,d] eprevself(tmpabtets[0]); esymself(tmpabtets[0]); eprevself(tmpabtets[0]); // [d,a,e,b] fsym(tmpabtets[0], tmpabtets[1]); // [a,d,e,c] } else { // The flip edge is [a,c]. tmpabtets[1] = abtets[(t - 1 + i) % i]; // [a,b,e,d] enextself(tmpabtets[1]); esymself(tmpabtets[1]); enextself(tmpabtets[1]); // [b,d,e,a] fsym(tmpabtets[1], tmpabtets[0]); // [d,b,e,c] } // if (edgepivot == 2) // Do a n1-to-m1 flip to recover the flipped edge ([c,b] or [a,c]). flipnm_post(tmpabtets, n1, 2, edgepivot, fc); // Insert the two recovered tets into the original Star(ab). for (j = i - 1; j >= t; j--) { abtets[j + 1] = abtets[j]; // Downshift } if (edgepivot == 1) { // tmpabtets[0] is [c,b,d,a] ==> contains [a,b] // tmpabtets[1] is [c,b,a,e] ==> contains [a,b] // tmpabtets[2] is [c,b,e,d] fliptets[0] = tmpabtets[1]; enextself(fliptets[0]); esymself(fliptets[0]); // [a,b,e,c] fliptets[1] = tmpabtets[0]; esymself(fliptets[1]); eprevself(fliptets[1]); // [a,b,c,d] } else { // tmpabtets[0] is [a,c,d,b] ==> contains [a,b] // tmpabtets[1] is [a,c,b,e] ==> contains [a,b] // tmpabtets[2] is [a,c,e,d] fliptets[0] = tmpabtets[1]; eprevself(fliptets[0]); esymself(fliptets[0]); // [a,b,e,c] fliptets[1] = tmpabtets[0]; esymself(fliptets[1]); enextself(fliptets[1]); // [a,b,c,d] } // edgepivot == 2 // Insert the two recovered tets into Star(ab). abtets[((t - 1) + (i + 1)) % (i + 1)] = fliptets[0]; abtets[t] = fliptets[1]; } else { // Only free the spaces. flipnm_post(tmpabtets, n1, 2, edgepivot, fc); } // if (!unflip) if (b->verbose > 2) { printf(" Release %d spaces at f[%d].\n", n1, i); } delete[] tmpabtets; } } // i return 1; } /////////////////////////////////////////////////////////////////////////////// // // // insertpoint() Insert a point into current tetrahedralization. // // // // The Bowyer-Watson (B-W) algorithm is used to add a new point p into the // // tetrahedralization T. It first finds a "cavity", denoted as C, in T, C // // consists of tetrahedra in T that "conflict" with p. If T is a Delaunay // // tetrahedralization, then all boundary faces (triangles) of C are visible // // by p, i.e.,C is star-shaped. We can insert p into T by first deleting all // // tetrahedra in C, then creating new tetrahedra formed by boundary faces of // // C and p. If T is not a DT, then C may be not star-shaped. It must be // // modified so that it becomes star-shaped. // // // /////////////////////////////////////////////////////////////////////////////// int tetgenmesh::insertpoint(point insertpt, triface* searchtet, face* splitsh, face* splitseg, insertvertexflags* ivf) { arraypool* swaplist; triface *cavetet, spintet, neightet, neineitet, *parytet; triface oldtet, newtet, newneitet; face checksh, neighsh, *parysh; face checkseg, *paryseg; point *pts, pa, pb, pc, *parypt; enum locateresult loc = OUTSIDE; REAL sign, ori; REAL attrib, volume; bool enqflag; int t1ver; int i, j, k, s; if (b->verbose > 2) { printf(" Insert point %d\n", pointmark(insertpt)); } // Locate the point. if (searchtet->tet != NULL) { loc = (enum locateresult)ivf->iloc; } if (loc == OUTSIDE) { if (searchtet->tet == NULL) { if (!b->weighted) { randomsample(insertpt, searchtet); } else { // Weighted DT. There may exist dangling vertex. *searchtet = recenttet; } } // Locate the point. loc = locate(insertpt, searchtet); } ivf->iloc = (int)loc; // The return value. if (b->weighted) { if (loc != OUTSIDE) { // Check if this vertex is regular. pts = (point*)searchtet->tet; sign = orient4d_s(pts[4], pts[5], pts[6], pts[7], insertpt, pts[4][3], pts[5][3], pts[6][3], pts[7][3], insertpt[3]); if (sign > 0) { // This new vertex lies above the lower hull. Do not insert it. ivf->iloc = (int)NONREGULAR; return 0; } } } // Create the initial cavity C(p) which contains all tetrahedra that // intersect p. It may include 1, 2, or n tetrahedra. // If p lies on a segment or subface, also create the initial sub-cavity // sC(p) which contains all subfaces (and segment) which intersect p. if (loc == OUTSIDE) { flip14count++; // The current hull will be enlarged. // Add four adjacent boundary tets into list. for (i = 0; i < 4; i++) { decode(searchtet->tet[i], neightet); neightet.ver = epivot[neightet.ver]; cavebdrylist->newindex((void**)&parytet); *parytet = neightet; } infect(*searchtet); caveoldtetlist->newindex((void**)&parytet); *parytet = *searchtet; } else if (loc == INTETRAHEDRON) { flip14count++; // Add four adjacent boundary tets into list. for (i = 0; i < 4; i++) { decode(searchtet->tet[i], neightet); neightet.ver = epivot[neightet.ver]; cavebdrylist->newindex((void**)&parytet); *parytet = neightet; } infect(*searchtet); caveoldtetlist->newindex((void**)&parytet); *parytet = *searchtet; } else if (loc == ONFACE) { flip26count++; // Add six adjacent boundary tets into list. j = (searchtet->ver & 3); // The current face number. for (i = 1; i < 4; i++) { decode(searchtet->tet[(j + i) % 4], neightet); neightet.ver = epivot[neightet.ver]; cavebdrylist->newindex((void**)&parytet); *parytet = neightet; } decode(searchtet->tet[j], spintet); j = (spintet.ver & 3); // The current face number. for (i = 1; i < 4; i++) { decode(spintet.tet[(j + i) % 4], neightet); neightet.ver = epivot[neightet.ver]; cavebdrylist->newindex((void**)&parytet); *parytet = neightet; } infect(spintet); caveoldtetlist->newindex((void**)&parytet); *parytet = spintet; infect(*searchtet); caveoldtetlist->newindex((void**)&parytet); *parytet = *searchtet; if (ivf->splitbdflag) { if ((splitsh != NULL) && (splitsh->sh != NULL)) { // Create the initial sub-cavity sC(p). smarktest(*splitsh); caveshlist->newindex((void**)&parysh); *parysh = *splitsh; } } // if (splitbdflag) } else if (loc == ONEDGE) { flipn2ncount++; // Add all adjacent boundary tets into list. spintet = *searchtet; while (1) { eorgoppo(spintet, neightet); decode(neightet.tet[neightet.ver & 3], neightet); neightet.ver = epivot[neightet.ver]; cavebdrylist->newindex((void**)&parytet); *parytet = neightet; edestoppo(spintet, neightet); decode(neightet.tet[neightet.ver & 3], neightet); neightet.ver = epivot[neightet.ver]; cavebdrylist->newindex((void**)&parytet); *parytet = neightet; infect(spintet); caveoldtetlist->newindex((void**)&parytet); *parytet = spintet; fnextself(spintet); if (spintet.tet == searchtet->tet) break; } // while (1) if (ivf->splitbdflag) { // Create the initial sub-cavity sC(p). if ((splitseg != NULL) && (splitseg->sh != NULL)) { smarktest(*splitseg); splitseg->shver = 0; spivot(*splitseg, *splitsh); } if (splitsh != NULL) { if (splitsh->sh != NULL) { // Collect all subfaces share at this edge. pa = sorg(*splitsh); neighsh = *splitsh; while (1) { // Adjust the origin of its edge to be 'pa'. if (sorg(neighsh) != pa) { sesymself(neighsh); } // Add this face into list (in B-W cavity). smarktest(neighsh); caveshlist->newindex((void**)&parysh); *parysh = neighsh; // Add this face into face-at-splitedge list. cavesegshlist->newindex((void**)&parysh); *parysh = neighsh; // Go to the next face at the edge. spivotself(neighsh); // Stop if all faces at the edge have been visited. if (neighsh.sh == splitsh->sh) break; if (neighsh.sh == NULL) break; } // while (1) } // if (not a dangling segment) } } // if (splitbdflag) } else if (loc == INSTAR) { // We assume that all tets in the star are given in 'caveoldtetlist', // and they are all infected. // Collect the boundary faces of the star. for (i = 0; i < caveoldtetlist->objects; i++) { cavetet = (triface*)fastlookup(caveoldtetlist, i); // Check its 4 neighbor tets. for (j = 0; j < 4; j++) { decode(cavetet->tet[j], neightet); if (!infected(neightet)) { // It's a boundary face. neightet.ver = epivot[neightet.ver]; cavebdrylist->newindex((void**)&parytet); *parytet = neightet; } } } } else if (loc == ONVERTEX) { // The point already exist. Do nothing and return. return 0; } if (ivf->assignmeshsize) { // Assign mesh size for the new point. if (bgm != NULL) { // Interpolate the mesh size from the background mesh. bgm->decode(point2bgmtet(org(*searchtet)), neightet); int bgmloc = (int)bgm->scoutpoint(insertpt, &neightet, 0); if (bgmloc != (int)OUTSIDE) { insertpt[pointmtrindex] = bgm->getpointmeshsize(insertpt, &neightet, bgmloc); setpoint2bgmtet(insertpt, bgm->encode(neightet)); } } else { insertpt[pointmtrindex] = getpointmeshsize(insertpt, searchtet, (int)loc); } } // if (assignmeshsize) if (ivf->bowywat) { // Update the cavity C(p) using the Bowyer-Watson algorithm. swaplist = cavetetlist; cavetetlist = cavebdrylist; cavebdrylist = swaplist; for (i = 0; i < cavetetlist->objects; i++) { // 'cavetet' is an adjacent tet at outside of the cavity. cavetet = (triface*)fastlookup(cavetetlist, i); // The tet may be tested and included in the (enlarged) cavity. if (!infected(*cavetet)) { // Check for two possible cases for this tet: // (1) It is a cavity tet, or // (2) it is a cavity boundary face. enqflag = false; if (!marktested(*cavetet)) { // Do Delaunay (in-sphere) test. pts = (point*)cavetet->tet; if (pts[7] != dummypoint) { // A volume tet. Operate on it. if (b->weighted) { sign = orient4d_s(pts[4], pts[5], pts[6], pts[7], insertpt, pts[4][3], pts[5][3], pts[6][3], pts[7][3], insertpt[3]); } else { sign = insphere_s(pts[4], pts[5], pts[6], pts[7], insertpt); } enqflag = (sign < 0.0); } else { if (!nonconvex) { // Test if this hull face is visible by the new point. ori = orient3d(pts[4], pts[5], pts[6], insertpt); if (ori < 0) { // A visible hull face. // Include it in the cavity. The convex hull will be enlarged. enqflag = true; } else if (ori == 0.0) { // A coplanar hull face. We need to test if this hull face is // Delaunay or not. We test if the adjacent tet (not faked) // of this hull face is Delaunay or not. decode(cavetet->tet[3], neineitet); if (!infected(neineitet)) { if (!marktested(neineitet)) { // Do Delaunay test on this tet. pts = (point*)neineitet.tet; if (b->weighted) { sign = orient4d_s(pts[4], pts[5], pts[6], pts[7], insertpt, pts[4][3], pts[5][3], pts[6][3], pts[7][3], insertpt[3]); } else { sign = insphere_s(pts[4], pts[5], pts[6], pts[7], insertpt); } enqflag = (sign < 0.0); } } else { // The adjacent tet is non-Delaunay. The hull face is non- // Delaunay as well. Include it in the cavity. enqflag = true; } // if (!infected(neineitet)) } // if (ori == 0.0) } else { // A hull face (must be a subface). // We FIRST include it in the initial cavity if the adjacent tet // (not faked) of this hull face is not Delaunay wrt p. // Whether it belongs to the final cavity will be determined // during the validation process. 'validflag'. decode(cavetet->tet[3], neineitet); if (!infected(neineitet)) { if (!marktested(neineitet)) { // Do Delaunay test on this tet. pts = (point*)neineitet.tet; if (b->weighted) { sign = orient4d_s(pts[4], pts[5], pts[6], pts[7], insertpt, pts[4][3], pts[5][3], pts[6][3], pts[7][3], insertpt[3]); } else { sign = insphere_s(pts[4], pts[5], pts[6], pts[7], insertpt); } enqflag = (sign < 0.0); } } else { // The adjacent tet is non-Delaunay. The hull face is non- // Delaunay as well. Include it in the cavity. enqflag = true; } // if (infected(neineitet)) } // if (nonconvex) } // if (pts[7] != dummypoint) marktest(*cavetet); // Only test it once. } // if (!marktested(*cavetet)) if (enqflag) { // Found a tet in the cavity. Put other three faces in check list. k = (cavetet->ver & 3); // The current face number for (j = 1; j < 4; j++) { decode(cavetet->tet[(j + k) % 4], neightet); cavetetlist->newindex((void**)&parytet); *parytet = neightet; } infect(*cavetet); caveoldtetlist->newindex((void**)&parytet); *parytet = *cavetet; } else { // Found a boundary face of the cavity. cavetet->ver = epivot[cavetet->ver]; cavebdrylist->newindex((void**)&parytet); *parytet = *cavetet; } } // if (!infected(*cavetet)) } // i cavetetlist->restart(); // Clear the working list. } // if (ivf->bowywat) if (checksubsegflag) { // Collect all segments of C(p). shellface* ssptr; for (i = 0; i < caveoldtetlist->objects; i++) { cavetet = (triface*)fastlookup(caveoldtetlist, i); if ((ssptr = (shellface*)cavetet->tet[8]) != NULL) { for (j = 0; j < 6; j++) { if (ssptr[j]) { sdecode(ssptr[j], checkseg); if (!sinfected(checkseg)) { sinfect(checkseg); cavetetseglist->newindex((void**)&paryseg); *paryseg = checkseg; } } } // j } } // i // Uninfect collected segments. for (i = 0; i < cavetetseglist->objects; i++) { paryseg = (face*)fastlookup(cavetetseglist, i); suninfect(*paryseg); } if (ivf->rejflag & 1) { // Reject this point if it encroaches upon any segment. face* paryseg1; for (i = 0; i < cavetetseglist->objects; i++) { paryseg1 = (face*)fastlookup(cavetetseglist, i); if (checkseg4encroach((point)paryseg1->sh[3], (point)paryseg1->sh[4], insertpt)) { encseglist->newindex((void**)&paryseg); *paryseg = *paryseg1; } } // i if ((ivf->rejflag & 1) && (encseglist->objects > 0)) { insertpoint_abort(splitseg, ivf); ivf->iloc = (int)ENCSEGMENT; return 0; } } } // if (checksubsegflag) if (checksubfaceflag) { // Collect all subfaces of C(p). shellface* sptr; for (i = 0; i < caveoldtetlist->objects; i++) { cavetet = (triface*)fastlookup(caveoldtetlist, i); if ((sptr = (shellface*)cavetet->tet[9]) != NULL) { for (j = 0; j < 4; j++) { if (sptr[j]) { sdecode(sptr[j], checksh); if (!sinfected(checksh)) { sinfect(checksh); cavetetshlist->newindex((void**)&parysh); *parysh = checksh; } } } // j } } // i // Uninfect collected subfaces. for (i = 0; i < cavetetshlist->objects; i++) { parysh = (face*)fastlookup(cavetetshlist, i); suninfect(*parysh); } if (ivf->rejflag & 2) { REAL rd, cent[3]; badface* bface; // Reject this point if it encroaches upon any subface. for (i = 0; i < cavetetshlist->objects; i++) { parysh = (face*)fastlookup(cavetetshlist, i); if (checkfac4encroach((point)parysh->sh[3], (point)parysh->sh[4], (point)parysh->sh[5], insertpt, cent, &rd)) { encshlist->newindex((void**)&bface); bface->ss = *parysh; bface->forg = (point)parysh->sh[3]; // Not a dad one. for (j = 0; j < 3; j++) bface->cent[j] = cent[j]; bface->key = rd; } } if (encshlist->objects > 0) { insertpoint_abort(splitseg, ivf); ivf->iloc = (int)ENCSUBFACE; return 0; } } } // if (checksubfaceflag) if ((ivf->iloc == (int)OUTSIDE) && ivf->refineflag) { // The vertex lies outside of the domain. And it does not encroach // upon any boundary segment or subface. Do not insert it. insertpoint_abort(splitseg, ivf); return 0; } if (ivf->splitbdflag) { // The new point locates in surface mesh. Update the sC(p). // We have already 'smarktested' the subfaces which directly intersect // with p in 'caveshlist'. From them, we 'smarktest' their neighboring // subfaces which are included in C(p). Do not across a segment. for (i = 0; i < caveshlist->objects; i++) { parysh = (face*)fastlookup(caveshlist, i); checksh = *parysh; for (j = 0; j < 3; j++) { if (!isshsubseg(checksh)) { spivot(checksh, neighsh); if (!smarktested(neighsh)) { stpivot(neighsh, neightet); if (infected(neightet)) { fsymself(neightet); if (infected(neightet)) { // This subface is inside C(p). // Check if its diametrical circumsphere encloses 'p'. // The purpose of this check is to avoid forming invalid // subcavity in surface mesh. sign = incircle3d(sorg(neighsh), sdest(neighsh), sapex(neighsh), insertpt); if (sign < 0) { smarktest(neighsh); caveshlist->newindex((void**)&parysh); *parysh = neighsh; } } } } } senextself(checksh); } // j } // i } // if (ivf->splitbdflag) if (ivf->validflag) { // Validate C(p) and update it if it is not star-shaped. int cutcount = 0; if (ivf->respectbdflag) { // The initial cavity may include subfaces which are not on the facets // being splitting. Find them and make them as boundary of C(p). // Comment: We have already 'smarktested' the subfaces in sC(p). They // are completely inside C(p). for (i = 0; i < cavetetshlist->objects; i++) { parysh = (face*)fastlookup(cavetetshlist, i); stpivot(*parysh, neightet); if (infected(neightet)) { fsymself(neightet); if (infected(neightet)) { // Found a subface inside C(p). if (!smarktested(*parysh)) { // It is possible that this face is a boundary subface. // Check if it is a hull face. // assert(apex(neightet) != dummypoint); if (oppo(neightet) != dummypoint) { fsymself(neightet); } if (oppo(neightet) != dummypoint) { ori = orient3d(org(neightet), dest(neightet), apex(neightet), insertpt); if (ori < 0) { // A visible face, get its neighbor face. fsymself(neightet); ori = -ori; // It must be invisible by p. } } else { // A hull tet. It needs to be cut. ori = 1; } // Cut this tet if it is either invisible by or coplanar with p. if (ori >= 0) { uninfect(neightet); unmarktest(neightet); cutcount++; neightet.ver = epivot[neightet.ver]; cavebdrylist->newindex((void**)&parytet); *parytet = neightet; // Add three new faces to find new boundaries. for (j = 0; j < 3; j++) { esym(neightet, neineitet); neineitet.ver = epivot[neineitet.ver]; cavebdrylist->newindex((void**)&parytet); *parytet = neineitet; enextself(neightet); } } // if (ori >= 0) } } } } // i // The initial cavity may include segments in its interior. We need to // Update the cavity so that these segments are on the boundary of // the cavity. for (i = 0; i < cavetetseglist->objects; i++) { paryseg = (face*)fastlookup(cavetetseglist, i); // Check this segment if it is not a splitting segment. if (!smarktested(*paryseg)) { sstpivot1(*paryseg, neightet); spintet = neightet; while (1) { if (!infected(spintet)) break; fnextself(spintet); if (spintet.tet == neightet.tet) break; } if (infected(spintet)) { // Find an adjacent tet at this segment such that both faces // at this segment are not visible by p. pa = org(neightet); pb = dest(neightet); spintet = neightet; j = 0; while (1) { // Check if this face is visible by p. pc = apex(spintet); if (pc != dummypoint) { ori = orient3d(pa, pb, pc, insertpt); if (ori >= 0) { // Not visible. Check another face in this tet. esym(spintet, neineitet); pc = apex(neineitet); if (pc != dummypoint) { ori = orient3d(pb, pa, pc, insertpt); if (ori >= 0) { // Not visible. Found this face. j = 1; // Flag that it is found. break; } } } } fnextself(spintet); if (spintet.tet == neightet.tet) break; } if (j == 0) { // Not found such a face. terminatetetgen(this, 2); } neightet = spintet; if (b->verbose > 3) { printf(" Cut tet (%d, %d, %d, %d)\n", pointmark(org(neightet)), pointmark(dest(neightet)), pointmark(apex(neightet)), pointmark(oppo(neightet))); } uninfect(neightet); unmarktest(neightet); cutcount++; neightet.ver = epivot[neightet.ver]; cavebdrylist->newindex((void**)&parytet); *parytet = neightet; // Add three new faces to find new boundaries. for (j = 0; j < 3; j++) { esym(neightet, neineitet); neineitet.ver = epivot[neineitet.ver]; cavebdrylist->newindex((void**)&parytet); *parytet = neineitet; enextself(neightet); } } } } // i } // if (ivf->respectbdflag) // Update the cavity by removing invisible faces until it is star-shaped. for (i = 0; i < cavebdrylist->objects; i++) { cavetet = (triface*)fastlookup(cavebdrylist, i); // 'cavetet' is an exterior tet adjacent to the cavity. // Check if its neighbor is inside C(p). fsym(*cavetet, neightet); if (infected(neightet)) { if (apex(*cavetet) != dummypoint) { // It is a cavity boundary face. Check its visibility. if (oppo(neightet) != dummypoint) { // Check if this face is visible by the new point. if (issubface(neightet)) { // We should only create a new tet that has a reasonable volume. // Re-use 'volume' and 'attrib'. pa = org(*cavetet); pb = dest(*cavetet); pc = apex(*cavetet); volume = orient3dfast(pa, pb, pc, insertpt); attrib = distance(pa, pb) * distance(pb, pc) * distance(pc, pa); if ((fabs(volume) / attrib) < b->epsilon) { ori = 0.0; } else { ori = orient3d(pa, pb, pc, insertpt); } } else { ori = orient3d(org(*cavetet), dest(*cavetet), apex(*cavetet), insertpt); } enqflag = (ori > 0); // Comment: if ori == 0 (coplanar case), we also cut the tet. } else { // It is a hull face. And its adjacent tet (at inside of the // domain) has been cut from the cavity. Cut it as well. // assert(nonconvex); enqflag = false; } } else { enqflag = true; // A hull edge. } if (enqflag) { // This face is valid, save it. cavetetlist->newindex((void**)&parytet); *parytet = *cavetet; } else { uninfect(neightet); unmarktest(neightet); cutcount++; // Add three new faces to find new boundaries. for (j = 0; j < 3; j++) { esym(neightet, neineitet); neineitet.ver = epivot[neineitet.ver]; cavebdrylist->newindex((void**)&parytet); *parytet = neineitet; enextself(neightet); } // 'cavetet' is not on the cavity boundary anymore. unmarktest(*cavetet); } } else { // 'cavetet' is not on the cavity boundary anymore. unmarktest(*cavetet); } } // i if (cutcount > 0) { // The cavity has been updated. // Update the cavity boundary faces. cavebdrylist->restart(); for (i = 0; i < cavetetlist->objects; i++) { cavetet = (triface*)fastlookup(cavetetlist, i); // 'cavetet' was an exterior tet adjacent to the cavity. fsym(*cavetet, neightet); if (infected(neightet)) { // It is a cavity boundary face. cavebdrylist->newindex((void**)&parytet); *parytet = *cavetet; } else { // Not a cavity boundary face. unmarktest(*cavetet); } } // Update the list of old tets. cavetetlist->restart(); for (i = 0; i < caveoldtetlist->objects; i++) { cavetet = (triface*)fastlookup(caveoldtetlist, i); if (infected(*cavetet)) { cavetetlist->newindex((void**)&parytet); *parytet = *cavetet; } } // Swap 'cavetetlist' and 'caveoldtetlist'. swaplist = caveoldtetlist; caveoldtetlist = cavetetlist; cavetetlist = swaplist; // The cavity should contain at least one tet. if (caveoldtetlist->objects == 0l) { insertpoint_abort(splitseg, ivf); ivf->iloc = (int)BADELEMENT; return 0; } if (ivf->splitbdflag) { int cutshcount = 0; // Update the sub-cavity sC(p). for (i = 0; i < caveshlist->objects; i++) { parysh = (face*)fastlookup(caveshlist, i); if (smarktested(*parysh)) { enqflag = false; stpivot(*parysh, neightet); if (infected(neightet)) { fsymself(neightet); if (infected(neightet)) { enqflag = true; } } if (!enqflag) { sunmarktest(*parysh); // Use the last entry of this array to fill this entry. j = caveshlist->objects - 1; checksh = *(face*)fastlookup(caveshlist, j); *parysh = checksh; cutshcount++; caveshlist->objects--; // The list is shrinked. i--; } } } if (cutshcount > 0) { i = 0; // Count the number of invalid subfaces/segments. // Valid the updated sub-cavity sC(p). if (loc == ONFACE) { if ((splitsh != NULL) && (splitsh->sh != NULL)) { // The to-be split subface should be in sC(p). if (!smarktested(*splitsh)) i++; } } else if (loc == ONEDGE) { if ((splitseg != NULL) && (splitseg->sh != NULL)) { // The to-be split segment should be in sC(p). if (!smarktested(*splitseg)) i++; } if ((splitsh != NULL) && (splitsh->sh != NULL)) { // All subfaces at this edge should be in sC(p). pa = sorg(*splitsh); neighsh = *splitsh; while (1) { // Adjust the origin of its edge to be 'pa'. if (sorg(neighsh) != pa) { sesymself(neighsh); } // Add this face into list (in B-W cavity). if (!smarktested(neighsh)) i++; // Go to the next face at the edge. spivotself(neighsh); // Stop if all faces at the edge have been visited. if (neighsh.sh == splitsh->sh) break; if (neighsh.sh == NULL) break; } // while (1) } } if (i > 0) { // The updated sC(p) is invalid. Do not insert this vertex. insertpoint_abort(splitseg, ivf); ivf->iloc = (int)BADELEMENT; return 0; } } // if (cutshcount > 0) } // if (ivf->splitbdflag) } // if (cutcount > 0) } // if (ivf->validflag) if (ivf->refineflag) { // The new point is inserted by Delaunay refinement, i.e., it is the // circumcenter of a tetrahedron, or a subface, or a segment. // Do not insert this point if the tetrahedron, or subface, or segment // is not inside the final cavity. if (((ivf->refineflag == 1) && !infected(ivf->refinetet)) || ((ivf->refineflag == 2) && !smarktested(ivf->refinesh))) { insertpoint_abort(splitseg, ivf); ivf->iloc = (int)BADELEMENT; return 0; } } // if (ivf->refineflag) if (b->plc && (loc != INSTAR)) { // Reject the new point if it lies too close to an existing point (b->plc), // or it lies inside a protecting ball of near vertex (ivf->rejflag & 4). // Collect the list of vertices of the initial cavity. if (loc == OUTSIDE) { pts = (point*)&(searchtet->tet[4]); for (i = 0; i < 3; i++) { cavetetvertlist->newindex((void**)&parypt); *parypt = pts[i]; } } else if (loc == INTETRAHEDRON) { pts = (point*)&(searchtet->tet[4]); for (i = 0; i < 4; i++) { cavetetvertlist->newindex((void**)&parypt); *parypt = pts[i]; } } else if (loc == ONFACE) { pts = (point*)&(searchtet->tet[4]); for (i = 0; i < 3; i++) { cavetetvertlist->newindex((void**)&parypt); *parypt = pts[i]; } if (pts[3] != dummypoint) { cavetetvertlist->newindex((void**)&parypt); *parypt = pts[3]; } fsym(*searchtet, spintet); if (oppo(spintet) != dummypoint) { cavetetvertlist->newindex((void**)&parypt); *parypt = oppo(spintet); } } else if (loc == ONEDGE) { spintet = *searchtet; cavetetvertlist->newindex((void**)&parypt); *parypt = org(spintet); cavetetvertlist->newindex((void**)&parypt); *parypt = dest(spintet); while (1) { if (apex(spintet) != dummypoint) { cavetetvertlist->newindex((void**)&parypt); *parypt = apex(spintet); } fnextself(spintet); if (spintet.tet == searchtet->tet) break; } } int rejptflag = (ivf->rejflag & 4); REAL rd; pts = NULL; for (i = 0; i < cavetetvertlist->objects; i++) { parypt = (point*)fastlookup(cavetetvertlist, i); rd = distance(*parypt, insertpt); // Is the point very close to an existing point? if (rd < minedgelength) { pts = parypt; loc = NEARVERTEX; break; } if (rejptflag) { // Is the point encroaches upon an existing point? if (rd < (0.5 * (*parypt)[pointmtrindex])) { pts = parypt; loc = ENCVERTEX; break; } } } cavetetvertlist->restart(); // Clear the work list. if (pts != NULL) { // The point is either too close to an existing vertex (NEARVERTEX) // or encroaches upon (inside the protecting ball) of that vertex. if (loc == NEARVERTEX) { if (!issteinerpoint(insertpt) && b->nomergevertex) { // -M0/1 option. // 'insertpt' is an input vertex. // In this case, we still insert this vertex. Issue a warning. if (!b->quiet) { printf("Warning: Two points, %d and %d, are very close.\n", pointmark(insertpt), pointmark(*pts)); printf(" Creating a very short edge (len = %g) (< %g).\n", rd, minedgelength); printf(" You may try a smaller tolerance (-T) (current is %g)\n", b->epsilon); printf(" to avoid this warning.\n"); } } else { point2tetorg(*pts, *searchtet); insertpoint_abort(splitseg, ivf); ivf->iloc = (int)loc; return 0; } } else { // loc == ENCVERTEX // The point lies inside the protection ball. point2tetorg(*pts, *searchtet); insertpoint_abort(splitseg, ivf); ivf->iloc = (int)loc; return 0; } } } // if (b->plc && (loc != INSTAR)) if (b->weighted || ivf->cdtflag || ivf->smlenflag) { // There may be other vertices inside C(p). We need to find them. // Collect all vertices of C(p). for (i = 0; i < caveoldtetlist->objects; i++) { cavetet = (triface*)fastlookup(caveoldtetlist, i); // assert(infected(*cavetet)); pts = (point*)&(cavetet->tet[4]); for (j = 0; j < 4; j++) { if (pts[j] != dummypoint) { if (!pinfected(pts[j])) { pinfect(pts[j]); cavetetvertlist->newindex((void**)&parypt); *parypt = pts[j]; } } } // j } // i // Uninfect all collected (cavity) vertices. for (i = 0; i < cavetetvertlist->objects; i++) { parypt = (point*)fastlookup(cavetetvertlist, i); puninfect(*parypt); } if (ivf->smlenflag) { REAL len; // Get the length of the shortest edge connecting to 'newpt'. parypt = (point*)fastlookup(cavetetvertlist, 0); ivf->smlen = distance(*parypt, insertpt); ivf->parentpt = *parypt; for (i = 1; i < cavetetvertlist->objects; i++) { parypt = (point*)fastlookup(cavetetvertlist, i); len = distance(*parypt, insertpt); if (len < ivf->smlen) { ivf->smlen = len; ivf->parentpt = *parypt; } } } } if (ivf->cdtflag) { // Unmark tets. for (i = 0; i < caveoldtetlist->objects; i++) { cavetet = (triface*)fastlookup(caveoldtetlist, i); unmarktest(*cavetet); } for (i = 0; i < cavebdrylist->objects; i++) { cavetet = (triface*)fastlookup(cavebdrylist, i); unmarktest(*cavetet); } // Clean up arrays which are not needed. cavetetlist->restart(); if (checksubsegflag) { cavetetseglist->restart(); } if (checksubfaceflag) { cavetetshlist->restart(); } return 1; } // Before re-mesh C(p). Process the segments and subfaces which are on the // boundary of C(p). Make sure that each such segment or subface is // connecting to a tet outside C(p). So we can re-connect them to the // new tets inside the C(p) later. if (checksubsegflag) { for (i = 0; i < cavetetseglist->objects; i++) { paryseg = (face*)fastlookup(cavetetseglist, i); // Operate on it if it is not the splitting segment, i.e., in sC(p). if (!smarktested(*paryseg)) { // Check if the segment is inside the cavity. // 'j' counts the num of adjacent tets of this seg. // 'k' counts the num of adjacent tets which are 'sinfected'. j = k = 0; sstpivot1(*paryseg, neightet); spintet = neightet; while (1) { j++; if (!infected(spintet)) { neineitet = spintet; // An outer tet. Remember it. } else { k++; // An in tet. } fnextself(spintet); if (spintet.tet == neightet.tet) break; } // assert(j > 0); if (k == 0) { // The segment is not connect to C(p) anymore. Remove it by // Replacing it by the last entry of this list. s = cavetetseglist->objects - 1; checkseg = *(face*)fastlookup(cavetetseglist, s); *paryseg = checkseg; cavetetseglist->objects--; i--; } else if (k < j) { // The segment is on the boundary of C(p). sstbond1(*paryseg, neineitet); } else { // k == j // The segment is inside C(p). if (!ivf->splitbdflag) { checkseg = *paryseg; sinfect(checkseg); // Flag it as an interior segment. caveencseglist->newindex((void**)&paryseg); *paryseg = checkseg; } else { // assert(0); // Not possible. terminatetetgen(this, 2); } } } else { // assert(smarktested(*paryseg)); // Flag it as an interior segment. Do not queue it, since it will // be deleted after the segment splitting. sinfect(*paryseg); } } // i } // if (checksubsegflag) if (checksubfaceflag) { for (i = 0; i < cavetetshlist->objects; i++) { parysh = (face*)fastlookup(cavetetshlist, i); // Operate on it if it is not inside the sub-cavity sC(p). if (!smarktested(*parysh)) { // Check if this subface is inside the cavity. k = 0; for (j = 0; j < 2; j++) { stpivot(*parysh, neightet); if (!infected(neightet)) { checksh = *parysh; // Remember this side. } else { k++; } sesymself(*parysh); } if (k == 0) { // The subface is not connected to C(p). Remove it. s = cavetetshlist->objects - 1; checksh = *(face*)fastlookup(cavetetshlist, s); *parysh = checksh; cavetetshlist->objects--; i--; } else if (k == 1) { // This side is the outer boundary of C(p). *parysh = checksh; } else { // k == 2 if (!ivf->splitbdflag) { checksh = *parysh; sinfect(checksh); // Flag it. caveencshlist->newindex((void**)&parysh); *parysh = checksh; } else { // assert(0); // Not possible. terminatetetgen(this, 2); } } } else { // assert(smarktested(*parysh)); // Flag it as an interior subface. Do not queue it. It will be // deleted after the facet point insertion. sinfect(*parysh); } } // i } // if (checksubfaceflag) // Create new tetrahedra to fill the cavity. for (i = 0; i < cavebdrylist->objects; i++) { cavetet = (triface*)fastlookup(cavebdrylist, i); neightet = *cavetet; unmarktest(neightet); // Unmark it. // Get the oldtet (inside the cavity). fsym(neightet, oldtet); if (apex(neightet) != dummypoint) { // Create a new tet in the cavity. maketetrahedron(&newtet); setorg(newtet, dest(neightet)); setdest(newtet, org(neightet)); setapex(newtet, apex(neightet)); setoppo(newtet, insertpt); } else { // Create a new hull tet. hullsize++; maketetrahedron(&newtet); setorg(newtet, org(neightet)); setdest(newtet, dest(neightet)); setapex(newtet, insertpt); setoppo(newtet, dummypoint); // It must opposite to face 3. // Adjust back to the cavity bounday face. esymself(newtet); } // The new tet inherits attribtes from the old tet. for (j = 0; j < numelemattrib; j++) { attrib = elemattribute(oldtet.tet, j); setelemattribute(newtet.tet, j, attrib); } if (b->varvolume) { volume = volumebound(oldtet.tet); setvolumebound(newtet.tet, volume); } // Connect newtet <==> neightet, this also disconnect the old bond. bond(newtet, neightet); // oldtet still connects to neightet. *cavetet = oldtet; // *cavetet = newtet; } // i // Set a handle for speeding point location. recenttet = newtet; // setpoint2tet(insertpt, encode(newtet)); setpoint2tet(insertpt, (tetrahedron)(newtet.tet)); // Re-use this list to save new interior cavity faces. cavetetlist->restart(); // Connect adjacent new tetrahedra together. for (i = 0; i < cavebdrylist->objects; i++) { cavetet = (triface*)fastlookup(cavebdrylist, i); // cavtet is an oldtet, get the newtet at this face. oldtet = *cavetet; fsym(oldtet, neightet); fsym(neightet, newtet); // Comment: oldtet and newtet must be at the same directed edge. // Connect the three other faces of this newtet. for (j = 0; j < 3; j++) { esym(newtet, neightet); // Go to the face. if (neightet.tet[neightet.ver & 3] == NULL) { // Find the adjacent face of this newtet. spintet = oldtet; while (1) { fnextself(spintet); if (!infected(spintet)) break; } fsym(spintet, newneitet); esymself(newneitet); bond(neightet, newneitet); if (ivf->lawson > 1) { cavetetlist->newindex((void**)&parytet); *parytet = neightet; } } // setpoint2tet(org(newtet), encode(newtet)); setpoint2tet(org(newtet), (tetrahedron)(newtet.tet)); enextself(newtet); enextself(oldtet); } *cavetet = newtet; // Save the new tet. } // i if (checksubfaceflag) { // Connect subfaces on the boundary of the cavity to the new tets. for (i = 0; i < cavetetshlist->objects; i++) { parysh = (face*)fastlookup(cavetetshlist, i); // Connect it if it is not a missing subface. if (!sinfected(*parysh)) { stpivot(*parysh, neightet); fsym(neightet, spintet); sesymself(*parysh); tsbond(spintet, *parysh); } } } if (checksubsegflag) { // Connect segments on the boundary of the cavity to the new tets. for (i = 0; i < cavetetseglist->objects; i++) { paryseg = (face*)fastlookup(cavetetseglist, i); // Connect it if it is not a missing segment. if (!sinfected(*paryseg)) { sstpivot1(*paryseg, neightet); spintet = neightet; while (1) { tssbond1(spintet, *paryseg); fnextself(spintet); if (spintet.tet == neightet.tet) break; } } } } if (((splitsh != NULL) && (splitsh->sh != NULL)) || ((splitseg != NULL) && (splitseg->sh != NULL))) { // Split a subface or a segment. sinsertvertex(insertpt, splitsh, splitseg, ivf->sloc, ivf->sbowywat, 0); } if (checksubfaceflag) { if (ivf->splitbdflag) { // Recover new subfaces in C(p). for (i = 0; i < caveshbdlist->objects; i++) { // Get an old subface at edge [a, b]. parysh = (face*)fastlookup(caveshbdlist, i); spivot(*parysh, checksh); // The new subface [a, b, p]. // Do not recover a deleted new face (degenerated). if (checksh.sh[3] != NULL) { // Note that the old subface still connects to adjacent old tets // of C(p), which still connect to the tets outside C(p). stpivot(*parysh, neightet); // Find the adjacent tet containing the edge [a,b] outside C(p). spintet = neightet; while (1) { fnextself(spintet); if (!infected(spintet)) break; } // The adjacent tet connects to a new tet in C(p). fsym(spintet, neightet); // Find the tet containing the face [a, b, p]. spintet = neightet; while (1) { fnextself(spintet); if (apex(spintet) == insertpt) break; } // Adjust the edge direction in spintet and checksh. if (sorg(checksh) != org(spintet)) { sesymself(checksh); } // Connect the subface to two adjacent tets. tsbond(spintet, checksh); fsymself(spintet); sesymself(checksh); tsbond(spintet, checksh); } // if (checksh.sh[3] != NULL) } } else { // The Boundary recovery phase. // Put all new subfaces into stack for recovery. for (i = 0; i < caveshbdlist->objects; i++) { // Get an old subface at edge [a, b]. parysh = (face*)fastlookup(caveshbdlist, i); spivot(*parysh, checksh); // The new subface [a, b, p]. // Do not recover a deleted new face (degenerated). if (checksh.sh[3] != NULL) { subfacstack->newindex((void**)&parysh); *parysh = checksh; } } // Put all interior subfaces into stack for recovery. for (i = 0; i < caveencshlist->objects; i++) { parysh = (face*)fastlookup(caveencshlist, i); // Some subfaces inside C(p) might be split in sinsertvertex(). // Only queue those faces which are not split. if (!smarktested(*parysh)) { checksh = *parysh; suninfect(checksh); stdissolve(checksh); // Detach connections to old tets. subfacstack->newindex((void**)&parysh); *parysh = checksh; } } } } // if (checksubfaceflag) if (checksubsegflag) { if (ivf->splitbdflag) { if (splitseg != NULL) { // Recover the two new subsegments in C(p). for (i = 0; i < cavesegshlist->objects; i++) { paryseg = (face*)fastlookup(cavesegshlist, i); // Insert this subsegment into C(p). checkseg = *paryseg; // Get the adjacent new subface. checkseg.shver = 0; spivot(checkseg, checksh); if (checksh.sh != NULL) { // Get the adjacent new tetrahedron. stpivot(checksh, neightet); } else { // It's a dangling segment. point2tetorg(sorg(checkseg), neightet); finddirection(&neightet, sdest(checkseg)); } sstbond1(checkseg, neightet); spintet = neightet; while (1) { tssbond1(spintet, checkseg); fnextself(spintet); if (spintet.tet == neightet.tet) break; } } } // if (splitseg != NULL) } else { // The Boundary Recovery Phase. // Queue missing segments in C(p) for recovery. if (splitseg != NULL) { // Queue two new subsegments in C(p) for recovery. for (i = 0; i < cavesegshlist->objects; i++) { paryseg = (face*)fastlookup(cavesegshlist, i); checkseg = *paryseg; // sstdissolve1(checkseg); // It has not been connected yet. s = randomnation(subsegstack->objects + 1); subsegstack->newindex((void**)&paryseg); *paryseg = *(face*)fastlookup(subsegstack, s); paryseg = (face*)fastlookup(subsegstack, s); *paryseg = checkseg; } } // if (splitseg != NULL) for (i = 0; i < caveencseglist->objects; i++) { paryseg = (face*)fastlookup(caveencseglist, i); if (!smarktested(*paryseg)) { // It may be split. checkseg = *paryseg; suninfect(checkseg); sstdissolve1(checkseg); // Detach connections to old tets. s = randomnation(subsegstack->objects + 1); subsegstack->newindex((void**)&paryseg); *paryseg = *(face*)fastlookup(subsegstack, s); paryseg = (face*)fastlookup(subsegstack, s); *paryseg = checkseg; } } } } // if (checksubsegflag) if (b->weighted) { // Some vertices may be completed inside the cavity. They must be // detected and added to recovering list. // Since every "live" vertex must contain a pointer to a non-dead // tetrahedron, we can check for each vertex this pointer. for (i = 0; i < cavetetvertlist->objects; i++) { pts = (point*)fastlookup(cavetetvertlist, i); decode(point2tet(*pts), *searchtet); if (infected(*searchtet)) { if (b->weighted) { if (b->verbose > 1) { printf(" Point #%d is non-regular after the insertion of #%d.\n", pointmark(*pts), pointmark(insertpt)); } setpointtype(*pts, NREGULARVERTEX); nonregularcount++; } } } } if (ivf->chkencflag & 1) { // Queue all segment outside C(p). for (i = 0; i < cavetetseglist->objects; i++) { paryseg = (face*)fastlookup(cavetetseglist, i); // Skip if it is the split segment. if (!sinfected(*paryseg)) { enqueuesubface(badsubsegs, paryseg); } } if (splitseg != NULL) { // Queue the two new subsegments inside C(p). for (i = 0; i < cavesegshlist->objects; i++) { paryseg = (face*)fastlookup(cavesegshlist, i); enqueuesubface(badsubsegs, paryseg); } } } // if (chkencflag & 1) if (ivf->chkencflag & 2) { // Queue all subfaces outside C(p). for (i = 0; i < cavetetshlist->objects; i++) { parysh = (face*)fastlookup(cavetetshlist, i); // Skip if it is a split subface. if (!sinfected(*parysh)) { enqueuesubface(badsubfacs, parysh); } } // Queue all new subfaces inside C(p). for (i = 0; i < caveshbdlist->objects; i++) { // Get an old subface at edge [a, b]. parysh = (face*)fastlookup(caveshbdlist, i); spivot(*parysh, checksh); // checksh is a new subface [a, b, p]. // Do not recover a deleted new face (degenerated). if (checksh.sh[3] != NULL) { enqueuesubface(badsubfacs, &checksh); } } } // if (chkencflag & 2) if (ivf->chkencflag & 4) { // Queue all new tetrahedra in C(p). for (i = 0; i < cavebdrylist->objects; i++) { cavetet = (triface*)fastlookup(cavebdrylist, i); enqueuetetrahedron(cavetet); } } // C(p) is re-meshed successfully. // Delete the old tets in C(p). for (i = 0; i < caveoldtetlist->objects; i++) { searchtet = (triface*)fastlookup(caveoldtetlist, i); if (ishulltet(*searchtet)) { hullsize--; } tetrahedrondealloc(searchtet->tet); } if (((splitsh != NULL) && (splitsh->sh != NULL)) || ((splitseg != NULL) && (splitseg->sh != NULL))) { // Delete the old subfaces in sC(p). for (i = 0; i < caveshlist->objects; i++) { parysh = (face*)fastlookup(caveshlist, i); if (checksubfaceflag) { // if (bowywat == 2) { // It is possible that this subface still connects to adjacent // tets which are not in C(p). If so, clear connections in the // adjacent tets at this subface. stpivot(*parysh, neightet); if (neightet.tet != NULL) { if (neightet.tet[4] != NULL) { // Found an adjacent tet. It must be not in C(p). tsdissolve(neightet); fsymself(neightet); tsdissolve(neightet); } } } shellfacedealloc(subfaces, parysh->sh); } if ((splitseg != NULL) && (splitseg->sh != NULL)) { // Delete the old segment in sC(p). shellfacedealloc(subsegs, splitseg->sh); } } if (ivf->lawson) { for (i = 0; i < cavebdrylist->objects; i++) { searchtet = (triface*)fastlookup(cavebdrylist, i); flippush(flipstack, searchtet); } if (ivf->lawson > 1) { for (i = 0; i < cavetetlist->objects; i++) { searchtet = (triface*)fastlookup(cavetetlist, i); flippush(flipstack, searchtet); } } } // Clean the working lists. caveoldtetlist->restart(); cavebdrylist->restart(); cavetetlist->restart(); if (checksubsegflag) { cavetetseglist->restart(); caveencseglist->restart(); } if (checksubfaceflag) { cavetetshlist->restart(); caveencshlist->restart(); } if (b->weighted || ivf->smlenflag) { cavetetvertlist->restart(); } if (((splitsh != NULL) && (splitsh->sh != NULL)) || ((splitseg != NULL) && (splitseg->sh != NULL))) { caveshlist->restart(); caveshbdlist->restart(); cavesegshlist->restart(); } return 1; // Point is inserted. } /////////////////////////////////////////////////////////////////////////////// // // // insertpoint_abort() Abort the insertion of a new vertex. // // // // The cavity will be restored. All working lists are cleared. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::insertpoint_abort(face* splitseg, insertvertexflags* ivf) { triface* cavetet; face* parysh; int i; for (i = 0; i < caveoldtetlist->objects; i++) { cavetet = (triface*)fastlookup(caveoldtetlist, i); uninfect(*cavetet); unmarktest(*cavetet); } for (i = 0; i < cavebdrylist->objects; i++) { cavetet = (triface*)fastlookup(cavebdrylist, i); unmarktest(*cavetet); } cavetetlist->restart(); cavebdrylist->restart(); caveoldtetlist->restart(); cavetetseglist->restart(); cavetetshlist->restart(); if (ivf->splitbdflag) { if ((splitseg != NULL) && (splitseg->sh != NULL)) { sunmarktest(*splitseg); } for (i = 0; i < caveshlist->objects; i++) { parysh = (face*)fastlookup(caveshlist, i); sunmarktest(*parysh); } caveshlist->restart(); cavesegshlist->restart(); } } //// //// //// //// //// flip_cxx ///////////////////////////////////////////////////////////////// //// delaunay_cxx ///////////////////////////////////////////////////////////// //// //// //// //// /////////////////////////////////////////////////////////////////////////////// // // // transfernodes() Read the vertices from the input (tetgenio). // // // // Transferring all points from input ('in->pointlist') to TetGen's 'points'.// // All points are indexed (the first point index is 'in->firstnumber'). Each // // point's type is initialized as UNUSEDVERTEX. The bounding box (xmax, xmin,// // ...) and the diameter (longest) of the point set are calculated. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::transfernodes() { point pointloop; REAL x, y, z, w; int coordindex; int attribindex; int mtrindex; int i, j; // Read the points. coordindex = 0; attribindex = 0; mtrindex = 0; for (i = 0; i < in->numberofpoints; i++) { makepoint(&pointloop, UNUSEDVERTEX); // Read the point coordinates. x = pointloop[0] = in->pointlist[coordindex++]; y = pointloop[1] = in->pointlist[coordindex++]; z = pointloop[2] = in->pointlist[coordindex++]; // Read the point attributes. (Including point weights.) for (j = 0; j < in->numberofpointattributes; j++) { pointloop[3 + j] = in->pointattributelist[attribindex++]; } // Read the point metric tensor. for (j = 0; j < in->numberofpointmtrs; j++) { pointloop[pointmtrindex + j] = in->pointmtrlist[mtrindex++]; } if (b->weighted) { // -w option if (in->numberofpointattributes > 0) { // The first point attribute is its weight. // w = in->pointattributelist[in->numberofpointattributes * i]; w = pointloop[3]; } else { // No given weight available. Default choose the maximum // absolute value among its coordinates. w = fabs(x); if (w < fabs(y)) w = fabs(y); if (w < fabs(z)) w = fabs(z); } if (b->weighted_param == 0) { pointloop[3] = x * x + y * y + z * z - w; // Weighted DT. } else { // -w1 option pointloop[3] = w; // Regular tetrahedralization. } } // Determine the smallest and largest x, y and z coordinates. if (i == 0) { xmin = xmax = x; ymin = ymax = y; zmin = zmax = z; } else { xmin = (x < xmin) ? x : xmin; xmax = (x > xmax) ? x : xmax; ymin = (y < ymin) ? y : ymin; ymax = (y > ymax) ? y : ymax; zmin = (z < zmin) ? z : zmin; zmax = (z > zmax) ? z : zmax; } if (b->psc) { // Read the geometry parameters. setpointgeomuv(pointloop, 0, in->pointparamlist[i].uv[0]); setpointgeomuv(pointloop, 1, in->pointparamlist[i].uv[1]); setpointgeomtag(pointloop, in->pointparamlist[i].tag); if (in->pointparamlist[i].type == 0) { setpointtype(pointloop, RIDGEVERTEX); } else if (in->pointparamlist[i].type == 1) { setpointtype(pointloop, FREESEGVERTEX); } else if (in->pointparamlist[i].type == 2) { setpointtype(pointloop, FREEFACETVERTEX); } else if (in->pointparamlist[i].type == 3) { setpointtype(pointloop, FREEVOLVERTEX); } } } // 'longest' is the largest possible edge length formed by input vertices. x = xmax - xmin; y = ymax - ymin; z = zmax - zmin; longest = sqrt(x * x + y * y + z * z); if (longest == 0.0) { printf("Error: The point set is trivial.\n"); terminatetetgen(this, 10); } // Two identical points are distinguished by 'minedgelength'. minedgelength = longest * b->epsilon; } /////////////////////////////////////////////////////////////////////////////// // // // hilbert_init() Initialize the Gray code permutation table. // // // // The table 'transgc' has 8 x 3 x 8 entries. It contains all possible Gray // // code sequences traveled by the 1st order Hilbert curve in 3 dimensions. // // The first column is the Gray code of the entry point of the curve, and // // the second column is the direction (0, 1, or 2, 0 means the x-axis) where // // the exit point of curve lies. // // // // The table 'tsb1mod3' contains the numbers of trailing set '1' bits of the // // indices from 0 to 7, modulo by '3'. The code for generating this table is // // from: http://graphics.stanford.edu/~seander/bithacks.html. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::hilbert_init(int n) { int gc[8], N, mask, travel_bit; int e, d, f, k, g; int v, c; int i; N = (n == 2) ? 4 : 8; mask = (n == 2) ? 3 : 7; // Generate the Gray code sequence. for (i = 0; i < N; i++) { gc[i] = i ^ (i >> 1); } for (e = 0; e < N; e++) { for (d = 0; d < n; d++) { // Calculate the end point (f). f = e ^ (1 << d); // Toggle the d-th bit of 'e'. // travel_bit = 2**p, the bit we want to travel. travel_bit = e ^ f; for (i = 0; i < N; i++) { // // Rotate gc[i] left by (p + 1) % n bits. k = gc[i] * (travel_bit * 2); g = ((k | (k / N)) & mask); // Calculate the permuted Gray code by xor with the start point (e). transgc[e][d][i] = (g ^ e); } } // d } // e // Count the consecutive '1' bits (trailing) on the right. tsb1mod3[0] = 0; for (i = 1; i < N; i++) { v = ~i; // Count the 0s. v = (v ^ (v - 1)) >> 1; // Set v's trailing 0s to 1s and zero rest for (c = 0; v; c++) { v >>= 1; } tsb1mod3[i] = c % n; } } /////////////////////////////////////////////////////////////////////////////// // // // hilbert_sort3() Sort points using the 3d Hilbert curve. // // // /////////////////////////////////////////////////////////////////////////////// int tetgenmesh::hilbert_split(point* vertexarray, int arraysize, int gc0, int gc1, REAL bxmin, REAL bxmax, REAL bymin, REAL bymax, REAL bzmin, REAL bzmax) { point swapvert; int axis, d; REAL split; int i, j; // Find the current splitting axis. 'axis' is a value 0, or 1, or 2, which // correspoding to x-, or y- or z-axis. axis = (gc0 ^ gc1) >> 1; // Calulate the split position along the axis. if (axis == 0) { split = 0.5 * (bxmin + bxmax); } else if (axis == 1) { split = 0.5 * (bymin + bymax); } else { // == 2 split = 0.5 * (bzmin + bzmax); } // Find the direction (+1 or -1) of the axis. If 'd' is +1, the direction // of the axis is to the positive of the axis, otherwise, it is -1. d = ((gc0 & (1 << axis)) == 0) ? 1 : -1; // Partition the vertices into left- and right-arrays such that left points // have Hilbert indices lower than the right points. i = 0; j = arraysize - 1; // Partition the vertices into left- and right-arrays. if (d > 0) { do { for (; i < arraysize; i++) { if (vertexarray[i][axis] >= split) break; } for (; j >= 0; j--) { if (vertexarray[j][axis] < split) break; } // Is the partition finished? if (i == (j + 1)) break; // Swap i-th and j-th vertices. swapvert = vertexarray[i]; vertexarray[i] = vertexarray[j]; vertexarray[j] = swapvert; // Continue patitioning the array; } while (true); } else { do { for (; i < arraysize; i++) { if (vertexarray[i][axis] <= split) break; } for (; j >= 0; j--) { if (vertexarray[j][axis] > split) break; } // Is the partition finished? if (i == (j + 1)) break; // Swap i-th and j-th vertices. swapvert = vertexarray[i]; vertexarray[i] = vertexarray[j]; vertexarray[j] = swapvert; // Continue patitioning the array; } while (true); } return i; } void tetgenmesh::hilbert_sort3(point* vertexarray, int arraysize, int e, int d, REAL bxmin, REAL bxmax, REAL bymin, REAL bymax, REAL bzmin, REAL bzmax, int depth) { REAL x1, x2, y1, y2, z1, z2; int p[9], w, e_w, d_w, k, ei, di; int n = 3, mask = 7; p[0] = 0; p[8] = arraysize; // Sort the points according to the 1st order Hilbert curve in 3d. p[4] = hilbert_split(vertexarray, p[8], transgc[e][d][3], transgc[e][d][4], bxmin, bxmax, bymin, bymax, bzmin, bzmax); p[2] = hilbert_split(vertexarray, p[4], transgc[e][d][1], transgc[e][d][2], bxmin, bxmax, bymin, bymax, bzmin, bzmax); p[1] = hilbert_split(vertexarray, p[2], transgc[e][d][0], transgc[e][d][1], bxmin, bxmax, bymin, bymax, bzmin, bzmax); p[3] = hilbert_split(&(vertexarray[p[2]]), p[4] - p[2], transgc[e][d][2], transgc[e][d][3], bxmin, bxmax, bymin, bymax, bzmin, bzmax) + p[2]; p[6] = hilbert_split(&(vertexarray[p[4]]), p[8] - p[4], transgc[e][d][5], transgc[e][d][6], bxmin, bxmax, bymin, bymax, bzmin, bzmax) + p[4]; p[5] = hilbert_split(&(vertexarray[p[4]]), p[6] - p[4], transgc[e][d][4], transgc[e][d][5], bxmin, bxmax, bymin, bymax, bzmin, bzmax) + p[4]; p[7] = hilbert_split(&(vertexarray[p[6]]), p[8] - p[6], transgc[e][d][6], transgc[e][d][7], bxmin, bxmax, bymin, bymax, bzmin, bzmax) + p[6]; if (b->hilbert_order > 0) { // A maximum order is prescribed. if ((depth + 1) == b->hilbert_order) { // The maximum prescribed order is reached. return; } } // Recursively sort the points in sub-boxes. for (w = 0; w < 8; w++) { // w is the local Hilbert index (NOT Gray code). // Sort into the sub-box either there are more than 2 points in it, or // the prescribed order of the curve is not reached yet. // if ((p[w+1] - p[w] > b->hilbert_limit) || (b->hilbert_order > 0)) { if ((p[w + 1] - p[w]) > b->hilbert_limit) { // Calculcate the start point (ei) of the curve in this sub-box. // update e = e ^ (e(w) left_rotate (d+1)). if (w == 0) { e_w = 0; } else { // calculate e(w) = gc(2 * floor((w - 1) / 2)). k = 2 * ((w - 1) / 2); e_w = k ^ (k >> 1); // = gc(k). } k = e_w; e_w = ((k << (d + 1)) & mask) | ((k >> (n - d - 1)) & mask); ei = e ^ e_w; // Calulcate the direction (di) of the curve in this sub-box. // update d = (d + d(w) + 1) % n if (w == 0) { d_w = 0; } else { d_w = ((w % 2) == 0) ? tsb1mod3[w - 1] : tsb1mod3[w]; } di = (d + d_w + 1) % n; // Calculate the bounding box of the sub-box. if (transgc[e][d][w] & 1) { // x-axis x1 = 0.5 * (bxmin + bxmax); x2 = bxmax; } else { x1 = bxmin; x2 = 0.5 * (bxmin + bxmax); } if (transgc[e][d][w] & 2) { // y-axis y1 = 0.5 * (bymin + bymax); y2 = bymax; } else { y1 = bymin; y2 = 0.5 * (bymin + bymax); } if (transgc[e][d][w] & 4) { // z-axis z1 = 0.5 * (bzmin + bzmax); z2 = bzmax; } else { z1 = bzmin; z2 = 0.5 * (bzmin + bzmax); } hilbert_sort3(&(vertexarray[p[w]]), p[w + 1] - p[w], ei, di, x1, x2, y1, y2, z1, z2, depth + 1); } // if (p[w+1] - p[w] > 1) } // w } /////////////////////////////////////////////////////////////////////////////// // // // brio_multiscale_sort() Sort the points using BRIO and Hilbert curve. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::brio_multiscale_sort(point* vertexarray, int arraysize, int threshold, REAL ratio, int* depth) { int middle; middle = 0; if (arraysize >= threshold) { (*depth)++; middle = arraysize * ratio; brio_multiscale_sort(vertexarray, middle, threshold, ratio, depth); } // Sort the right-array (rnd-th round) using the Hilbert curve. hilbert_sort3(&(vertexarray[middle]), arraysize - middle, 0, 0, // e, d xmin, xmax, ymin, ymax, zmin, zmax, 0); // depth. } /////////////////////////////////////////////////////////////////////////////// // // // randomnation() Generate a random number between 0 and 'choices' - 1. // // // /////////////////////////////////////////////////////////////////////////////// unsigned long tetgenmesh::randomnation(unsigned int choices) { unsigned long newrandom; if (choices >= 714025l) { newrandom = (randomseed * 1366l + 150889l) % 714025l; randomseed = (newrandom * 1366l + 150889l) % 714025l; newrandom = newrandom * (choices / 714025l) + randomseed; if (newrandom >= choices) { return newrandom - choices; } else { return newrandom; } } else { randomseed = (randomseed * 1366l + 150889l) % 714025l; return randomseed % choices; } } /////////////////////////////////////////////////////////////////////////////// // // // randomsample() Randomly sample the tetrahedra for point loation. // // // // Searching begins from one of handles: the input 'searchtet', a recently // // encountered tetrahedron 'recenttet', or from one chosen from a random // // sample. The choice is made by determining which one's origin is closest // // to the point we are searching for. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::randomsample(point searchpt, triface* searchtet) { tetrahedron *firsttet, *tetptr; point torg; void** sampleblock; uintptr_t alignptr; long sampleblocks, samplesperblock, samplenum; long tetblocks, i, j; REAL searchdist, dist; if (b->verbose > 2) { printf(" Random sampling tetrahedra for searching point %d.\n", pointmark(searchpt)); } if (!nonconvex) { if (searchtet->tet == NULL) { // A null tet. Choose the recenttet as the starting tet. *searchtet = recenttet; } // 'searchtet' should be a valid tetrahedron. Choose the base face // whose vertices must not be 'dummypoint'. searchtet->ver = 3; // Record the distance from its origin to the searching point. torg = org(*searchtet); searchdist = (searchpt[0] - torg[0]) * (searchpt[0] - torg[0]) + (searchpt[1] - torg[1]) * (searchpt[1] - torg[1]) + (searchpt[2] - torg[2]) * (searchpt[2] - torg[2]); // If a recently encountered tetrahedron has been recorded and has not // been deallocated, test it as a good starting point. if (recenttet.tet != searchtet->tet) { recenttet.ver = 3; torg = org(recenttet); dist = (searchpt[0] - torg[0]) * (searchpt[0] - torg[0]) + (searchpt[1] - torg[1]) * (searchpt[1] - torg[1]) + (searchpt[2] - torg[2]) * (searchpt[2] - torg[2]); if (dist < searchdist) { *searchtet = recenttet; searchdist = dist; } } } else { // The mesh is non-convex. Do not use 'recenttet'. searchdist = longest; } // Select "good" candidate using k random samples, taking the closest one. // The number of random samples taken is proportional to the fourth root // of the number of tetrahedra in the mesh. while (samples * samples * samples * samples < tetrahedrons->items) { samples++; } // Find how much blocks in current tet pool. tetblocks = (tetrahedrons->maxitems + b->tetrahedraperblock - 1) / b->tetrahedraperblock; // Find the average samples per block. Each block at least have 1 sample. samplesperblock = 1 + (samples / tetblocks); sampleblocks = samples / samplesperblock; sampleblock = tetrahedrons->firstblock; for (i = 0; i < sampleblocks; i++) { alignptr = (uintptr_t)(sampleblock + 1); firsttet = (tetrahedron*)(alignptr + (uintptr_t)tetrahedrons->alignbytes - (alignptr % (uintptr_t)tetrahedrons->alignbytes)); for (j = 0; j < samplesperblock; j++) { if (i == tetblocks - 1) { // This is the last block. samplenum = randomnation((int)(tetrahedrons->maxitems - (i * b->tetrahedraperblock))); } else { samplenum = randomnation(b->tetrahedraperblock); } tetptr = (tetrahedron*)(firsttet + (samplenum * tetrahedrons->itemwords)); torg = (point)tetptr[4]; if (torg != (point)NULL) { dist = (searchpt[0] - torg[0]) * (searchpt[0] - torg[0]) + (searchpt[1] - torg[1]) * (searchpt[1] - torg[1]) + (searchpt[2] - torg[2]) * (searchpt[2] - torg[2]); if (dist < searchdist) { searchtet->tet = tetptr; searchtet->ver = 11; // torg = org(t); searchdist = dist; } } else { // A dead tet. Re-sample it. if (i != tetblocks - 1) j--; } } sampleblock = (void**)*sampleblock; } } /////////////////////////////////////////////////////////////////////////////// // // // locate() Find a tetrahedron containing a given point. // // // // Begins its search from 'searchtet', assume there is a line segment L from // // a vertex of 'searchtet' to the query point 'searchpt', and simply walk // // towards 'searchpt' by traversing all faces intersected by L. // // // // On completion, 'searchtet' is a tetrahedron that contains 'searchpt'. The // // returned value indicates one of the following cases: // // - ONVERTEX, the search point lies on the origin of 'searchtet'. // // - ONEDGE, the search point lies on an edge of 'searchtet'. // // - ONFACE, the search point lies on a face of 'searchtet'. // // - INTET, the search point lies in the interior of 'searchtet'. // // - OUTSIDE, the search point lies outside the mesh. 'searchtet' is a // // hull face which is visible by the search point. // // // // WARNING: This routine is designed for convex triangulations, and will not // // generally work after the holes and concavities have been carved. // // // /////////////////////////////////////////////////////////////////////////////// enum tetgenmesh::locateresult tetgenmesh::locate(point searchpt, triface* searchtet, int chkencflag) { point torg, tdest, tapex, toppo; enum { ORGMOVE, DESTMOVE, APEXMOVE } nextmove; REAL ori, oriorg, oridest, oriapex; enum locateresult loc = OUTSIDE; int t1ver; int s; torg = tdest = tapex = toppo = NULL; if (searchtet->tet == NULL) { // A null tet. Choose the recenttet as the starting tet. searchtet->tet = recenttet.tet; } // Check if we are in the outside of the convex hull. if (ishulltet(*searchtet)) { // Get its adjacent tet (inside the hull). searchtet->ver = 3; fsymself(*searchtet); } // Let searchtet be the face such that 'searchpt' lies above to it. for (searchtet->ver = 0; searchtet->ver < 4; searchtet->ver++) { torg = org(*searchtet); tdest = dest(*searchtet); tapex = apex(*searchtet); ori = orient3d(torg, tdest, tapex, searchpt); if (ori < 0.0) break; } if (searchtet->ver == 4) { terminatetetgen(this, 2); } // Walk through tetrahedra to locate the point. while (true) { toppo = oppo(*searchtet); // Check if the vertex is we seek. if (toppo == searchpt) { // Adjust the origin of searchtet to be searchpt. esymself(*searchtet); eprevself(*searchtet); loc = ONVERTEX; // return ONVERTEX; break; } // We enter from one of serarchtet's faces, which face do we exit? oriorg = orient3d(tdest, tapex, toppo, searchpt); oridest = orient3d(tapex, torg, toppo, searchpt); oriapex = orient3d(torg, tdest, toppo, searchpt); // Now decide which face to move. It is possible there are more than one // faces are viable moves. If so, randomly choose one. if (oriorg < 0) { if (oridest < 0) { if (oriapex < 0) { // All three faces are possible. s = randomnation(3); // 's' is in {0,1,2}. if (s == 0) { nextmove = ORGMOVE; } else if (s == 1) { nextmove = DESTMOVE; } else { nextmove = APEXMOVE; } } else { // Two faces, opposite to origin and destination, are viable. // s = randomnation(2); // 's' is in {0,1}. if (randomnation(2)) { nextmove = ORGMOVE; } else { nextmove = DESTMOVE; } } } else { if (oriapex < 0) { // Two faces, opposite to origin and apex, are viable. // s = randomnation(2); // 's' is in {0,1}. if (randomnation(2)) { nextmove = ORGMOVE; } else { nextmove = APEXMOVE; } } else { // Only the face opposite to origin is viable. nextmove = ORGMOVE; } } } else { if (oridest < 0) { if (oriapex < 0) { // Two faces, opposite to destination and apex, are viable. // s = randomnation(2); // 's' is in {0,1}. if (randomnation(2)) { nextmove = DESTMOVE; } else { nextmove = APEXMOVE; } } else { // Only the face opposite to destination is viable. nextmove = DESTMOVE; } } else { if (oriapex < 0) { // Only the face opposite to apex is viable. nextmove = APEXMOVE; } else { // The point we seek must be on the boundary of or inside this // tetrahedron. Check for boundary cases. if (oriorg == 0) { // Go to the face opposite to origin. enextesymself(*searchtet); if (oridest == 0) { eprevself(*searchtet); // edge oppo->apex if (oriapex == 0) { // oppo is duplicated with p. loc = ONVERTEX; // return ONVERTEX; break; } loc = ONEDGE; // return ONEDGE; break; } if (oriapex == 0) { enextself(*searchtet); // edge dest->oppo loc = ONEDGE; // return ONEDGE; break; } loc = ONFACE; // return ONFACE; break; } if (oridest == 0) { // Go to the face opposite to destination. eprevesymself(*searchtet); if (oriapex == 0) { eprevself(*searchtet); // edge oppo->org loc = ONEDGE; // return ONEDGE; break; } loc = ONFACE; // return ONFACE; break; } if (oriapex == 0) { // Go to the face opposite to apex esymself(*searchtet); loc = ONFACE; // return ONFACE; break; } loc = INTETRAHEDRON; // return INTETRAHEDRON; break; } } } // Move to the selected face. if (nextmove == ORGMOVE) { enextesymself(*searchtet); } else if (nextmove == DESTMOVE) { eprevesymself(*searchtet); } else { esymself(*searchtet); } if (chkencflag) { // Check if we are walking across a subface. if (issubface(*searchtet)) { loc = ENCSUBFACE; break; } } // Move to the adjacent tetrahedron (maybe a hull tetrahedron). fsymself(*searchtet); if (oppo(*searchtet) == dummypoint) { loc = OUTSIDE; // return OUTSIDE; break; } // Retreat the three vertices of the base face. torg = org(*searchtet); tdest = dest(*searchtet); tapex = apex(*searchtet); } // while (true) return loc; } /////////////////////////////////////////////////////////////////////////////// // // // flippush() Push a face (possibly will be flipped) into flipstack. // // // // The face is marked. The flag is used to check the validity of the face on // // its popup. Some other flips may change it already. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::flippush(badface*& fstack, triface* flipface) { if (!facemarked(*flipface)) { badface* newflipface = (badface*)flippool->alloc(); newflipface->tt = *flipface; markface(newflipface->tt); // Push this face into stack. newflipface->nextitem = fstack; fstack = newflipface; } } /////////////////////////////////////////////////////////////////////////////// // // // incrementalflip() Incrementally flipping to construct DT. // // // // Faces need to be checked for flipping are already queued in 'flipstack'. // // Return the total number of performed flips. // // // // Comment: This routine should be only used in the incremental Delaunay // // construction. In other cases, lawsonflip3d() should be used. // // // // If the new point lies outside of the convex hull ('hullflag' is set). The // // incremental flip algorithm still works as usual. However, we must ensure // // that every flip (2-to-3 or 3-to-2) does not create a duplicated (existing)// // edge or face. Otherwise, the underlying space of the triangulation becomes// // non-manifold and it is not possible to flip further. // // Thanks to Joerg Rambau and Frank Lutz for helping in this issue. // // // /////////////////////////////////////////////////////////////////////////////// int tetgenmesh::incrementalflip(point newpt, int hullflag, flipconstraints* fc) { badface* popface; triface fliptets[5], *parytet; point *pts, *parypt, pe; REAL sign, ori; int flipcount = 0; int t1ver; int i; if (b->verbose > 2) { printf(" Lawson flip (%ld faces).\n", flippool->items); } if (hullflag) { // 'newpt' lies in the outside of the convex hull. // Mark all hull vertices which are connecting to it. popface = flipstack; while (popface != NULL) { pts = (point*)popface->tt.tet; for (i = 4; i < 8; i++) { if ((pts[i] != newpt) && (pts[i] != dummypoint)) { if (!pinfected(pts[i])) { pinfect(pts[i]); cavetetvertlist->newindex((void**)&parypt); *parypt = pts[i]; } } } popface = popface->nextitem; } } // Loop until the queue is empty. while (flipstack != NULL) { // Pop a face from the stack. popface = flipstack; fliptets[0] = popface->tt; flipstack = flipstack->nextitem; // The next top item in stack. flippool->dealloc((void*)popface); // Skip it if it is a dead tet (destroyed by previous flips). if (isdeadtet(fliptets[0])) continue; // Skip it if it is not the same tet as we saved. if (!facemarked(fliptets[0])) continue; unmarkface(fliptets[0]); if ((point)fliptets[0].tet[7] == dummypoint) { // It must be a hull edge. fliptets[0].ver = epivot[fliptets[0].ver]; // A hull edge. The current convex hull may be enlarged. fsym(fliptets[0], fliptets[1]); pts = (point*)fliptets[1].tet; ori = orient3d(pts[4], pts[5], pts[6], newpt); if (ori < 0) { // Visible. The convex hull will be enlarged. // Decide which flip (2-to-3, 3-to-2, or 4-to-1) to use. // Check if the tet [a,c,e,d] or [c,b,e,d] exists. enext(fliptets[1], fliptets[2]); eprev(fliptets[1], fliptets[3]); fnextself(fliptets[2]); // [a,c,e,*] fnextself(fliptets[3]); // [c,b,e,*] if (oppo(fliptets[2]) == newpt) { if (oppo(fliptets[3]) == newpt) { // Both tets exist! A 4-to-1 flip is found. terminatetetgen(this, 2); // Report a bug. } else { esym(fliptets[2], fliptets[0]); fnext(fliptets[0], fliptets[1]); fnext(fliptets[1], fliptets[2]); // Perform a 3-to-2 flip. Replace edge [c,a] by face [d,e,b]. // This corresponds to my standard labels, where edge [e,d] is // repalced by face [a,b,c], and a is the new vertex. // [0] [c,a,d,e] (d = newpt) // [1] [c,a,e,b] (c = dummypoint) // [2] [c,a,b,d] flip32(fliptets, 1, fc); } } else { if (oppo(fliptets[3]) == newpt) { fnext(fliptets[3], fliptets[0]); fnext(fliptets[0], fliptets[1]); fnext(fliptets[1], fliptets[2]); // Perform a 3-to-2 flip. Replace edge [c,b] by face [d,a,e]. // [0] [c,b,d,a] (d = newpt) // [1] [c,b,a,e] (c = dummypoint) // [2] [c,b,e,d] flip32(fliptets, 1, fc); } else { if (hullflag) { // Reject this flip if pe is already marked. pe = oppo(fliptets[1]); if (!pinfected(pe)) { pinfect(pe); cavetetvertlist->newindex((void**)&parypt); *parypt = pe; // Perform a 2-to-3 flip. flip23(fliptets, 1, fc); } else { // Reject this flip. flipcount--; } } else { // Perform a 2-to-3 flip. Replace face [a,b,c] by edge [e,d]. // [0] [a,b,c,d], d = newpt. // [1] [b,a,c,e], c = dummypoint. flip23(fliptets, 1, fc); } } } flipcount++; } continue; } // if (dummypoint) fsym(fliptets[0], fliptets[1]); if ((point)fliptets[1].tet[7] == dummypoint) { // A hull face is locally Delaunay. continue; } // Check if the adjacent tet has already been tested. if (marktested(fliptets[1])) { // It has been tested and it is Delaunay. continue; } // Test whether the face is locally Delaunay or not. pts = (point*)fliptets[1].tet; if (b->weighted) { sign = orient4d_s(pts[4], pts[5], pts[6], pts[7], newpt, pts[4][3], pts[5][3], pts[6][3], pts[7][3], newpt[3]); } else { sign = insphere_s(pts[4], pts[5], pts[6], pts[7], newpt); } if (sign < 0) { point pd = newpt; point pe = oppo(fliptets[1]); // Check the convexity of its three edges. Stop checking either a // locally non-convex edge (ori < 0) or a flat edge (ori = 0) is // encountered, and 'fliptet' represents that edge. for (i = 0; i < 3; i++) { ori = orient3d(org(fliptets[0]), dest(fliptets[0]), pd, pe); if (ori <= 0) break; enextself(fliptets[0]); } if (ori > 0) { // A 2-to-3 flip is found. // [0] [a,b,c,d], // [1] [b,a,c,e]. no dummypoint. flip23(fliptets, 0, fc); flipcount++; } else { // ori <= 0 // The edge ('fliptets[0]' = [a',b',c',d]) is non-convex or flat, // where the edge [a',b'] is one of [a,b], [b,c], and [c,a]. // Check if there are three or four tets sharing at this edge. esymself(fliptets[0]); // [b,a,d,c] for (i = 0; i < 3; i++) { fnext(fliptets[i], fliptets[i + 1]); } if (fliptets[3].tet == fliptets[0].tet) { // A 3-to-2 flip is found. (No hull tet.) flip32(fliptets, 0, fc); flipcount++; } else { // There are more than 3 tets at this edge. fnext(fliptets[3], fliptets[4]); if (fliptets[4].tet == fliptets[0].tet) { if (ori == 0) { // A 4-to-4 flip is found. (Two hull tets may be involved.) // Current tets in 'fliptets': // [0] [b,a,d,c] (d may be newpt) // [1] [b,a,c,e] // [2] [b,a,e,f] (f may be dummypoint) // [3] [b,a,f,d] esymself(fliptets[0]); // [a,b,c,d] // A 2-to-3 flip replaces face [a,b,c] by edge [e,d]. // This creates a degenerate tet [e,d,a,b] (tmpfliptets[0]). // It will be removed by the followed 3-to-2 flip. flip23(fliptets, 0, fc); // No hull tet. fnext(fliptets[3], fliptets[1]); fnext(fliptets[1], fliptets[2]); // Current tets in 'fliptets': // [0] [...] // [1] [b,a,d,e] (degenerated, d may be new point). // [2] [b,a,e,f] (f may be dummypoint) // [3] [b,a,f,d] // A 3-to-2 flip replaces edge [b,a] by face [d,e,f]. // Hull tets may be involved (f may be dummypoint). flip32(&(fliptets[1]), (apex(fliptets[3]) == dummypoint), fc); flipcount++; } } } } // ori } else { // The adjacent tet is Delaunay. Mark it to avoid testing it again. marktest(fliptets[1]); // Save it for unmarking it later. cavebdrylist->newindex((void**)&parytet); *parytet = fliptets[1]; } } // while (flipstack) // Unmark saved tetrahedra. for (i = 0; i < cavebdrylist->objects; i++) { parytet = (triface*)fastlookup(cavebdrylist, i); unmarktest(*parytet); } cavebdrylist->restart(); if (hullflag) { // Unmark infected vertices. for (i = 0; i < cavetetvertlist->objects; i++) { parypt = (point*)fastlookup(cavetetvertlist, i); puninfect(*parypt); } cavetetvertlist->restart(); } return flipcount; } /////////////////////////////////////////////////////////////////////////////// // // // initialdelaunay() Create an initial Delaunay tetrahedralization. // // // // The tetrahedralization contains only one tetrahedron abcd, and four hull // // tetrahedra. The points pa, pb, pc, and pd must be linearly independent. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::initialdelaunay(point pa, point pb, point pc, point pd) { triface firsttet, tetopa, tetopb, tetopc, tetopd; triface worktet, worktet1; if (b->verbose > 2) { printf(" Create init tet (%d, %d, %d, %d)\n", pointmark(pa), pointmark(pb), pointmark(pc), pointmark(pd)); } // Create the first tetrahedron. maketetrahedron(&firsttet); setvertices(firsttet, pa, pb, pc, pd); // Create four hull tetrahedra. maketetrahedron(&tetopa); setvertices(tetopa, pb, pc, pd, dummypoint); maketetrahedron(&tetopb); setvertices(tetopb, pc, pa, pd, dummypoint); maketetrahedron(&tetopc); setvertices(tetopc, pa, pb, pd, dummypoint); maketetrahedron(&tetopd); setvertices(tetopd, pb, pa, pc, dummypoint); hullsize += 4; // Connect hull tetrahedra to firsttet (at four faces of firsttet). bond(firsttet, tetopd); esym(firsttet, worktet); bond(worktet, tetopc); // ab enextesym(firsttet, worktet); bond(worktet, tetopa); // bc eprevesym(firsttet, worktet); bond(worktet, tetopb); // ca // Connect hull tetrahedra together (at six edges of firsttet). esym(tetopc, worktet); esym(tetopd, worktet1); bond(worktet, worktet1); // ab esym(tetopa, worktet); eprevesym(tetopd, worktet1); bond(worktet, worktet1); // bc esym(tetopb, worktet); enextesym(tetopd, worktet1); bond(worktet, worktet1); // ca eprevesym(tetopc, worktet); enextesym(tetopb, worktet1); bond(worktet, worktet1); // da eprevesym(tetopa, worktet); enextesym(tetopc, worktet1); bond(worktet, worktet1); // db eprevesym(tetopb, worktet); enextesym(tetopa, worktet1); bond(worktet, worktet1); // dc // Set the vertex type. if (pointtype(pa) == UNUSEDVERTEX) { setpointtype(pa, VOLVERTEX); } if (pointtype(pb) == UNUSEDVERTEX) { setpointtype(pb, VOLVERTEX); } if (pointtype(pc) == UNUSEDVERTEX) { setpointtype(pc, VOLVERTEX); } if (pointtype(pd) == UNUSEDVERTEX) { setpointtype(pd, VOLVERTEX); } setpoint2tet(pa, encode(firsttet)); setpoint2tet(pb, encode(firsttet)); setpoint2tet(pc, encode(firsttet)); setpoint2tet(pd, encode(firsttet)); // Remember the first tetrahedron. recenttet = firsttet; } /////////////////////////////////////////////////////////////////////////////// // // // incrementaldelaunay() Create a Delaunay tetrahedralization by // // the incremental approach. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::incrementaldelaunay(clock_t& tv) { triface searchtet; point *permutarray, swapvertex; REAL v1[3], v2[3], n[3]; REAL bboxsize, bboxsize2, bboxsize3, ori; int randindex; int ngroup = 0; int i, j; if (!b->quiet) { printf("Delaunizing vertices...\n"); } // Form a random permuation (uniformly at random) of the set of vertices. permutarray = new point[in->numberofpoints]; points->traversalinit(); if (b->no_sort) { if (b->verbose) { printf(" Using the input order.\n"); } for (i = 0; i < in->numberofpoints; i++) { permutarray[i] = (point)points->traverse(); } } else { if (b->verbose) { printf(" Permuting vertices.\n"); } srand(in->numberofpoints); for (i = 0; i < in->numberofpoints; i++) { randindex = rand() % (i + 1); // randomnation(i + 1); permutarray[i] = permutarray[randindex]; permutarray[randindex] = (point)points->traverse(); } if (b->brio_hilbert) { // -b option if (b->verbose) { printf(" Sorting vertices.\n"); } hilbert_init(in->mesh_dim); brio_multiscale_sort(permutarray, in->numberofpoints, b->brio_threshold, b->brio_ratio, &ngroup); } } tv = clock(); // Remember the time for sorting points. // Calculate the diagonal size of its bounding box. bboxsize = sqrt(norm2(xmax - xmin, ymax - ymin, zmax - zmin)); bboxsize2 = bboxsize * bboxsize; bboxsize3 = bboxsize2 * bboxsize; // Make sure the second vertex is not identical with the first one. i = 1; while ((distance(permutarray[0], permutarray[i]) / bboxsize) < b->epsilon) { i++; if (i == in->numberofpoints - 1) { printf("Exception: All vertices are (nearly) identical (Tol = %g).\n", b->epsilon); terminatetetgen(this, 10); } } if (i > 1) { // Swap to move the non-identical vertex from index i to index 1. swapvertex = permutarray[i]; permutarray[i] = permutarray[1]; permutarray[1] = swapvertex; } // Make sure the third vertex is not collinear with the first two. // Acknowledgement: Thanks Jan Pomplun for his correction by using // epsilon^2 and epsilon^3 (instead of epsilon). 2013-08-15. i = 2; for (j = 0; j < 3; j++) { v1[j] = permutarray[1][j] - permutarray[0][j]; v2[j] = permutarray[i][j] - permutarray[0][j]; } cross(v1, v2, n); while ((sqrt(norm2(n[0], n[1], n[2])) / bboxsize2) < b->epsilon) { i++; if (i == in->numberofpoints - 1) { printf("Exception: All vertices are (nearly) collinear (Tol = %g).\n", b->epsilon); terminatetetgen(this, 10); } for (j = 0; j < 3; j++) { v2[j] = permutarray[i][j] - permutarray[0][j]; } cross(v1, v2, n); } if (i > 2) { // Swap to move the non-identical vertex from index i to index 1. swapvertex = permutarray[i]; permutarray[i] = permutarray[2]; permutarray[2] = swapvertex; } // Make sure the fourth vertex is not coplanar with the first three. i = 3; ori = orient3dfast(permutarray[0], permutarray[1], permutarray[2], permutarray[i]); while ((fabs(ori) / bboxsize3) < b->epsilon) { i++; if (i == in->numberofpoints) { printf("Exception: All vertices are coplanar (Tol = %g).\n", b->epsilon); terminatetetgen(this, 10); } ori = orient3dfast(permutarray[0], permutarray[1], permutarray[2], permutarray[i]); } if (i > 3) { // Swap to move the non-identical vertex from index i to index 1. swapvertex = permutarray[i]; permutarray[i] = permutarray[3]; permutarray[3] = swapvertex; } // Orient the first four vertices in permutarray so that they follow the // right-hand rule. if (ori > 0.0) { // Swap the first two vertices. swapvertex = permutarray[0]; permutarray[0] = permutarray[1]; permutarray[1] = swapvertex; } // Create the initial Delaunay tetrahedralization. initialdelaunay(permutarray[0], permutarray[1], permutarray[2], permutarray[3]); if (b->verbose) { printf(" Incrementally inserting vertices.\n"); } insertvertexflags ivf; flipconstraints fc; // Choose algorithm: Bowyer-Watson (default) or Incremental Flip if (b->incrflip) { ivf.bowywat = 0; ivf.lawson = 1; fc.enqflag = 1; } else { ivf.bowywat = 1; ivf.lawson = 0; } for (i = 4; i < in->numberofpoints; i++) { if (pointtype(permutarray[i]) == UNUSEDVERTEX) { setpointtype(permutarray[i], VOLVERTEX); } if (b->brio_hilbert || b->no_sort) { // -b or -b/1 // Start the last updated tet. searchtet.tet = recenttet.tet; } else { // -b0 // Randomly choose the starting tet for point location. searchtet.tet = NULL; } ivf.iloc = (int)OUTSIDE; // Insert the vertex. if (insertpoint(permutarray[i], &searchtet, NULL, NULL, &ivf)) { if (flipstack != NULL) { // Perform flip to recover Delaunayness. incrementalflip(permutarray[i], (ivf.iloc == (int)OUTSIDE), &fc); } } else { if (ivf.iloc == (int)ONVERTEX) { // The point already exists. Mark it and do nothing on it. swapvertex = org(searchtet); if (b->object != tetgenbehavior::STL) { if (!b->quiet) { printf("Warning: Point #%d is coincident with #%d. Ignored!\n", pointmark(permutarray[i]), pointmark(swapvertex)); } } setpoint2ppt(permutarray[i], swapvertex); setpointtype(permutarray[i], DUPLICATEDVERTEX); dupverts++; } else if (ivf.iloc == (int)NEARVERTEX) { swapvertex = org(searchtet); if (!b->quiet) { printf("Warning: Point %d is replaced by point %d.\n", pointmark(permutarray[i]), pointmark(swapvertex)); printf(" Avoid creating a very short edge (len = %g) (< %g).\n", permutarray[i][3], minedgelength); printf(" You may try a smaller tolerance (-T) (current is %g)\n", b->epsilon); printf(" or use the option -M0/1 to avoid such replacement.\n"); } // Remember it is a duplicated point. setpoint2ppt(permutarray[i], swapvertex); setpointtype(permutarray[i], DUPLICATEDVERTEX); dupverts++; } else if (ivf.iloc == (int)NONREGULAR) { // The point is non-regular. Skipped. if (b->verbose) { printf(" Point #%d is non-regular, skipped.\n", pointmark(permutarray[i])); } setpointtype(permutarray[i], NREGULARVERTEX); nonregularcount++; } } } delete[] permutarray; } //// //// //// //// //// delaunay_cxx ///////////////////////////////////////////////////////////// //// surface_cxx ////////////////////////////////////////////////////////////// //// //// //// //// /////////////////////////////////////////////////////////////////////////////// // // // flipshpush() Push a facet edge into flip stack. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::flipshpush(face* flipedge) { badface* newflipface; newflipface = (badface*)flippool->alloc(); newflipface->ss = *flipedge; newflipface->forg = sorg(*flipedge); newflipface->fdest = sdest(*flipedge); newflipface->nextitem = flipstack; flipstack = newflipface; } /////////////////////////////////////////////////////////////////////////////// // // // flip22() Perform a 2-to-2 flip in surface mesh. // // // // 'flipfaces' is an array of two subfaces. On input, they are [a,b,c] and // // [b,a,d]. On output, they are [c,d,b] and [d,c,a]. As a result, edge [a,b] // // is replaced by edge [c,d]. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::flip22(face* flipfaces, int flipflag, int chkencflag) { face bdedges[4], outfaces[4], infaces[4]; face bdsegs[4]; face checkface; point pa, pb, pc, pd; int i; pa = sorg(flipfaces[0]); pb = sdest(flipfaces[0]); pc = sapex(flipfaces[0]); pd = sapex(flipfaces[1]); if (sorg(flipfaces[1]) != pb) { sesymself(flipfaces[1]); } flip22count++; // Collect the four boundary edges. senext(flipfaces[0], bdedges[0]); senext2(flipfaces[0], bdedges[1]); senext(flipfaces[1], bdedges[2]); senext2(flipfaces[1], bdedges[3]); // Collect outer boundary faces. for (i = 0; i < 4; i++) { spivot(bdedges[i], outfaces[i]); infaces[i] = outfaces[i]; sspivot(bdedges[i], bdsegs[i]); if (outfaces[i].sh != NULL) { if (isshsubseg(bdedges[i])) { spivot(infaces[i], checkface); while (checkface.sh != bdedges[i].sh) { infaces[i] = checkface; spivot(infaces[i], checkface); } } } } // The flags set in these two subfaces do not change. // Shellmark does not change. // area constraint does not change. // Transform [a,b,c] -> [c,d,b]. setshvertices(flipfaces[0], pc, pd, pb); // Transform [b,a,d] -> [d,c,a]. setshvertices(flipfaces[1], pd, pc, pa); // Update the point-to-subface map. if (pointtype(pa) == FREEFACETVERTEX) { setpoint2sh(pa, sencode(flipfaces[1])); } if (pointtype(pb) == FREEFACETVERTEX) { setpoint2sh(pb, sencode(flipfaces[0])); } if (pointtype(pc) == FREEFACETVERTEX) { setpoint2sh(pc, sencode(flipfaces[0])); } if (pointtype(pd) == FREEFACETVERTEX) { setpoint2sh(pd, sencode(flipfaces[0])); } // Reconnect boundary edges to outer boundary faces. for (i = 0; i < 4; i++) { if (outfaces[(3 + i) % 4].sh != NULL) { // Make sure that the subface has the ori as the segment. if (bdsegs[(3 + i) % 4].sh != NULL) { bdsegs[(3 + i) % 4].shver = 0; if (sorg(bdedges[i]) != sorg(bdsegs[(3 + i) % 4])) { sesymself(bdedges[i]); } } sbond1(bdedges[i], outfaces[(3 + i) % 4]); sbond1(infaces[(3 + i) % 4], bdedges[i]); } else { sdissolve(bdedges[i]); } if (bdsegs[(3 + i) % 4].sh != NULL) { ssbond(bdedges[i], bdsegs[(3 + i) % 4]); if (chkencflag & 1) { // Queue this segment for encroaching check. enqueuesubface(badsubsegs, &(bdsegs[(3 + i) % 4])); } } else { ssdissolve(bdedges[i]); } } if (chkencflag & 2) { // Queue the flipped subfaces for quality/encroaching checks. for (i = 0; i < 2; i++) { enqueuesubface(badsubfacs, &(flipfaces[i])); } } recentsh = flipfaces[0]; if (flipflag) { // Put the boundary edges into flip stack. for (i = 0; i < 4; i++) { flipshpush(&(bdedges[i])); } } } /////////////////////////////////////////////////////////////////////////////// // // // flip31() Remove a vertex by transforming 3-to-1 subfaces. // // // // 'flipfaces' is an array of subfaces. Its length is at least 4. On input, // // the first three faces are: [p,a,b], [p,b,c], and [p,c,a]. This routine // // replaces them by one face [a,b,c], it is returned in flipfaces[3]. // // // // NOTE: The three old subfaces are not deleted within this routine. They // // still hold pointers to their adjacent subfaces. These informations are // // needed by the routine 'sremovevertex()' for recovering a segment. // // The caller of this routine must delete the old subfaces after their uses. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::flip31(face* flipfaces, int flipflag) { face bdedges[3], outfaces[3], infaces[3]; face bdsegs[3]; face checkface; point pa, pb, pc; int i; pa = sdest(flipfaces[0]); pb = sdest(flipfaces[1]); pc = sdest(flipfaces[2]); flip31count++; // Collect all infos at the three boundary edges. for (i = 0; i < 3; i++) { senext(flipfaces[i], bdedges[i]); spivot(bdedges[i], outfaces[i]); infaces[i] = outfaces[i]; sspivot(bdedges[i], bdsegs[i]); if (outfaces[i].sh != NULL) { if (isshsubseg(bdedges[i])) { spivot(infaces[i], checkface); while (checkface.sh != bdedges[i].sh) { infaces[i] = checkface; spivot(infaces[i], checkface); } } } } // i // Create a new subface. makeshellface(subfaces, &(flipfaces[3])); setshvertices(flipfaces[3], pa, pb, pc); setshellmark(flipfaces[3], shellmark(flipfaces[0])); if (checkconstraints) { // area = areabound(flipfaces[0]); setareabound(flipfaces[3], areabound(flipfaces[0])); } if (useinsertradius) { setfacetindex(flipfaces[3], getfacetindex(flipfaces[0])); } // Update the point-to-subface map. if (pointtype(pa) == FREEFACETVERTEX) { setpoint2sh(pa, sencode(flipfaces[3])); } if (pointtype(pb) == FREEFACETVERTEX) { setpoint2sh(pb, sencode(flipfaces[3])); } if (pointtype(pc) == FREEFACETVERTEX) { setpoint2sh(pc, sencode(flipfaces[3])); } // Update the three new boundary edges. bdedges[0] = flipfaces[3]; // [a,b] senext(flipfaces[3], bdedges[1]); // [b,c] senext2(flipfaces[3], bdedges[2]); // [c,a] // Reconnect boundary edges to outer boundary faces. for (i = 0; i < 3; i++) { if (outfaces[i].sh != NULL) { // Make sure that the subface has the ori as the segment. if (bdsegs[i].sh != NULL) { bdsegs[i].shver = 0; if (sorg(bdedges[i]) != sorg(bdsegs[i])) { sesymself(bdedges[i]); } } sbond1(bdedges[i], outfaces[i]); sbond1(infaces[i], bdedges[i]); } if (bdsegs[i].sh != NULL) { ssbond(bdedges[i], bdsegs[i]); } } recentsh = flipfaces[3]; if (flipflag) { // Put the boundary edges into flip stack. for (i = 0; i < 3; i++) { flipshpush(&(bdedges[i])); } } } /////////////////////////////////////////////////////////////////////////////// // // // lawsonflip() Flip non-locally Delaunay edges. // // // /////////////////////////////////////////////////////////////////////////////// long tetgenmesh::lawsonflip() { badface* popface; face flipfaces[2]; point pa, pb, pc, pd; REAL sign; long flipcount = 0; if (b->verbose > 2) { printf(" Lawson flip %ld edges.\n", flippool->items); } while (flipstack != (badface*)NULL) { // Pop an edge from the stack. popface = flipstack; flipfaces[0] = popface->ss; pa = popface->forg; pb = popface->fdest; flipstack = popface->nextitem; // The next top item in stack. flippool->dealloc((void*)popface); // Skip it if it is dead. if (flipfaces[0].sh[3] == NULL) continue; // Skip it if it is not the same edge as we saved. if ((sorg(flipfaces[0]) != pa) || (sdest(flipfaces[0]) != pb)) continue; // Skip it if it is a subsegment. if (isshsubseg(flipfaces[0])) continue; // Get the adjacent face. spivot(flipfaces[0], flipfaces[1]); if (flipfaces[1].sh == NULL) continue; // Skip a hull edge. pc = sapex(flipfaces[0]); pd = sapex(flipfaces[1]); sign = incircle3d(pa, pb, pc, pd); if (sign < 0) { // It is non-locally Delaunay. Flip it. flip22(flipfaces, 1, 0); flipcount++; } } if (b->verbose > 2) { printf(" Performed %ld flips.\n", flipcount); } return flipcount; } /////////////////////////////////////////////////////////////////////////////// // // // sinsertvertex() Insert a vertex into a triangulation of a facet. // // // // This function uses three global arrays: 'caveshlist', 'caveshbdlist', and // // 'caveshseglist'. On return, 'caveshlist' contains old subfaces in C(p), // // 'caveshbdlist' contains new subfaces in C(p). If the new point lies on a // // segment, 'cavesegshlist' returns the two new subsegments. // // // // 'iloc' suggests the location of the point. If it is OUTSIDE, this routine // // will first locate the point. It starts searching from 'searchsh' or 'rec- // // entsh' if 'searchsh' is NULL. // // // // If 'bowywat' is set (1), the Bowyer-Watson algorithm is used to insert // // the vertex. Otherwise, only insert the vertex in the initial cavity. // // // // If 'iloc' is 'INSTAR', this means the cavity of this vertex was already // // provided in the list 'caveshlist'. // // // // If 'splitseg' is not NULL, the new vertex lies on the segment and it will // // be split. 'iloc' must be either 'ONEDGE' or 'INSTAR'. // // // // 'rflag' (rounding) is a parameter passed to slocate() function. If it is // // set, after the location of the point is found, either ONEDGE or ONFACE, // // round the result using an epsilon. // // // // NOTE: the old subfaces in C(p) are not deleted. They're needed in case we // // want to remove the new point immediately. // // // /////////////////////////////////////////////////////////////////////////////// int tetgenmesh::sinsertvertex(point insertpt, face* searchsh, face* splitseg, int iloc, int bowywat, int rflag) { face cavesh, neighsh, *parysh; face newsh, casout, casin; face checkseg; point pa, pb; enum locateresult loc = OUTSIDE; REAL sign, ori; int i, j; if (b->verbose > 2) { printf(" Insert facet point %d.\n", pointmark(insertpt)); } if (bowywat == 3) { loc = INSTAR; } if ((splitseg != NULL) && (splitseg->sh != NULL)) { // A segment is going to be split, no point location. spivot(*splitseg, *searchsh); if (loc != INSTAR) loc = ONEDGE; } else { if (loc != INSTAR) loc = (enum locateresult)iloc; if (loc == OUTSIDE) { // Do point location in surface mesh. if (searchsh->sh == NULL) { *searchsh = recentsh; } // Search the vertex. An above point must be provided ('aflag' = 1). loc = slocate(insertpt, searchsh, 1, 1, rflag); } } // Form the initial sC(p). if (loc == ONFACE) { // Add the face into list (in B-W cavity). smarktest(*searchsh); caveshlist->newindex((void**)&parysh); *parysh = *searchsh; } else if (loc == ONEDGE) { if ((splitseg != NULL) && (splitseg->sh != NULL)) { splitseg->shver = 0; pa = sorg(*splitseg); } else { pa = sorg(*searchsh); } if (searchsh->sh != NULL) { // Collect all subfaces share at this edge. neighsh = *searchsh; while (1) { // Adjust the origin of its edge to be 'pa'. if (sorg(neighsh) != pa) sesymself(neighsh); // Add this face into list (in B-W cavity). smarktest(neighsh); caveshlist->newindex((void**)&parysh); *parysh = neighsh; // Add this face into face-at-splitedge list. cavesegshlist->newindex((void**)&parysh); *parysh = neighsh; // Go to the next face at the edge. spivotself(neighsh); // Stop if all faces at the edge have been visited. if (neighsh.sh == searchsh->sh) break; if (neighsh.sh == NULL) break; } } // If (not a non-dangling segment). } else if (loc == ONVERTEX) { return (int)loc; } else if (loc == OUTSIDE) { // Comment: This should only happen during the surface meshing step. // Enlarge the convex hull of the triangulation by including p. // An above point of the facet is set in 'dummypoint' to replace // orient2d tests by orient3d tests. // Imagine that the current edge a->b (in 'searchsh') is horizontal in a // plane, and a->b is directed from left to right, p lies above a->b. // Find the right-most edge of the triangulation which is visible by p. neighsh = *searchsh; while (1) { senext2self(neighsh); spivot(neighsh, casout); if (casout.sh == NULL) { // A convex hull edge. Is it visible by p. ori = orient3d(sorg(neighsh), sdest(neighsh), dummypoint, insertpt); if (ori < 0) { *searchsh = neighsh; // Visible, update 'searchsh'. } else { break; // 'searchsh' is the right-most visible edge. } } else { if (sorg(casout) != sdest(neighsh)) sesymself(casout); neighsh = casout; } } // Create new triangles for all visible edges of p (from right to left). casin.sh = NULL; // No adjacent face at right. pa = sorg(*searchsh); pb = sdest(*searchsh); while (1) { // Create a new subface on top of the (visible) edge. makeshellface(subfaces, &newsh); setshvertices(newsh, pb, pa, insertpt); setshellmark(newsh, shellmark(*searchsh)); if (checkconstraints) { // area = areabound(*searchsh); setareabound(newsh, areabound(*searchsh)); } if (useinsertradius) { setfacetindex(newsh, getfacetindex(*searchsh)); } // Connect the new subface to the bottom subfaces. sbond1(newsh, *searchsh); sbond1(*searchsh, newsh); // Connect the new subface to its right-adjacent subface. if (casin.sh != NULL) { senext(newsh, casout); sbond1(casout, casin); sbond1(casin, casout); } // The left-adjacent subface has not been created yet. senext2(newsh, casin); // Add the new face into list (inside the B-W cavity). smarktest(newsh); caveshlist->newindex((void**)&parysh); *parysh = newsh; // Move to the convex hull edge at the left of 'searchsh'. neighsh = *searchsh; while (1) { senextself(neighsh); spivot(neighsh, casout); if (casout.sh == NULL) { *searchsh = neighsh; break; } if (sorg(casout) != sdest(neighsh)) sesymself(casout); neighsh = casout; } // A convex hull edge. Is it visible by p. pa = sorg(*searchsh); pb = sdest(*searchsh); ori = orient3d(pa, pb, dummypoint, insertpt); // Finish the process if p is not visible by the hull edge. if (ori >= 0) break; } } else if (loc == INSTAR) { // Under this case, the sub-cavity sC(p) has already been formed in // insertvertex(). } // Form the Bowyer-Watson cavity sC(p). for (i = 0; i < caveshlist->objects; i++) { cavesh = *(face*)fastlookup(caveshlist, i); for (j = 0; j < 3; j++) { if (!isshsubseg(cavesh)) { spivot(cavesh, neighsh); if (neighsh.sh != NULL) { // The adjacent face exists. if (!smarktested(neighsh)) { if (bowywat) { if (loc == INSTAR) { // if (bowywat > 2) { // It must be a boundary edge. sign = 1; } else { // Check if this subface is connected to adjacent tet(s). if (!isshtet(neighsh)) { // Check if the subface is non-Delaunay wrt. the new pt. sign = incircle3d(sorg(neighsh), sdest(neighsh), sapex(neighsh), insertpt); } else { // It is connected to an adjacent tet. A boundary edge. sign = 1; } } if (sign < 0) { // Add the adjacent face in list (in B-W cavity). smarktest(neighsh); caveshlist->newindex((void**)&parysh); *parysh = neighsh; } } else { sign = 1; // A boundary edge. } } else { sign = -1; // Not a boundary edge. } } else { // No adjacent face. It is a hull edge. if (loc == OUTSIDE) { // It is a boundary edge if it does not contain p. if ((sorg(cavesh) == insertpt) || (sdest(cavesh) == insertpt)) { sign = -1; // Not a boundary edge. } else { sign = 1; // A boundary edge. } } else { sign = 1; // A boundary edge. } } } else { // Do not across a segment. It is a boundary edge. sign = 1; } if (sign >= 0) { // Add a boundary edge. caveshbdlist->newindex((void**)&parysh); *parysh = cavesh; } senextself(cavesh); } // j } // i // Creating new subfaces. for (i = 0; i < caveshbdlist->objects; i++) { parysh = (face*)fastlookup(caveshbdlist, i); sspivot(*parysh, checkseg); if ((parysh->shver & 01) != 0) sesymself(*parysh); pa = sorg(*parysh); pb = sdest(*parysh); // Create a new subface. makeshellface(subfaces, &newsh); setshvertices(newsh, pa, pb, insertpt); setshellmark(newsh, shellmark(*parysh)); if (checkconstraints) { // area = areabound(*parysh); setareabound(newsh, areabound(*parysh)); } if (useinsertradius) { setfacetindex(newsh, getfacetindex(*parysh)); } // Update the point-to-subface map. if (pointtype(pa) == FREEFACETVERTEX) { setpoint2sh(pa, sencode(newsh)); } if (pointtype(pb) == FREEFACETVERTEX) { setpoint2sh(pb, sencode(newsh)); } // Connect newsh to outer subfaces. spivot(*parysh, casout); if (casout.sh != NULL) { casin = casout; if (checkseg.sh != NULL) { // Make sure that newsh has the right ori at this segment. checkseg.shver = 0; if (sorg(newsh) != sorg(checkseg)) { sesymself(newsh); sesymself(*parysh); // This side should also be inverse. } spivot(casin, neighsh); while (neighsh.sh != parysh->sh) { casin = neighsh; spivot(casin, neighsh); } } sbond1(newsh, casout); sbond1(casin, newsh); } if (checkseg.sh != NULL) { ssbond(newsh, checkseg); } // Connect oldsh <== newsh (for connecting adjacent new subfaces). // *parysh and newsh point to the same edge and the same ori. sbond1(*parysh, newsh); } if (newsh.sh != NULL) { // Set a handle for searching. recentsh = newsh; } // Update the point-to-subface map. if (pointtype(insertpt) == FREEFACETVERTEX) { setpoint2sh(insertpt, sencode(newsh)); } // Connect adjacent new subfaces together. for (i = 0; i < caveshbdlist->objects; i++) { // Get an old subface at edge [a, b]. parysh = (face*)fastlookup(caveshbdlist, i); spivot(*parysh, newsh); // The new subface [a, b, p]. senextself(newsh); // At edge [b, p]. spivot(newsh, neighsh); if (neighsh.sh == NULL) { // Find the adjacent new subface at edge [b, p]. pb = sdest(*parysh); neighsh = *parysh; while (1) { senextself(neighsh); spivotself(neighsh); if (neighsh.sh == NULL) break; if (!smarktested(neighsh)) break; if (sdest(neighsh) != pb) sesymself(neighsh); } if (neighsh.sh != NULL) { // Now 'neighsh' is a new subface at edge [b, #]. if (sorg(neighsh) != pb) sesymself(neighsh); senext2self(neighsh); // Go to the open edge [p, b]. sbond(newsh, neighsh); } } spivot(*parysh, newsh); // The new subface [a, b, p]. senext2self(newsh); // At edge [p, a]. spivot(newsh, neighsh); if (neighsh.sh == NULL) { // Find the adjacent new subface at edge [p, a]. pa = sorg(*parysh); neighsh = *parysh; while (1) { senext2self(neighsh); spivotself(neighsh); if (neighsh.sh == NULL) break; if (!smarktested(neighsh)) break; if (sorg(neighsh) != pa) sesymself(neighsh); } if (neighsh.sh != NULL) { // Now 'neighsh' is a new subface at edge [#, a]. if (sdest(neighsh) != pa) sesymself(neighsh); senextself(neighsh); // Go to the open edge [a, p]. sbond(newsh, neighsh); } } } if ((loc == ONEDGE) || ((splitseg != NULL) && (splitseg->sh != NULL)) || (cavesegshlist->objects > 0l)) { // An edge is being split. We distinguish two cases: // (1) the edge is not on the boundary of the cavity; // (2) the edge is on the boundary of the cavity. // In case (2), the edge is either a segment or a hull edge. There are // degenerated new faces in the cavity. They must be removed. face aseg, bseg, aoutseg, boutseg; for (i = 0; i < cavesegshlist->objects; i++) { // Get the saved old subface. parysh = (face*)fastlookup(cavesegshlist, i); // Get a possible new degenerated subface. spivot(*parysh, cavesh); if (sapex(cavesh) == insertpt) { // Found a degenerated new subface, i.e., case (2). if (cavesegshlist->objects > 1) { // There are more than one subface share at this edge. j = (i + 1) % (int)cavesegshlist->objects; parysh = (face*)fastlookup(cavesegshlist, j); spivot(*parysh, neighsh); // Adjust cavesh and neighsh both at edge a->b, and has p as apex. if (sorg(neighsh) != sorg(cavesh)) { sesymself(neighsh); } // Connect adjacent faces at two other edges of cavesh and neighsh. // As a result, the two degenerated new faces are squeezed from the // new triangulation of the cavity. Note that the squeezed faces // still hold the adjacent informations which will be used in // re-connecting subsegments (if they exist). for (j = 0; j < 2; j++) { senextself(cavesh); senextself(neighsh); spivot(cavesh, newsh); spivot(neighsh, casout); sbond1(newsh, casout); // newsh <- casout. } } else { // There is only one subface containing this edge [a,b]. Squeeze the // degenerated new face [a,b,c] by disconnecting it from its two // adjacent subfaces at edges [b,c] and [c,a]. Note that the face // [a,b,c] still hold the connection to them. for (j = 0; j < 2; j++) { senextself(cavesh); spivot(cavesh, newsh); sdissolve(newsh); } } // recentsh = newsh; // Update the point-to-subface map. if (pointtype(insertpt) == FREEFACETVERTEX) { setpoint2sh(insertpt, sencode(newsh)); } } } if ((splitseg != NULL) && (splitseg->sh != NULL)) { if (loc != INSTAR) { // if (bowywat < 3) { smarktest(*splitseg); // Mark it as being processed. } aseg = *splitseg; pa = sorg(*splitseg); pb = sdest(*splitseg); // Insert the new point p. makeshellface(subsegs, &aseg); makeshellface(subsegs, &bseg); setshvertices(aseg, pa, insertpt, NULL); setshvertices(bseg, insertpt, pb, NULL); setshellmark(aseg, shellmark(*splitseg)); setshellmark(bseg, shellmark(*splitseg)); if (checkconstraints) { setareabound(aseg, areabound(*splitseg)); setareabound(bseg, areabound(*splitseg)); } if (useinsertradius) { setfacetindex(aseg, getfacetindex(*splitseg)); setfacetindex(bseg, getfacetindex(*splitseg)); } // Connect [#, a]<->[a, p]. senext2(*splitseg, boutseg); // Temporarily use boutseg. spivotself(boutseg); if (boutseg.sh != NULL) { senext2(aseg, aoutseg); sbond(boutseg, aoutseg); } // Connect [p, b]<->[b, #]. senext(*splitseg, aoutseg); spivotself(aoutseg); if (aoutseg.sh != NULL) { senext(bseg, boutseg); sbond(boutseg, aoutseg); } // Connect [a, p] <-> [p, b]. senext(aseg, aoutseg); senext2(bseg, boutseg); sbond(aoutseg, boutseg); // Connect subsegs [a, p] and [p, b] to adjacent new subfaces. // Although the degenerated new faces have been squeezed. They still // hold the connections to the actual new faces. for (i = 0; i < cavesegshlist->objects; i++) { parysh = (face*)fastlookup(cavesegshlist, i); spivot(*parysh, neighsh); // neighsh is a degenerated new face. if (sorg(neighsh) != pa) { sesymself(neighsh); } senext2(neighsh, newsh); spivotself(newsh); // The edge [p, a] in newsh ssbond(newsh, aseg); senext(neighsh, newsh); spivotself(newsh); // The edge [b, p] in newsh ssbond(newsh, bseg); } // Let the point remember the segment it lies on. if (pointtype(insertpt) == FREESEGVERTEX) { setpoint2sh(insertpt, sencode(aseg)); } // Update the point-to-seg map. if (pointtype(pa) == FREESEGVERTEX) { setpoint2sh(pa, sencode(aseg)); } if (pointtype(pb) == FREESEGVERTEX) { setpoint2sh(pb, sencode(bseg)); } } // if ((splitseg != NULL) && (splitseg->sh != NULL)) // Delete all degenerated new faces. for (i = 0; i < cavesegshlist->objects; i++) { parysh = (face*)fastlookup(cavesegshlist, i); spivotself(*parysh); if (sapex(*parysh) == insertpt) { shellfacedealloc(subfaces, parysh->sh); } } cavesegshlist->restart(); if ((splitseg != NULL) && (splitseg->sh != NULL)) { // Return the two new subsegments (for further process). // Re-use 'cavesegshlist'. cavesegshlist->newindex((void**)&parysh); *parysh = aseg; cavesegshlist->newindex((void**)&parysh); *parysh = bseg; } } // if (loc == ONEDGE) return (int)loc; } /////////////////////////////////////////////////////////////////////////////// // // // sremovevertex() Remove a vertex from the surface mesh. // // // // 'delpt' (p) is the vertex to be removed. If 'parentseg' is not NULL, p is // // a segment vertex, and the origin of 'parentseg' is p. Otherwise, p is a // // facet vertex, and the origin of 'parentsh' is p. // // // // Within each facet, we first use a sequence of 2-to-2 flips to flip any // // edge at p, finally use a 3-to-1 flip to remove p. // // // // All new created subfaces are returned in the global array 'caveshbdlist'. // // The new segment (when p is on segment) is returned in 'parentseg'. // // // // If 'lawson' > 0, the Lawson flip algorithm is used to recover Delaunay- // // ness after p is removed. // // // /////////////////////////////////////////////////////////////////////////////// int tetgenmesh::sremovevertex(point delpt, face* parentsh, face* parentseg, int lawson) { face flipfaces[4], spinsh, *parysh; point pa, pb, pc, pd; REAL ori1, ori2; int it, i, j; if (parentseg != NULL) { // 'delpt' (p) should be a Steiner point inserted in a segment [a,b], // where 'parentseg' should be [p,b]. Find the segment [a,p]. face startsh, neighsh, nextsh; face abseg, prevseg, checkseg; face adjseg1, adjseg2; face fakesh; senext2(*parentseg, prevseg); spivotself(prevseg); prevseg.shver = 0; // Restore the original segment [a,b]. pa = sorg(prevseg); pb = sdest(*parentseg); if (b->verbose > 2) { printf(" Remove vertex %d from segment [%d, %d].\n", pointmark(delpt), pointmark(pa), pointmark(pb)); } makeshellface(subsegs, &abseg); setshvertices(abseg, pa, pb, NULL); setshellmark(abseg, shellmark(*parentseg)); if (checkconstraints) { setareabound(abseg, areabound(*parentseg)); } if (useinsertradius) { setfacetindex(abseg, getfacetindex(*parentseg)); } // Connect [#, a]<->[a, b]. senext2(prevseg, adjseg1); spivotself(adjseg1); if (adjseg1.sh != NULL) { adjseg1.shver = 0; senextself(adjseg1); senext2(abseg, adjseg2); sbond(adjseg1, adjseg2); } // Connect [a, b]<->[b, #]. senext(*parentseg, adjseg1); spivotself(adjseg1); if (adjseg1.sh != NULL) { adjseg1.shver = 0; senext2self(adjseg1); senext(abseg, adjseg2); sbond(adjseg1, adjseg2); } // Update the point-to-segment map. setpoint2sh(pa, sencode(abseg)); setpoint2sh(pb, sencode(abseg)); // Get the faces in face ring at segment [p, b]. // Re-use array 'caveshlist'. spivot(*parentseg, *parentsh); if (parentsh->sh != NULL) { spinsh = *parentsh; while (1) { // Save this face in list. caveshlist->newindex((void**)&parysh); *parysh = spinsh; // Go to the next face in the ring. spivotself(spinsh); if (spinsh.sh == NULL) { break; // It is possible there is only one facet. } if (spinsh.sh == parentsh->sh) break; } } // Create the face ring of the new segment [a,b]. Each face in the ring // is [a,b,p] (degenerated!). It will be removed (automatically). for (i = 0; i < caveshlist->objects; i++) { parysh = (face*)fastlookup(caveshlist, i); startsh = *parysh; if (sorg(startsh) != delpt) { sesymself(startsh); } // startsh is [p, b, #1], find the subface [a, p, #2]. neighsh = startsh; while (1) { senext2self(neighsh); sspivot(neighsh, checkseg); if (checkseg.sh != NULL) { // It must be the segment [a, p]. break; } spivotself(neighsh); if (sorg(neighsh) != delpt) sesymself(neighsh); } // Now neighsh is [a, p, #2]. if (neighsh.sh != startsh.sh) { // Detach the two subsegments [a,p] and [p,b] from subfaces. ssdissolve(startsh); ssdissolve(neighsh); // Create a degenerated subface [a,b,p]. It is used to: (1) hold the // new segment [a,b]; (2) connect to the two adjacent subfaces // [p,b,#] and [a,p,#]. makeshellface(subfaces, &fakesh); setshvertices(fakesh, pa, pb, delpt); setshellmark(fakesh, shellmark(startsh)); // Connect fakesh to the segment [a,b]. ssbond(fakesh, abseg); // Connect fakesh to adjacent subfaces: [p,b,#1] and [a,p,#2]. senext(fakesh, nextsh); sbond(nextsh, startsh); senext2(fakesh, nextsh); sbond(nextsh, neighsh); smarktest(fakesh); // Mark it as faked. } else { // Special case. There exists already a degenerated face [a,b,p]! // There is no need to create a faked subface here. senext2self(neighsh); // [a,b,p] // Since we will re-connect the face ring using the faked subfaces. // We put the adjacent face of [a,b,p] to the list. spivot(neighsh, startsh); // The original adjacent subface. if (sorg(startsh) != pa) sesymself(startsh); sdissolve(startsh); // Connect fakesh to the segment [a,b]. ssbond(startsh, abseg); fakesh = startsh; // Do not mark it! // Delete the degenerated subface. shellfacedealloc(subfaces, neighsh.sh); } // Save the fakesh in list (for re-creating the face ring). cavesegshlist->newindex((void**)&parysh); *parysh = fakesh; } // i caveshlist->restart(); // Re-create the face ring. if (cavesegshlist->objects > 1) { for (i = 0; i < cavesegshlist->objects; i++) { parysh = (face*)fastlookup(cavesegshlist, i); fakesh = *parysh; // Get the next face in the ring. j = (i + 1) % cavesegshlist->objects; parysh = (face*)fastlookup(cavesegshlist, j); nextsh = *parysh; sbond1(fakesh, nextsh); } } // Delete the two subsegments containing p. shellfacedealloc(subsegs, parentseg->sh); shellfacedealloc(subsegs, prevseg.sh); // Return the new segment. *parentseg = abseg; } else { // p is inside the surface. if (b->verbose > 2) { printf(" Remove vertex %d from surface.\n", pointmark(delpt)); } // Let 'delpt' be its apex. senextself(*parentsh); // For unifying the code, we add parentsh to list. cavesegshlist->newindex((void**)&parysh); *parysh = *parentsh; } // Remove the point (p). for (it = 0; it < cavesegshlist->objects; it++) { parentsh = (face*)fastlookup(cavesegshlist, it); // [a,b,p] senextself(*parentsh); // [b,p,a]. spivotself(*parentsh); if (sorg(*parentsh) != delpt) sesymself(*parentsh); // now parentsh is [p,b,#]. if (sorg(*parentsh) != delpt) { // The vertex has already been removed in above special case. continue; } while (1) { // Initialize the flip edge list. Re-use 'caveshlist'. spinsh = *parentsh; // [p, b, #] while (1) { caveshlist->newindex((void**)&parysh); *parysh = spinsh; senext2self(spinsh); spivotself(spinsh); if (spinsh.sh == parentsh->sh) break; if (sorg(spinsh) != delpt) sesymself(spinsh); } // while (1) if (caveshlist->objects == 3) { // Delete the point by a 3-to-1 flip. for (i = 0; i < 3; i++) { parysh = (face*)fastlookup(caveshlist, i); flipfaces[i] = *parysh; } flip31(flipfaces, lawson); for (i = 0; i < 3; i++) { shellfacedealloc(subfaces, flipfaces[i].sh); } caveshlist->restart(); // Save the new subface. caveshbdlist->newindex((void**)&parysh); *parysh = flipfaces[3]; // The vertex is removed. break; } // Search an edge to flip. for (i = 0; i < caveshlist->objects; i++) { parysh = (face*)fastlookup(caveshlist, i); flipfaces[0] = *parysh; spivot(flipfaces[0], flipfaces[1]); if (sorg(flipfaces[0]) != sdest(flipfaces[1])) sesymself(flipfaces[1]); // Skip this edge if it belongs to a faked subface. if (!smarktested(flipfaces[0]) && !smarktested(flipfaces[1])) { pa = sorg(flipfaces[0]); pb = sdest(flipfaces[0]); pc = sapex(flipfaces[0]); pd = sapex(flipfaces[1]); calculateabovepoint4(pa, pb, pc, pd); // Check if a 2-to-2 flip is possible. ori1 = orient3d(pc, pd, dummypoint, pa); ori2 = orient3d(pc, pd, dummypoint, pb); if (ori1 * ori2 < 0) { // A 2-to-2 flip is found. flip22(flipfaces, lawson, 0); // The i-th edge is flipped. The i-th and (i-1)-th subfaces are // changed. The 'flipfaces[1]' contains p as its apex. senext2(flipfaces[1], *parentsh); // Save the new subface. caveshbdlist->newindex((void**)&parysh); *parysh = flipfaces[0]; break; } } // } // i if (i == caveshlist->objects) { // Do a flip22 and a flip31 to remove p. parysh = (face*)fastlookup(caveshlist, 0); flipfaces[0] = *parysh; spivot(flipfaces[0], flipfaces[1]); if (sorg(flipfaces[0]) != sdest(flipfaces[1])) { sesymself(flipfaces[1]); } flip22(flipfaces, lawson, 0); senext2(flipfaces[1], *parentsh); // Save the new subface. caveshbdlist->newindex((void**)&parysh); *parysh = flipfaces[0]; } // The edge list at p are changed. caveshlist->restart(); } // while (1) } // it cavesegshlist->restart(); if (b->verbose > 2) { printf(" Created %ld new subfaces.\n", caveshbdlist->objects); } if (lawson) { lawsonflip(); } return 0; } /////////////////////////////////////////////////////////////////////////////// // // // slocate() Locate a point in a surface triangulation. // // // // Staring the search from 'searchsh'(it should not be NULL). Perform a line // // walk search for a subface containing the point (p). // // // // If 'aflag' is set, the 'dummypoint' is pre-calculated so that it lies // // above the 'searchsh' in its current orientation. The test if c is CCW to // // the line a->b can be done by the test if c is below the oriented plane // // a->b->dummypoint. // // // // If 'cflag' is not TRUE, the triangulation may not be convex. Stop search // // when a segment is met and return OUTSIDE. // // // // If 'rflag' (rounding) is set, after the location of the point is found, // // either ONEDGE or ONFACE, round the result using an epsilon. // // // // The returned value indicates the following cases: // // - ONVERTEX, p is the origin of 'searchsh'. // // - ONEDGE, p lies on the edge of 'searchsh'. // // - ONFACE, p lies in the interior of 'searchsh'. // // - OUTSIDE, p lies outside of the triangulation, p is on the left-hand // // side of the edge 'searchsh'(s), i.e., org(s), dest(s), p are CW. // // // /////////////////////////////////////////////////////////////////////////////// enum tetgenmesh::locateresult tetgenmesh::slocate(point searchpt, face* searchsh, int aflag, int cflag, int rflag) { face neighsh; point pa, pb, pc; enum locateresult loc; enum { MOVE_BC, MOVE_CA } nextmove; REAL ori, ori_bc, ori_ca; int i; pa = sorg(*searchsh); pb = sdest(*searchsh); pc = sapex(*searchsh); if (!aflag) { // No above point is given. Calculate an above point for this facet. calculateabovepoint4(pa, pb, pc, searchpt); } // 'dummypoint' is given. Make sure it is above [a,b,c] ori = orient3d(pa, pb, pc, dummypoint); if (ori > 0) { sesymself(*searchsh); // Reverse the face orientation. } else if (ori == 0.0) { // This case should not happen theoretically. But... return UNKNOWN; } // Find an edge of the face s.t. p lies on its right-hand side (CCW). for (i = 0; i < 3; i++) { pa = sorg(*searchsh); pb = sdest(*searchsh); ori = orient3d(pa, pb, dummypoint, searchpt); if (ori > 0) break; senextself(*searchsh); } if (i == 3) { return UNKNOWN; } pc = sapex(*searchsh); if (pc == searchpt) { senext2self(*searchsh); return ONVERTEX; } while (1) { ori_bc = orient3d(pb, pc, dummypoint, searchpt); ori_ca = orient3d(pc, pa, dummypoint, searchpt); if (ori_bc < 0) { if (ori_ca < 0) { // (--) // Any of the edges is a viable move. if (randomnation(2)) { nextmove = MOVE_CA; } else { nextmove = MOVE_BC; } } else { // (-#) // Edge [b, c] is viable. nextmove = MOVE_BC; } } else { if (ori_ca < 0) { // (#-) // Edge [c, a] is viable. nextmove = MOVE_CA; } else { if (ori_bc > 0) { if (ori_ca > 0) { // (++) loc = ONFACE; // Inside [a, b, c]. break; } else { // (+0) senext2self(*searchsh); // On edge [c, a]. loc = ONEDGE; break; } } else { // ori_bc == 0 if (ori_ca > 0) { // (0+) senextself(*searchsh); // On edge [b, c]. loc = ONEDGE; break; } else { // (00) // p is coincident with vertex c. senext2self(*searchsh); return ONVERTEX; } } } } // Move to the next face. if (nextmove == MOVE_BC) { senextself(*searchsh); } else { senext2self(*searchsh); } if (!cflag) { // NON-convex case. Check if we will cross a boundary. if (isshsubseg(*searchsh)) { return ENCSEGMENT; } } spivot(*searchsh, neighsh); if (neighsh.sh == NULL) { return OUTSIDE; // A hull edge. } // Adjust the edge orientation. if (sorg(neighsh) != sdest(*searchsh)) { sesymself(neighsh); } // Update the newly discovered face and its endpoints. *searchsh = neighsh; pa = sorg(*searchsh); pb = sdest(*searchsh); pc = sapex(*searchsh); if (pc == searchpt) { senext2self(*searchsh); return ONVERTEX; } } // while (1) // assert(loc == ONFACE || loc == ONEDGE); if (rflag) { // Round the locate result before return. REAL n[3], area_abc, area_abp, area_bcp, area_cap; pa = sorg(*searchsh); pb = sdest(*searchsh); pc = sapex(*searchsh); facenormal(pa, pb, pc, n, 1, NULL); area_abc = sqrt(dot(n, n)); facenormal(pb, pc, searchpt, n, 1, NULL); area_bcp = sqrt(dot(n, n)); if ((area_bcp / area_abc) < b->epsilon) { area_bcp = 0; // Rounding. } facenormal(pc, pa, searchpt, n, 1, NULL); area_cap = sqrt(dot(n, n)); if ((area_cap / area_abc) < b->epsilon) { area_cap = 0; // Rounding } if ((loc == ONFACE) || (loc == OUTSIDE)) { facenormal(pa, pb, searchpt, n, 1, NULL); area_abp = sqrt(dot(n, n)); if ((area_abp / area_abc) < b->epsilon) { area_abp = 0; // Rounding } } else { // loc == ONEDGE area_abp = 0; } if (area_abp == 0) { if (area_bcp == 0) { senextself(*searchsh); loc = ONVERTEX; // p is close to b. } else { if (area_cap == 0) { loc = ONVERTEX; // p is close to a. } else { loc = ONEDGE; // p is on edge [a,b]. } } } else if (area_bcp == 0) { if (area_cap == 0) { senext2self(*searchsh); loc = ONVERTEX; // p is close to c. } else { senextself(*searchsh); loc = ONEDGE; // p is on edge [b,c]. } } else if (area_cap == 0) { senext2self(*searchsh); loc = ONEDGE; // p is on edge [c,a]. } else { loc = ONFACE; // p is on face [a,b,c]. } } // if (rflag) return loc; } /////////////////////////////////////////////////////////////////////////////// // // // sscoutsegment() Look for a segment in the surface triangulation. // // // // The segment is given by the origin of 'searchsh' and 'endpt'. // // // // If an edge in T is found matching this segment, the segment is "locked" // // in T at the edge. Otherwise, flip the first edge in T that the segment // // crosses. Continue the search from the flipped face. // // // // This routine uses 'orisent3d' to determine the search direction. It uses // // 'dummypoint' as the 'lifted point' in 3d, and it assumes that it (dummy- // // point) lies above the 'searchsh' (w.r.t the Right-hand rule). // // // /////////////////////////////////////////////////////////////////////////////// enum tetgenmesh::interresult tetgenmesh::sscoutsegment(face* searchsh, point endpt, int insertsegflag, int reporterrorflag, int chkencflag) { face flipshs[2], neighsh; point startpt, pa, pb, pc, pd; enum interresult dir; enum { MOVE_AB, MOVE_CA } nextmove; REAL ori_ab, ori_ca, len; pc = NULL; // Avoid warnings from MSVC // The origin of 'searchsh' is fixed. startpt = sorg(*searchsh); nextmove = MOVE_AB; // Avoid compiler warning. if (b->verbose > 2) { printf(" Scout segment (%d, %d).\n", pointmark(startpt), pointmark(endpt)); } len = distance(startpt, endpt); // Search an edge in 'searchsh' on the path of this segment. while (1) { pb = sdest(*searchsh); if (pb == endpt) { dir = SHAREEDGE; // Found! break; } pc = sapex(*searchsh); if (pc == endpt) { senext2self(*searchsh); sesymself(*searchsh); dir = SHAREEDGE; // Found! break; } // Round the results. if ((sqrt(triarea(startpt, pb, endpt)) / len) < b->epsilon) { ori_ab = 0.0; } else { ori_ab = orient3d(startpt, pb, dummypoint, endpt); } if ((sqrt(triarea(pc, startpt, endpt)) / len) < b->epsilon) { ori_ca = 0.0; } else { ori_ca = orient3d(pc, startpt, dummypoint, endpt); } if (ori_ab < 0) { if (ori_ca < 0) { // (--) // Both sides are viable moves. if (randomnation(2)) { nextmove = MOVE_CA; } else { nextmove = MOVE_AB; } } else { // (-#) nextmove = MOVE_AB; } } else { if (ori_ca < 0) { // (#-) nextmove = MOVE_CA; } else { if (ori_ab > 0) { if (ori_ca > 0) { // (++) // The segment intersects with edge [b, c]. dir = ACROSSEDGE; break; } else { // (+0) // The segment collinear with edge [c, a]. senext2self(*searchsh); sesymself(*searchsh); dir = ACROSSVERT; break; } } else { if (ori_ca > 0) { // (0+) // The segment is collinear with edge [a, b]. dir = ACROSSVERT; break; } else { // (00) // startpt == endpt. Not possible. terminatetetgen(this, 2); } } } } // Move 'searchsh' to the next face, keep the origin unchanged. if (nextmove == MOVE_AB) { if (chkencflag) { // Do not cross boundary. if (isshsubseg(*searchsh)) { return ACROSSEDGE; // ACROSS_SEG } } spivot(*searchsh, neighsh); if (neighsh.sh != NULL) { if (sorg(neighsh) != pb) sesymself(neighsh); senext(neighsh, *searchsh); } else { // This side (startpt->pb) is outside. It is caused by rounding error. // Try the next side, i.e., (pc->startpt). senext2(*searchsh, neighsh); if (chkencflag) { // Do not cross boundary. if (isshsubseg(neighsh)) { *searchsh = neighsh; return ACROSSEDGE; // ACROSS_SEG } } spivotself(neighsh); if (sdest(neighsh) != pc) sesymself(neighsh); *searchsh = neighsh; } } else { // MOVE_CA senext2(*searchsh, neighsh); if (chkencflag) { // Do not cross boundary. if (isshsubseg(neighsh)) { *searchsh = neighsh; return ACROSSEDGE; // ACROSS_SEG } } spivotself(neighsh); if (neighsh.sh != NULL) { if (sdest(neighsh) != pc) sesymself(neighsh); *searchsh = neighsh; } else { // The same reason as above. // Try the next side, i.e., (startpt->pb). if (chkencflag) { // Do not cross boundary. if (isshsubseg(*searchsh)) { return ACROSSEDGE; // ACROSS_SEG } } spivot(*searchsh, neighsh); if (sorg(neighsh) != pb) sesymself(neighsh); senext(neighsh, *searchsh); } } } // while if (dir == SHAREEDGE) { if (insertsegflag) { // Insert the segment into the triangulation. face newseg; makeshellface(subsegs, &newseg); setshvertices(newseg, startpt, endpt, NULL); // Set the default segment marker. setshellmark(newseg, -1); ssbond(*searchsh, newseg); spivot(*searchsh, neighsh); if (neighsh.sh != NULL) { ssbond(neighsh, newseg); } } return dir; } if (dir == ACROSSVERT) { // A point is found collinear with this segment. if (reporterrorflag) { point pp = sdest(*searchsh); printf("PLC Error: A vertex lies in a segment in facet #%d.\n", shellmark(*searchsh)); printf(" Vertex: [%d] (%g,%g,%g).\n", pointmark(pp), pp[0], pp[1], pp[2]); printf(" Segment: [%d, %d]\n", pointmark(startpt), pointmark(endpt)); } return dir; } if (dir == ACROSSEDGE) { // Edge [b, c] intersects with the segment. senext(*searchsh, flipshs[0]); if (isshsubseg(flipshs[0])) { if (reporterrorflag) { REAL P[3], Q[3], tp = 0, tq = 0; linelineint(startpt, endpt, pb, pc, P, Q, &tp, &tq); printf("PLC Error: Two segments intersect at point (%g,%g,%g),", P[0], P[1], P[2]); printf(" in facet #%d.\n", shellmark(*searchsh)); printf(" Segment 1: [%d, %d]\n", pointmark(pb), pointmark(pc)); printf(" Segment 2: [%d, %d]\n", pointmark(startpt), pointmark(endpt)); } return dir; // ACROSS_SEG } // Flip edge [b, c], queue unflipped edges (for Delaunay checks). spivot(flipshs[0], flipshs[1]); if (sorg(flipshs[1]) != sdest(flipshs[0])) sesymself(flipshs[1]); flip22(flipshs, 1, 0); // The flip may create an inverted triangle, check it. pa = sapex(flipshs[1]); pb = sapex(flipshs[0]); pc = sorg(flipshs[0]); pd = sdest(flipshs[0]); // Check if pa and pb are on the different sides of [pc, pd]. // Re-use ori_ab, ori_ca for the tests. ori_ab = orient3d(pc, pd, dummypoint, pb); ori_ca = orient3d(pd, pc, dummypoint, pa); if (ori_ab <= 0) { flipshpush(&(flipshs[0])); } else if (ori_ca <= 0) { flipshpush(&(flipshs[1])); } // Set 'searchsh' s.t. its origin is 'startpt'. *searchsh = flipshs[0]; } return sscoutsegment(searchsh, endpt, insertsegflag, reporterrorflag, chkencflag); } /////////////////////////////////////////////////////////////////////////////// // // // scarveholes() Remove triangles not in the facet. // // // // This routine re-uses the two global arrays: caveshlist and caveshbdlist. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::scarveholes(int holes, REAL* holelist) { face *parysh, searchsh, neighsh; enum locateresult loc; int i, j; // Get all triangles. Infect unprotected convex hull triangles. smarktest(recentsh); caveshlist->newindex((void**)&parysh); *parysh = recentsh; for (i = 0; i < caveshlist->objects; i++) { parysh = (face*)fastlookup(caveshlist, i); searchsh = *parysh; searchsh.shver = 0; for (j = 0; j < 3; j++) { spivot(searchsh, neighsh); // Is this side on the convex hull? if (neighsh.sh != NULL) { if (!smarktested(neighsh)) { smarktest(neighsh); caveshlist->newindex((void**)&parysh); *parysh = neighsh; } } else { // A hull side. Check if it is protected by a segment. if (!isshsubseg(searchsh)) { // Not protected. Save this face. if (!sinfected(searchsh)) { sinfect(searchsh); caveshbdlist->newindex((void**)&parysh); *parysh = searchsh; } } } senextself(searchsh); } } // Infect the triangles in the holes. for (i = 0; i < 3 * holes; i += 3) { searchsh = recentsh; loc = slocate(&(holelist[i]), &searchsh, 1, 1, 0); if (loc != OUTSIDE) { sinfect(searchsh); caveshbdlist->newindex((void**)&parysh); *parysh = searchsh; } } // Find and infect all exterior triangles. for (i = 0; i < caveshbdlist->objects; i++) { parysh = (face*)fastlookup(caveshbdlist, i); searchsh = *parysh; searchsh.shver = 0; for (j = 0; j < 3; j++) { spivot(searchsh, neighsh); if (neighsh.sh != NULL) { if (!isshsubseg(searchsh)) { if (!sinfected(neighsh)) { sinfect(neighsh); caveshbdlist->newindex((void**)&parysh); *parysh = neighsh; } } else { sdissolve(neighsh); // Disconnect a protected face. } } senextself(searchsh); } } // Delete exterior triangles, unmark interior triangles. for (i = 0; i < caveshlist->objects; i++) { parysh = (face*)fastlookup(caveshlist, i); if (sinfected(*parysh)) { shellfacedealloc(subfaces, parysh->sh); } else { sunmarktest(*parysh); } } caveshlist->restart(); caveshbdlist->restart(); } /////////////////////////////////////////////////////////////////////////////// // // // triangulate() Create a CDT for the facet. // // // // All vertices of the triangulation have type FACETVERTEX. The actual type // // of boundary vertices are set by the routine unifysements(). // // // // All segments created here will have a default marker '-1'. Some of these // // segments will get their actual marker defined in 'edgemarkerlist'. // // // /////////////////////////////////////////////////////////////////////////////// int tetgenmesh::triangulate(int shmark, arraypool* ptlist, arraypool* conlist, int holes, REAL* holelist) { face searchsh, newsh, *parysh; face newseg, *paryseg; point pa, pb, pc, *ppt, *cons; int iloc; int i, j; if (b->verbose > 2) { printf(" f%d: %ld vertices, %ld segments", shmark, ptlist->objects, conlist->objects); if (holes > 0) { printf(", %d holes", holes); } printf(".\n"); } if (ptlist->objects < 2l) { // Not a segment or a facet. return 1; } else if (ptlist->objects == 2l) { pa = *(point*)fastlookup(ptlist, 0); pb = *(point*)fastlookup(ptlist, 1); if (distance(pa, pb) > 0) { // It is a single segment. makeshellface(subsegs, &newseg); setshvertices(newseg, pa, pb, NULL); setshellmark(newseg, -1); } if (pointtype(pa) == VOLVERTEX) { setpointtype(pa, FACETVERTEX); } if (pointtype(pb) == VOLVERTEX) { setpointtype(pb, FACETVERTEX); } return 1; } else if (ptlist->objects == 3) { pa = *(point*)fastlookup(ptlist, 0); pb = *(point*)fastlookup(ptlist, 1); pc = *(point*)fastlookup(ptlist, 2); } else { // Calculate an above point of this facet. if (!calculateabovepoint(ptlist, &pa, &pb, &pc)) { if (!b->quiet) { printf("Warning: Unable to triangulate facet #%d. Skipped!\n", shmark); } return 0; // The point set is degenerate. } } // Create an initial triangulation. makeshellface(subfaces, &newsh); setshvertices(newsh, pa, pb, pc); setshellmark(newsh, shmark); recentsh = newsh; if (pointtype(pa) == VOLVERTEX) { setpointtype(pa, FACETVERTEX); } if (pointtype(pb) == VOLVERTEX) { setpointtype(pb, FACETVERTEX); } if (pointtype(pc) == VOLVERTEX) { setpointtype(pc, FACETVERTEX); } // Are there area constraints? if (b->quality && (in->facetconstraintlist != NULL)) { for (i = 0; i < in->numberoffacetconstraints; i++) { if (shmark == ((int)in->facetconstraintlist[i * 2])) { REAL area = in->facetconstraintlist[i * 2 + 1]; setareabound(newsh, area); break; } } } if (ptlist->objects == 3) { // The triangulation only has one element. for (i = 0; i < 3; i++) { makeshellface(subsegs, &newseg); setshvertices(newseg, sorg(newsh), sdest(newsh), NULL); setshellmark(newseg, -1); ssbond(newsh, newseg); senextself(newsh); } return 1; } // Triangulate the facet. It may not success (due to rounding error, or // incorrect input data), use 'caveencshlist' and 'caveencseglist' are // re-used to store all the newly created subfaces and segments. So we // can clean them if the triangulation is not successful. caveencshlist->newindex((void**)&parysh); *parysh = newsh; // Incrementally build the triangulation. pinfect(pa); pinfect(pb); pinfect(pc); for (i = 0; i < ptlist->objects; i++) { ppt = (point*)fastlookup(ptlist, i); if (!pinfected(*ppt)) { searchsh = recentsh; // Start from 'recentsh'. iloc = (int)OUTSIDE; // Insert the vertex. Use Bowyer-Watson algo. Round the location. iloc = sinsertvertex(*ppt, &searchsh, NULL, iloc, 1, 1); if (iloc != ((int)ONVERTEX)) { // Point inserted successfully. if (pointtype(*ppt) == VOLVERTEX) { setpointtype(*ppt, FACETVERTEX); } // Save the set of new subfaces. for (j = 0; j < caveshbdlist->objects; j++) { // Get an old subface at edge [a, b]. parysh = (face*)fastlookup(caveshbdlist, j); spivot(*parysh, searchsh); // The new subface [a, b, p]. // Do not save a deleted new face (degenerated). if (searchsh.sh[3] != NULL) { caveencshlist->newindex((void**)&parysh); *parysh = searchsh; } } // Delete all removed subfaces. for (j = 0; j < caveshlist->objects; j++) { parysh = (face*)fastlookup(caveshlist, j); shellfacedealloc(subfaces, parysh->sh); } // Clear the global lists. caveshbdlist->restart(); caveshlist->restart(); cavesegshlist->restart(); } else { // The facet triangulation is failed. break; } } } // i puninfect(pa); puninfect(pb); puninfect(pc); if (i < ptlist->objects) { // The facet triangulation is failed. Clean the new subfaces. // There is no new segment be created yet. if (!b->quiet) { printf("Warning: Fail to triangulate facet #%d. Skipped!\n", shmark); } for (i = 0; i < caveencshlist->objects; i++) { parysh = (face*)fastlookup(caveencshlist, i); if (parysh->sh[3] != NULL) { shellfacedealloc(subfaces, parysh->sh); } } caveencshlist->restart(); return 0; } // Insert the segments. for (i = 0; i < conlist->objects; i++) { cons = (point*)fastlookup(conlist, i); searchsh = recentsh; iloc = (int)slocate(cons[0], &searchsh, 1, 1, 0); if (iloc != (int)ONVERTEX) { // Not found due to roundoff errors. Do a brute-force search. subfaces->traversalinit(); searchsh.sh = shellfacetraverse(subfaces); while (searchsh.sh != NULL) { // Only search the subface in the same facet. if (shellmark(searchsh) == shmark) { if ((point)searchsh.sh[3] == cons[0]) { searchsh.shver = 0; break; } else if ((point)searchsh.sh[4] == cons[0]) { searchsh.shver = 2; break; } else if ((point)searchsh.sh[5] == cons[0]) { searchsh.shver = 4; break; } } searchsh.sh = shellfacetraverse(subfaces); } } // Recover the segment. Some edges may be flipped. if (sscoutsegment(&searchsh, cons[1], 1, 1, 0) != SHAREEDGE) { break; // Fail to recover a segment. } // Save this newseg. sspivot(searchsh, newseg); caveencseglist->newindex((void**)&paryseg); *paryseg = newseg; if (flipstack != NULL) { // Recover locally Delaunay edges. lawsonflip(); } } // i if (i < conlist->objects) { if (!b->quiet) { printf("Warning: Fail to recover a segment in facet #%d. Skipped!\n", shmark); } for (i = 0; i < caveencshlist->objects; i++) { parysh = (face*)fastlookup(caveencshlist, i); if (parysh->sh[3] != NULL) { shellfacedealloc(subfaces, parysh->sh); } } for (i = 0; i < caveencseglist->objects; i++) { paryseg = (face*)fastlookup(caveencseglist, i); if (paryseg->sh[3] != NULL) { shellfacedealloc(subsegs, paryseg->sh); } } caveencshlist->restart(); caveencseglist->restart(); return 0; } // Remove exterior and hole triangles. scarveholes(holes, holelist); caveencshlist->restart(); caveencseglist->restart(); return 1; } /////////////////////////////////////////////////////////////////////////////// // // // unifysegments() Remove redundant segments and create face links. // // // // After this routine, although segments are unique, but some of them may be // // removed later by mergefacet(). All vertices still have type FACETVERTEX. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::unifysegments() { badface *facelink = NULL, *newlinkitem, *f1, *f2; face *facperverlist, sface; face subsegloop, testseg; point torg, tdest; REAL ori1, ori2, ori3; REAL n1[3], n2[3]; REAL cosang, ang, ang_tol; int* idx2faclist; int idx, k, m; if (b->verbose > 1) { printf(" Unifying segments.\n"); } // The limit dihedral angle that two facets are not overlapping. ang_tol = b->facet_overlap_ang_tol / 180.0 * PI; if (ang_tol < 0.0) ang_tol = 0.0; // Create a mapping from vertices to subfaces. makepoint2submap(subfaces, idx2faclist, facperverlist); subsegloop.shver = 0; subsegs->traversalinit(); subsegloop.sh = shellfacetraverse(subsegs); while (subsegloop.sh != (shellface*)NULL) { torg = sorg(subsegloop); tdest = sdest(subsegloop); idx = pointmark(torg) - in->firstnumber; // Loop through the set of subfaces containing 'torg'. Get all the // subfaces containing the edge (torg, tdest). Save and order them // in 'sfacelist', the ordering is defined by the right-hand rule // with thumb points from torg to tdest. for (k = idx2faclist[idx]; k < idx2faclist[idx + 1]; k++) { sface = facperverlist[k]; // The face may be deleted if it is a duplicated face. if (sface.sh[3] == NULL) continue; // Search the edge torg->tdest. if (sdest(sface) != tdest) { senext2self(sface); sesymself(sface); } if (sdest(sface) != tdest) continue; // Save the face f in facelink. if (flippool->items >= 2) { f1 = facelink; for (m = 0; m < flippool->items - 1; m++) { f2 = f1->nextitem; ori1 = orient3d(torg, tdest, sapex(f1->ss), sapex(f2->ss)); ori2 = orient3d(torg, tdest, sapex(f1->ss), sapex(sface)); if (ori1 > 0) { // apex(f2) is below f1. if (ori2 > 0) { // apex(f) is below f1 (see Fig.1). ori3 = orient3d(torg, tdest, sapex(f2->ss), sapex(sface)); if (ori3 > 0) { // apex(f) is below f2, insert it. break; } else if (ori3 < 0) { // apex(f) is above f2, continue. } else { // ori3 == 0; // f is coplanar and codirection with f2. report_overlapping_facets(&(f2->ss), &sface); break; } } else if (ori2 < 0) { // apex(f) is above f1 below f2, inset it (see Fig. 2). break; } else { // ori2 == 0; // apex(f) is coplanar with f1 (see Fig. 5). ori3 = orient3d(torg, tdest, sapex(f2->ss), sapex(sface)); if (ori3 > 0) { // apex(f) is below f2, insert it. break; } else { // f is coplanar and codirection with f1. report_overlapping_facets(&(f1->ss), &sface); break; } } } else if (ori1 < 0) { // apex(f2) is above f1. if (ori2 > 0) { // apex(f) is below f1, continue (see Fig. 3). } else if (ori2 < 0) { // apex(f) is above f1 (see Fig.4). ori3 = orient3d(torg, tdest, sapex(f2->ss), sapex(sface)); if (ori3 > 0) { // apex(f) is below f2, insert it. break; } else if (ori3 < 0) { // apex(f) is above f2, continue. } else { // ori3 == 0; // f is coplanar and codirection with f2. report_overlapping_facets(&(f2->ss), &sface); break; } } else { // ori2 == 0; // f is coplanar and with f1 (see Fig. 6). ori3 = orient3d(torg, tdest, sapex(f2->ss), sapex(sface)); if (ori3 > 0) { // f is also codirection with f1. report_overlapping_facets(&(f1->ss), &sface); break; } else { // f is above f2, continue. } } } else { // ori1 == 0; // apex(f2) is coplanar with f1. By assumption, f1 is not // coplanar and codirection with f2. if (ori2 > 0) { // apex(f) is below f1, continue (see Fig. 7). } else if (ori2 < 0) { // apex(f) is above f1, insert it (see Fig. 7). break; } else { // ori2 == 0. // apex(f) is coplanar with f1 (see Fig. 8). // f is either codirection with f1 or is codirection with f2. facenormal(torg, tdest, sapex(f1->ss), n1, 1, NULL); facenormal(torg, tdest, sapex(sface), n2, 1, NULL); if (dot(n1, n2) > 0) { report_overlapping_facets(&(f1->ss), &sface); } else { report_overlapping_facets(&(f2->ss), &sface); } break; } } // Go to the next item; f1 = f2; } // for (m = 0; ...) if (sface.sh[3] != NULL) { // Insert sface between f1 and f2. newlinkitem = (badface*)flippool->alloc(); newlinkitem->ss = sface; newlinkitem->nextitem = f1->nextitem; f1->nextitem = newlinkitem; } } else if (flippool->items == 1) { f1 = facelink; // Make sure that f is not coplanar and codirection with f1. ori1 = orient3d(torg, tdest, sapex(f1->ss), sapex(sface)); if (ori1 == 0) { // f is coplanar with f1 (see Fig. 8). facenormal(torg, tdest, sapex(f1->ss), n1, 1, NULL); facenormal(torg, tdest, sapex(sface), n2, 1, NULL); if (dot(n1, n2) > 0) { // The two faces are codirectional as well. report_overlapping_facets(&(f1->ss), &sface); } } // Add this face to link if it is not deleted. if (sface.sh[3] != NULL) { // Add this face into link. newlinkitem = (badface*)flippool->alloc(); newlinkitem->ss = sface; newlinkitem->nextitem = NULL; f1->nextitem = newlinkitem; } } else { // The first face. newlinkitem = (badface*)flippool->alloc(); newlinkitem->ss = sface; newlinkitem->nextitem = NULL; facelink = newlinkitem; } } // for (k = idx2faclist[idx]; ...) // Set the connection between this segment and faces containing it, // at the same time, remove redundant segments. f1 = facelink; for (k = 0; k < flippool->items; k++) { sspivot(f1->ss, testseg); // If 'testseg' is not 'subsegloop' and is not dead, it is redundant. if ((testseg.sh != subsegloop.sh) && (testseg.sh[3] != NULL)) { shellfacedealloc(subsegs, testseg.sh); } // Bonds the subface and the segment together. ssbond(f1->ss, subsegloop); f1 = f1->nextitem; } // Create the face ring at the segment. if (flippool->items > 1) { f1 = facelink; for (k = 1; k <= flippool->items; k++) { k < flippool->items ? f2 = f1->nextitem : f2 = facelink; // Calculate the dihedral angle between the two facet. facenormal(torg, tdest, sapex(f1->ss), n1, 1, NULL); facenormal(torg, tdest, sapex(f2->ss), n2, 1, NULL); cosang = dot(n1, n2) / (sqrt(dot(n1, n1)) * sqrt(dot(n2, n2))); // Rounding. if (cosang > 1.0) cosang = 1.0; else if (cosang < -1.0) cosang = -1.0; ang = acos(cosang); if (ang < ang_tol) { // Two facets are treated as overlapping each other. report_overlapping_facets(&(f1->ss), &(f2->ss), ang); } else { // Record the smallest input dihedral angle. if (ang < minfacetdihed) { minfacetdihed = ang; } sbond1(f1->ss, f2->ss); } f1 = f2; } } flippool->restart(); // Are there length constraints? if (b->quality && (in->segmentconstraintlist != (REAL*)NULL)) { int e1, e2; REAL len; for (k = 0; k < in->numberofsegmentconstraints; k++) { e1 = (int)in->segmentconstraintlist[k * 3]; e2 = (int)in->segmentconstraintlist[k * 3 + 1]; if (((pointmark(torg) == e1) && (pointmark(tdest) == e2)) || ((pointmark(torg) == e2) && (pointmark(tdest) == e1))) { len = in->segmentconstraintlist[k * 3 + 2]; setareabound(subsegloop, len); break; } } } subsegloop.sh = shellfacetraverse(subsegs); } delete[] idx2faclist; delete[] facperverlist; } /////////////////////////////////////////////////////////////////////////////// // // // identifyinputedges() Identify input edges. // // // // A set of input edges is provided in the 'in->edgelist'. We find these // // edges in the surface mesh and make them segments of the mesh. // // // // It is possible that an input edge is not in any facet, i.e.,it is a float-// // segment inside the volume. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::identifyinputedges(point* idx2verlist) { face* shperverlist; int* idx2shlist; face searchsh, neighsh; face segloop, checkseg, newseg; point checkpt, pa = NULL, pb = NULL; int* endpts; int edgemarker; int idx, i, j; int e1, e2; REAL len; if (!b->quiet) { printf("Inserting edges ...\n"); } // Construct a map from points to subfaces. makepoint2submap(subfaces, idx2shlist, shperverlist); // Process the set of input edges. for (i = 0; i < in->numberofedges; i++) { endpts = &(in->edgelist[(i << 1)]); if (endpts[0] == endpts[1]) { if (!b->quiet) { printf("Warning: Edge #%d is degenerated. Skipped.\n", i); } continue; // Skip a degenerated edge. } // Recall that all existing segments have a default marker '-1'. // We assign all identified segments a default marker '-2'. edgemarker = in->edgemarkerlist ? in->edgemarkerlist[i] : -2; // Find a face contains the edge. newseg.sh = NULL; searchsh.sh = NULL; idx = endpts[0] - in->firstnumber; for (j = idx2shlist[idx]; j < idx2shlist[idx + 1]; j++) { checkpt = sdest(shperverlist[j]); if (pointmark(checkpt) == endpts[1]) { searchsh = shperverlist[j]; break; // Found. } else { checkpt = sapex(shperverlist[j]); if (pointmark(checkpt) == endpts[1]) { senext2(shperverlist[j], searchsh); sesymself(searchsh); break; } } } // j if (searchsh.sh != NULL) { // Check if this edge is already a segment of the mesh. sspivot(searchsh, checkseg); if (checkseg.sh != NULL) { // This segment already exist. newseg = checkseg; } else { // Create a new segment at this edge. pa = sorg(searchsh); pb = sdest(searchsh); makeshellface(subsegs, &newseg); setshvertices(newseg, pa, pb, NULL); ssbond(searchsh, newseg); spivot(searchsh, neighsh); if (neighsh.sh != NULL) { ssbond(neighsh, newseg); } } } else { // It is a dangling segment (not belong to any facets). // Get the two endpoints of this segment. pa = idx2verlist[endpts[0]]; pb = idx2verlist[endpts[1]]; if (pa == pb) { if (!b->quiet) { printf("Warning: Edge #%d is degenerated. Skipped.\n", i); } continue; } // Check if segment [a,b] already exists. // TODO: Change the brute-force search. Slow! point* ppt; subsegs->traversalinit(); segloop.sh = shellfacetraverse(subsegs); while (segloop.sh != NULL) { ppt = (point*)&(segloop.sh[3]); if (((ppt[0] == pa) && (ppt[1] == pb)) || ((ppt[0] == pb) && (ppt[1] == pa))) { // Found! newseg = segloop; break; } segloop.sh = shellfacetraverse(subsegs); } if (newseg.sh == NULL) { makeshellface(subsegs, &newseg); setshvertices(newseg, pa, pb, NULL); } } setshellmark(newseg, edgemarker); if (b->quality && (in->segmentconstraintlist != (REAL*)NULL)) { for (i = 0; i < in->numberofsegmentconstraints; i++) { e1 = (int)in->segmentconstraintlist[i * 3]; e2 = (int)in->segmentconstraintlist[i * 3 + 1]; if (((pointmark(pa) == e1) && (pointmark(pb) == e2)) || ((pointmark(pa) == e2) && (pointmark(pb) == e1))) { len = in->segmentconstraintlist[i * 3 + 2]; setareabound(newseg, len); break; } } } } // i delete[] shperverlist; delete[] idx2shlist; } /////////////////////////////////////////////////////////////////////////////// // // // mergefacets() Merge adjacent facets. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::mergefacets() { face parentsh, neighsh, neineish; face segloop; point pa, pb, pc, pd; REAL n1[3], n2[3]; REAL cosang, cosang_tol; // Allocate an array to save calcaulated dihedral angles at segments. arraypool* dihedangarray = new arraypool(sizeof(double), 10); REAL* paryang = NULL; // First, remove coplanar segments. // The dihedral angle bound for two different facets. cosang_tol = cos(b->facet_separate_ang_tol / 180.0 * PI); subsegs->traversalinit(); segloop.sh = shellfacetraverse(subsegs); while (segloop.sh != (shellface*)NULL) { // Only remove a segment if it has a marker '-1'. if (shellmark(segloop) != -1) { segloop.sh = shellfacetraverse(subsegs); continue; } spivot(segloop, parentsh); if (parentsh.sh != NULL) { spivot(parentsh, neighsh); if (neighsh.sh != NULL) { spivot(neighsh, neineish); if (neineish.sh == parentsh.sh) { // Exactly two subfaces at this segment. // Only merge them if they have the same boundary marker. if (shellmark(parentsh) == shellmark(neighsh)) { pa = sorg(segloop); pb = sdest(segloop); pc = sapex(parentsh); pd = sapex(neighsh); // Calculate the dihedral angle at the segment [a,b]. facenormal(pa, pb, pc, n1, 1, NULL); facenormal(pa, pb, pd, n2, 1, NULL); cosang = dot(n1, n2) / (sqrt(dot(n1, n1)) * sqrt(dot(n2, n2))); if (cosang < cosang_tol) { ssdissolve(parentsh); ssdissolve(neighsh); shellfacedealloc(subsegs, segloop.sh); // Add the edge to flip stack. flipshpush(&parentsh); } else { // Save 'cosang' to avoid re-calculate it. // Re-use the pointer at the first segment. dihedangarray->newindex((void**)&paryang); *paryang = cosang; segloop.sh[6] = (shellface)paryang; } } } // if (neineish.sh == parentsh.sh) } } segloop.sh = shellfacetraverse(subsegs); } // Second, remove ridge segments at small angles. // The dihedral angle bound for two different facets. cosang_tol = cos(b->facet_small_ang_tol / 180.0 * PI); REAL cosang_sep_tol = cos((b->facet_separate_ang_tol - 5.0) / 180.0 * PI); face shloop; face seg1, seg2; REAL cosang1, cosang2; int i, j; subfaces->traversalinit(); shloop.sh = shellfacetraverse(subfaces); while (shloop.sh != (shellface*)NULL) { for (i = 0; i < 3; i++) { if (isshsubseg(shloop)) { senext(shloop, neighsh); if (isshsubseg(neighsh)) { // Found two segments sharing at one vertex. // Check if they form a small angle. pa = sorg(shloop); pb = sdest(shloop); pc = sapex(shloop); for (j = 0; j < 3; j++) n1[j] = pa[j] - pb[j]; for (j = 0; j < 3; j++) n2[j] = pc[j] - pb[j]; cosang = dot(n1, n2) / (sqrt(dot(n1, n1)) * sqrt(dot(n2, n2))); if (cosang > cosang_tol) { // Found a small angle. segloop.sh = NULL; sspivot(shloop, seg1); sspivot(neighsh, seg2); if (seg1.sh[6] != NULL) { paryang = (REAL*)(seg1.sh[6]); cosang1 = *paryang; } else { cosang1 = 1.0; // 0 degree; } if (seg2.sh[6] != NULL) { paryang = (REAL*)(seg2.sh[6]); cosang2 = *paryang; } else { cosang2 = 1.0; // 0 degree; } if (cosang1 < cosang_sep_tol) { if (cosang2 < cosang_sep_tol) { if (cosang1 < cosang2) { segloop = seg1; } else { segloop = seg2; } } else { segloop = seg1; } } else { if (cosang2 < cosang_sep_tol) { segloop = seg2; } } if (segloop.sh != NULL) { // Remove this segment. segloop.shver = 0; spivot(segloop, parentsh); spivot(parentsh, neighsh); ssdissolve(parentsh); ssdissolve(neighsh); shellfacedealloc(subsegs, segloop.sh); // Add the edge to flip stack. flipshpush(&parentsh); break; } } } // if (isshsubseg) } // if (isshsubseg) senextself(shloop); } shloop.sh = shellfacetraverse(subfaces); } delete dihedangarray; if (flipstack != NULL) { lawsonflip(); // Recover Delaunayness. } } /////////////////////////////////////////////////////////////////////////////// // // // meshsurface() Create a surface mesh of the input PLC. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::meshsurface() { arraypool *ptlist, *conlist; point* idx2verlist; point tstart, tend, *pnewpt, *cons; tetgenio::facet* f; tetgenio::polygon* p; int end1, end2; int shmark, i, j; if (!b->quiet) { printf("Creating surface mesh ...\n"); } // Create a map from indices to points. makeindex2pointmap(idx2verlist); // Initialize arrays (block size: 2^8 = 256). ptlist = new arraypool(sizeof(point*), 8); conlist = new arraypool(2 * sizeof(point*), 8); // Loop the facet list, triangulate each facet. for (shmark = 1; shmark <= in->numberoffacets; shmark++) { // Get a facet F. f = &in->facetlist[shmark - 1]; // Process the duplicated points first, they are marked with type // DUPLICATEDVERTEX. If p and q are duplicated, and p'index > q's, // then p is substituted by q. if (dupverts > 0l) { // Loop all polygons of this facet. for (i = 0; i < f->numberofpolygons; i++) { p = &(f->polygonlist[i]); // Loop other vertices of this polygon. for (j = 0; j < p->numberofvertices; j++) { end1 = p->vertexlist[j]; tstart = idx2verlist[end1]; if (pointtype(tstart) == DUPLICATEDVERTEX) { // Reset the index of vertex-j. tend = point2ppt(tstart); end2 = pointmark(tend); p->vertexlist[j] = end2; } } } } // Loop polygons of F, get the set of vertices and segments. for (i = 0; i < f->numberofpolygons; i++) { // Get a polygon. p = &(f->polygonlist[i]); // Get the first vertex. end1 = p->vertexlist[0]; if ((end1 < in->firstnumber) || (end1 >= in->firstnumber + in->numberofpoints)) { if (!b->quiet) { printf("Warning: Invalid the 1st vertex %d of polygon", end1); printf(" %d in facet %d.\n", i + 1, shmark); } continue; // Skip this polygon. } tstart = idx2verlist[end1]; // Add tstart to V if it haven't been added yet. if (!pinfected(tstart)) { pinfect(tstart); ptlist->newindex((void**)&pnewpt); *pnewpt = tstart; } // Loop other vertices of this polygon. for (j = 1; j <= p->numberofvertices; j++) { // get a vertex. if (j < p->numberofvertices) { end2 = p->vertexlist[j]; } else { end2 = p->vertexlist[0]; // Form a loop from last to first. } if ((end2 < in->firstnumber) || (end2 >= in->firstnumber + in->numberofpoints)) { if (!b->quiet) { printf("Warning: Invalid vertex %d in polygon %d", end2, i + 1); printf(" in facet %d.\n", shmark); } } else { if (end1 != end2) { // 'end1' and 'end2' form a segment. tend = idx2verlist[end2]; // Add tstart to V if it haven't been added yet. if (!pinfected(tend)) { pinfect(tend); ptlist->newindex((void**)&pnewpt); *pnewpt = tend; } // Save the segment in S (conlist). conlist->newindex((void**)&cons); cons[0] = tstart; cons[1] = tend; // Set the start for next continuous segment. end1 = end2; tstart = tend; } else { // Two identical vertices mean an isolated vertex of F. if (p->numberofvertices > 2) { // This may be an error in the input, anyway, we can continue // by simply skipping this segment. if (!b->quiet) { printf("Warning: Polygon %d has two identical verts", i + 1); printf(" in facet %d.\n", shmark); } } // Ignore this vertex. } } // Is the polygon degenerate (a segment or a vertex)? if (p->numberofvertices == 2) break; } } // Unmark vertices. for (i = 0; i < ptlist->objects; i++) { pnewpt = (point*)fastlookup(ptlist, i); puninfect(*pnewpt); } // Triangulate F into a CDT. // If in->facetmarklist is NULL, use the default marker -1. triangulate(in->facetmarkerlist ? in->facetmarkerlist[shmark - 1] : -1, ptlist, conlist, f->numberofholes, f->holelist); // Clear working lists. ptlist->restart(); conlist->restart(); } if (!b->diagnose) { // Remove redundant segments and build the face links. unifysegments(); if (in->numberofedges > 0) { // There are input segments. Insert them. identifyinputedges(idx2verlist); } if (!b->psc && !b->nomergefacet && (!b->nobisect || (b->nobisect && !b->nobisect_nomerge))) { // Merge coplanar facets. mergefacets(); } } if (b->object == tetgenbehavior::STL) { // Remove redundant vertices (for .stl input mesh). jettisonnodes(); } if (b->verbose) { printf(" %ld (%ld) subfaces (segments).\n", subfaces->items, subsegs->items); } // The total number of iunput segments. insegments = subsegs->items; delete[] idx2verlist; delete ptlist; delete conlist; } /////////////////////////////////////////////////////////////////////////////// // // // interecursive() Recursively do intersection test on a set of triangles.// // // // Recursively split the set 'subfacearray' of subfaces into two sets using // // a cut plane parallel to x-, or, y-, or z-axis. The split criteria are // // follows. Assume the cut plane is H, and H+ denotes the left halfspace of // // H, and H- denotes the right halfspace of H; and s be a subface: // // // // (1) If all points of s lie at H+, put it into left array; // // (2) If all points of s lie at H-, put it into right array; // // (3) If some points of s lie at H+ and some of lie at H-, or some // // points lie on H, put it into both arraies. // // // // Partitions by x-axis if axis == '0'; by y-axis if axis == '1'; by z-axis // // if axis == '2'. If current cut plane is parallel to the x-axis, the next // // one will be parallel to y-axis, and the next one after the next is z-axis,// // and then alternately return back to x-axis. // // // // Stop splitting when the number of triangles of the input array is not // // decreased anymore. Do tests on the current set. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::interecursive(shellface** subfacearray, int arraysize, int axis, REAL bxmin, REAL bxmax, REAL bymin, REAL bymax, REAL bzmin, REAL bzmax, int* internum) { shellface **leftarray, **rightarray; face sface1, sface2; point p1, p2, p3; point p4, p5, p6; enum interresult intersect; REAL split; bool toleft, toright; int leftsize, rightsize; int i, j; if (b->verbose > 2) { printf(" Recur %d faces. Bbox (%g, %g, %g),(%g, %g, %g). %s-axis\n", arraysize, bxmin, bymin, bzmin, bxmax, bymax, bzmax, axis == 0 ? "x" : (axis == 1 ? "y" : "z")); } leftarray = new shellface*[arraysize]; if (leftarray == NULL) { terminatetetgen(this, 1); } rightarray = new shellface*[arraysize]; if (rightarray == NULL) { terminatetetgen(this, 1); } leftsize = rightsize = 0; if (axis == 0) { // Split along x-axis. split = 0.5 * (bxmin + bxmax); } else if (axis == 1) { // Split along y-axis. split = 0.5 * (bymin + bymax); } else { // Split along z-axis. split = 0.5 * (bzmin + bzmax); } for (i = 0; i < arraysize; i++) { sface1.sh = subfacearray[i]; p1 = (point)sface1.sh[3]; p2 = (point)sface1.sh[4]; p3 = (point)sface1.sh[5]; toleft = toright = false; if (p1[axis] < split) { toleft = true; if (p2[axis] >= split || p3[axis] >= split) { toright = true; } } else if (p1[axis] > split) { toright = true; if (p2[axis] <= split || p3[axis] <= split) { toleft = true; } } else { // p1[axis] == split; toleft = true; toright = true; } if (toleft) { leftarray[leftsize] = sface1.sh; leftsize++; } if (toright) { rightarray[rightsize] = sface1.sh; rightsize++; } } if (leftsize < arraysize && rightsize < arraysize) { // Continue to partition the input set. Now 'subfacearray' has been // split into two sets, it's memory can be freed. 'leftarray' and // 'rightarray' will be freed in the next recursive (after they're // partitioned again or performing tests). delete[] subfacearray; // Continue to split these two sets. if (axis == 0) { interecursive(leftarray, leftsize, 1, bxmin, split, bymin, bymax, bzmin, bzmax, internum); interecursive(rightarray, rightsize, 1, split, bxmax, bymin, bymax, bzmin, bzmax, internum); } else if (axis == 1) { interecursive(leftarray, leftsize, 2, bxmin, bxmax, bymin, split, bzmin, bzmax, internum); interecursive(rightarray, rightsize, 2, bxmin, bxmax, split, bymax, bzmin, bzmax, internum); } else { interecursive(leftarray, leftsize, 0, bxmin, bxmax, bymin, bymax, bzmin, split, internum); interecursive(rightarray, rightsize, 0, bxmin, bxmax, bymin, bymax, split, bzmax, internum); } } else { if (b->verbose > 1) { printf(" Checking intersecting faces.\n"); } // Perform a brute-force compare on the set. for (i = 0; i < arraysize; i++) { sface1.sh = subfacearray[i]; p1 = (point)sface1.sh[3]; p2 = (point)sface1.sh[4]; p3 = (point)sface1.sh[5]; for (j = i + 1; j < arraysize; j++) { sface2.sh = subfacearray[j]; p4 = (point)sface2.sh[3]; p5 = (point)sface2.sh[4]; p6 = (point)sface2.sh[5]; intersect = (enum interresult)tri_tri_inter(p1, p2, p3, p4, p5, p6); if (intersect == INTERSECT || intersect == SHAREFACE) { if (!b->quiet) { if (intersect == INTERSECT) { printf(" Facet #%d intersects facet #%d at triangles:\n", shellmark(sface1), shellmark(sface2)); printf(" (%4d, %4d, %4d) and (%4d, %4d, %4d)\n", pointmark(p1), pointmark(p2), pointmark(p3), pointmark(p4), pointmark(p5), pointmark(p6)); } else { printf(" Facet #%d duplicates facet #%d at triangle:\n", shellmark(sface1), shellmark(sface2)); printf(" (%4d, %4d, %4d) and (%4d, %4d, %4d)\n", pointmark(p1), pointmark(p2), pointmark(p3), pointmark(p4), pointmark(p5), pointmark(p6)); } } // Increase the number of intersecting pairs. (*internum)++; // Infect these two faces (although they may already be infected). sinfect(sface1); sinfect(sface2); } } } // Don't forget to free all three arrays. No further partition. delete[] leftarray; delete[] rightarray; delete[] subfacearray; } } /////////////////////////////////////////////////////////////////////////////// // // // detectinterfaces() Detect intersecting triangles. // // // // Given a set of triangles, find the pairs of intersecting triangles from // // them. Here the set of triangles is in 'subfaces' which is a surface mesh // // of a PLC (.poly or .smesh). // // // // To detect whether two triangles are intersecting is done by the routine // // 'tri_tri_inter()'. The algorithm for the test is very simple and stable. // // It is based on geometric orientation test which uses exact arithmetics. // // // // Use divide-and-conquer algorithm for reducing the number of intersection // // tests. Start from the bounding box of the input point set, recursively // // partition the box into smaller boxes, until the number of triangles in a // // box is not decreased anymore. Then perform triangle-triangle tests on the // // remaining set of triangles. The memory allocated in the input set is // // freed immediately after it has been partitioned into two arrays. So it // // can be re-used for the consequent partitions. // // // // On return, the pool 'subfaces' will be cleared, and only the intersecting // // triangles remain for output (to a .face file). // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::detectinterfaces() { shellface** subfacearray; face shloop; int internum; int i; if (!b->quiet) { printf("Detecting self-intersecting facets...\n"); } // Construct a map from indices to subfaces; subfacearray = new shellface*[subfaces->items]; subfaces->traversalinit(); shloop.sh = shellfacetraverse(subfaces); i = 0; while (shloop.sh != (shellface*)NULL) { subfacearray[i] = shloop.sh; shloop.sh = shellfacetraverse(subfaces); i++; } internum = 0; // Recursively split the set of triangles into two sets using a cut plane // parallel to x-, or, y-, or z-axis. Stop splitting when the number // of subfaces is not decreasing anymore. Do tests on the current set. interecursive(subfacearray, subfaces->items, 0, xmin, xmax, ymin, ymax, zmin, zmax, &internum); if (!b->quiet) { if (internum > 0) { printf("\n!! Found %d pairs of faces are intersecting.\n\n", internum); } else { printf("\nNo faces are intersecting.\n\n"); } } if (internum > 0) { // Traverse all subfaces, deallocate those have not been infected (they // are not intersecting faces). Uninfect those have been infected. // After this loop, only intersecting faces remain. subfaces->traversalinit(); shloop.sh = shellfacetraverse(subfaces); while (shloop.sh != (shellface*)NULL) { if (sinfected(shloop)) { suninfect(shloop); } else { shellfacedealloc(subfaces, shloop.sh); } shloop.sh = shellfacetraverse(subfaces); } } else { // Deallocate all subfaces. subfaces->restart(); } } //// //// //// //// //// surface_cxx ////////////////////////////////////////////////////////////// //// constrained_cxx ////////////////////////////////////////////////////////// //// //// //// //// /////////////////////////////////////////////////////////////////////////////// // // // makesegmentendpointsmap() Create a map from a segment to its endpoints.// // // // The map is saved in the array 'segmentendpointslist'. The length of this // // array is twice the number of segments. Each segment is assigned a unique // // index (starting from 0). // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::makesegmentendpointsmap() { arraypool* segptlist; face segloop, prevseg, nextseg; point eorg, edest, *parypt; int segindex = 0, idx = 0; int i; if (b->verbose > 0) { printf(" Creating the segment-endpoints map.\n"); } segptlist = new arraypool(2 * sizeof(point), 10); // A segment s may have been split into many subsegments. Operate the one // which contains the origin of s. Then mark the rest of subsegments. subsegs->traversalinit(); segloop.sh = shellfacetraverse(subsegs); segloop.shver = 0; while (segloop.sh != NULL) { senext2(segloop, prevseg); spivotself(prevseg); if (prevseg.sh == NULL) { eorg = sorg(segloop); edest = sdest(segloop); setfacetindex(segloop, segindex); senext(segloop, nextseg); spivotself(nextseg); while (nextseg.sh != NULL) { setfacetindex(nextseg, segindex); nextseg.shver = 0; if (sorg(nextseg) != edest) sesymself(nextseg); edest = sdest(nextseg); // Go the next connected subsegment at edest. senextself(nextseg); spivotself(nextseg); } segptlist->newindex((void**)&parypt); parypt[0] = eorg; parypt[1] = edest; segindex++; } segloop.sh = shellfacetraverse(subsegs); } if (b->verbose) { printf(" Found %ld segments.\n", segptlist->objects); } segmentendpointslist = new point[segptlist->objects * 2]; totalworkmemory += (segptlist->objects * 2) * sizeof(point*); for (i = 0; i < segptlist->objects; i++) { parypt = (point*)fastlookup(segptlist, i); segmentendpointslist[idx++] = parypt[0]; segmentendpointslist[idx++] = parypt[1]; } delete segptlist; } /////////////////////////////////////////////////////////////////////////////// // // // finddirection() Find the tet on the path from one point to another. // // // // The path starts from 'searchtet''s origin and ends at 'endpt'. On finish, // // 'searchtet' contains a tet on the path, its origin does not change. // // // // The return value indicates one of the following cases (let 'searchtet' be // // abcd, a is the origin of the path): // // - ACROSSVERT, edge ab is collinear with the path; // // - ACROSSEDGE, edge bc intersects with the path; // // - ACROSSFACE, face bcd intersects with the path. // // // // WARNING: This routine is designed for convex triangulations, and will not // // generally work after the holes and concavities have been carved. // // // /////////////////////////////////////////////////////////////////////////////// enum tetgenmesh::interresult tetgenmesh::finddirection(triface* searchtet, point endpt) { triface neightet; point pa, pb, pc, pd; enum { HMOVE, RMOVE, LMOVE } nextmove; REAL hori, rori, lori; int t1ver; int s; // The origin is fixed. pa = org(*searchtet); if ((point)searchtet->tet[7] == dummypoint) { // A hull tet. Choose the neighbor of its base face. decode(searchtet->tet[3], *searchtet); // Reset the origin to be pa. if ((point)searchtet->tet[4] == pa) { searchtet->ver = 11; } else if ((point)searchtet->tet[5] == pa) { searchtet->ver = 3; } else if ((point)searchtet->tet[6] == pa) { searchtet->ver = 7; } else { searchtet->ver = 0; } } pb = dest(*searchtet); // Check whether the destination or apex is 'endpt'. if (pb == endpt) { // pa->pb is the search edge. return ACROSSVERT; } pc = apex(*searchtet); if (pc == endpt) { // pa->pc is the search edge. eprevesymself(*searchtet); return ACROSSVERT; } // Walk through tets around pa until the right one is found. while (1) { pd = oppo(*searchtet); // Check whether the opposite vertex is 'endpt'. if (pd == endpt) { // pa->pd is the search edge. esymself(*searchtet); enextself(*searchtet); return ACROSSVERT; } // Check if we have entered outside of the domain. if (pd == dummypoint) { // This is possible when the mesh is non-convex. if (nonconvex) { return ACROSSFACE; // return ACROSSSUB; // Hit a bounday. } else { terminatetetgen(this, 2); } } // Now assume that the base face abc coincides with the horizon plane, // and d lies above the horizon. The search point 'endpt' may lie // above or below the horizon. We test the orientations of 'endpt' // with respect to three planes: abc (horizon), bad (right plane), // and acd (left plane). hori = orient3d(pa, pb, pc, endpt); rori = orient3d(pb, pa, pd, endpt); lori = orient3d(pa, pc, pd, endpt); // Now decide the tet to move. It is possible there are more than one // tets are viable moves. Is so, randomly choose one. if (hori > 0) { if (rori > 0) { if (lori > 0) { // Any of the three neighbors is a viable move. s = randomnation(3); if (s == 0) { nextmove = HMOVE; } else if (s == 1) { nextmove = RMOVE; } else { nextmove = LMOVE; } } else { // Two tets, below horizon and below right, are viable. if (randomnation(2)) { nextmove = HMOVE; } else { nextmove = RMOVE; } } } else { if (lori > 0) { // Two tets, below horizon and below left, are viable. if (randomnation(2)) { nextmove = HMOVE; } else { nextmove = LMOVE; } } else { // The tet below horizon is chosen. nextmove = HMOVE; } } } else { if (rori > 0) { if (lori > 0) { // Two tets, below right and below left, are viable. if (randomnation(2)) { nextmove = RMOVE; } else { nextmove = LMOVE; } } else { // The tet below right is chosen. nextmove = RMOVE; } } else { if (lori > 0) { // The tet below left is chosen. nextmove = LMOVE; } else { // 'endpt' lies either on the plane(s) or across face bcd. if (hori == 0) { if (rori == 0) { // pa->'endpt' is COLLINEAR with pa->pb. return ACROSSVERT; } if (lori == 0) { // pa->'endpt' is COLLINEAR with pa->pc. eprevesymself(*searchtet); // [a,c,d] return ACROSSVERT; } // pa->'endpt' crosses the edge pb->pc. return ACROSSEDGE; } if (rori == 0) { if (lori == 0) { // pa->'endpt' is COLLINEAR with pa->pd. esymself(*searchtet); // face bad. enextself(*searchtet); // face [a,d,b] return ACROSSVERT; } // pa->'endpt' crosses the edge pb->pd. esymself(*searchtet); // face bad. enextself(*searchtet); // face adb return ACROSSEDGE; } if (lori == 0) { // pa->'endpt' crosses the edge pc->pd. eprevesymself(*searchtet); // [a,c,d] return ACROSSEDGE; } // pa->'endpt' crosses the face bcd. return ACROSSFACE; } } } // Move to the next tet, fix pa as its origin. if (nextmove == RMOVE) { fnextself(*searchtet); } else if (nextmove == LMOVE) { eprevself(*searchtet); fnextself(*searchtet); enextself(*searchtet); } else { // HMOVE fsymself(*searchtet); enextself(*searchtet); } pb = dest(*searchtet); pc = apex(*searchtet); } // while (1) } /////////////////////////////////////////////////////////////////////////////// // // // scoutsegment() Search an edge in the tetrahedralization. // // // // If the edge is found, it returns SHAREEDGE, and 'searchtet' returns the // // edge from startpt to endpt. // // // // If the edge is missing, it returns either ACROSSEDGE or ACROSSFACE, which // // indicates that the edge intersects an edge or a face. If 'refpt' is NULL,// // 'searchtet' returns the edge or face. If 'refpt' is not NULL, it returns // // a vertex which encroaches upon this edge, and 'searchtet' returns a tet // // which containing 'refpt'. // // // // The parameter 'sedge' is used to report self-intersection. It is the // // whose endpoints are 'startpt' and 'endpt'. It must not be a NULL. // // /////////////////////////////////////////////////////////////////////////////// enum tetgenmesh::interresult tetgenmesh::scoutsegment(point startpt, point endpt, face* sedge, triface* searchtet, point* refpt, arraypool* intfacelist) { point pd; enum interresult dir; int t1ver; if (b->verbose > 2) { printf(" Scout seg (%d, %d).\n", pointmark(startpt), pointmark(endpt)); } point2tetorg(startpt, *searchtet); dir = finddirection(searchtet, endpt); if (dir == ACROSSVERT) { pd = dest(*searchtet); if (pd == endpt) { if (issubseg(*searchtet)) { report_selfint_edge(startpt, endpt, sedge, searchtet, dir); } return SHAREEDGE; } else { // A point is on the path. report_selfint_edge(startpt, endpt, sedge, searchtet, dir); return ACROSSVERT; } } // dir is either ACROSSEDGE or ACROSSFACE. enextesymself(*searchtet); // Go to the opposite face. fsymself(*searchtet); // Enter the adjacent tet. if (dir == ACROSSEDGE) { // Check whether two segments are intersecting. if (issubseg(*searchtet)) { report_selfint_edge(startpt, endpt, sedge, searchtet, dir); } } else if (dir == ACROSSFACE) { if (checksubfaceflag) { // Check whether a segment and a subface are intersecting. if (issubface(*searchtet)) { report_selfint_edge(startpt, endpt, sedge, searchtet, dir); } } } else { terminatetetgen(this, 2); } if (refpt == NULL) { // Do not need a reference point. Return. return dir; } triface neightet, reftet; point pa, pb, pc; REAL angmax, ang; int types[2], poss[4]; int pos = 0, i, j; pa = org(*searchtet); angmax = interiorangle(pa, startpt, endpt, NULL); *refpt = pa; pb = dest(*searchtet); ang = interiorangle(pb, startpt, endpt, NULL); if (ang > angmax) { angmax = ang; *refpt = pb; } pc = apex(*searchtet); ang = interiorangle(pc, startpt, endpt, NULL); if (ang > angmax) { angmax = ang; *refpt = pc; } reftet = *searchtet; // Save the tet containing the refpt. // Search intersecting faces along the segment. while (1) { pd = oppo(*searchtet); // Stop if we meet 'endpt'. if (pd == endpt) break; ang = interiorangle(pd, startpt, endpt, NULL); if (ang > angmax) { angmax = ang; *refpt = pd; reftet = *searchtet; } // Find a face intersecting the segment. if (dir == ACROSSFACE) { // One of the three oppo faces in 'searchtet' intersects the segment. neightet = *searchtet; j = (neightet.ver & 3); // j is the current face number. for (i = j + 1; i < j + 4; i++) { neightet.ver = (i % 4); pa = org(neightet); pb = dest(neightet); pc = apex(neightet); pd = oppo(neightet); // The above point. if (tri_edge_test(pa, pb, pc, startpt, endpt, pd, 1, types, poss)) { dir = (enum interresult)types[0]; pos = poss[0]; break; } else { dir = DISJOINT; pos = 0; } } } else if (dir == ACROSSEDGE) { // Check the two opposite faces (of the edge) in 'searchtet'. for (i = 0; i < 2; i++) { if (i == 0) { enextesym(*searchtet, neightet); } else { eprevesym(*searchtet, neightet); } pa = org(neightet); pb = dest(neightet); pc = apex(neightet); pd = oppo(neightet); // The above point. if (tri_edge_test(pa, pb, pc, startpt, endpt, pd, 1, types, poss)) { dir = (enum interresult)types[0]; pos = poss[0]; break; } else { dir = DISJOINT; pos = 0; } } if (dir == DISJOINT) { // No intersection. Rotate to the next tet at the edge. dir = ACROSSEDGE; fnextself(*searchtet); continue; } } if (dir == ACROSSVERT) { // This segment passing a vertex. Choose it and return. for (i = 0; i < pos; i++) { enextself(neightet); } eprev(neightet, *searchtet); // dest(*searchtet) lies on the segment. report_selfint_edge(startpt, endpt, sedge, searchtet, dir); return ACROSSVERT; } else if (dir == ACROSSEDGE) { // Get the edge intersects with the segment. for (i = 0; i < pos; i++) { enextself(neightet); } } // Go to the next tet. fsym(neightet, *searchtet); if (dir == ACROSSEDGE) { // Check whether two segments are intersecting. if (issubseg(*searchtet)) { report_selfint_edge(startpt, endpt, sedge, searchtet, dir); } } else if (dir == ACROSSFACE) { if (checksubfaceflag) { // Check whether a segment and a subface are intersecting. if (issubface(*searchtet)) { report_selfint_edge(startpt, endpt, sedge, searchtet, dir); } } } else { terminatetetgen(this, 2); } } // while (1) // A valid reference point should inside the diametrial circumsphere of // the missing segment, i.e., it encroaches upon it. if (2.0 * angmax < PI) { *refpt = NULL; } *searchtet = reftet; return dir; } /////////////////////////////////////////////////////////////////////////////// // // // getsteinerpointonsegment() Get a Steiner point on a segment. // // // // Return '1' if 'refpt' lies on an adjacent segment of this segment. Other- // // wise, return '0'. // // // /////////////////////////////////////////////////////////////////////////////// int tetgenmesh::getsteinerptonsegment(face* seg, point refpt, point steinpt) { point ei = sorg(*seg); point ej = sdest(*seg); int adjflag = 0, i; if (refpt != NULL) { REAL L, L1, t; if (pointtype(refpt) == FREESEGVERTEX) { face parentseg; sdecode(point2sh(refpt), parentseg); int sidx1 = getfacetindex(parentseg); point far_pi = segmentendpointslist[sidx1 * 2]; point far_pj = segmentendpointslist[sidx1 * 2 + 1]; int sidx2 = getfacetindex(*seg); point far_ei = segmentendpointslist[sidx2 * 2]; point far_ej = segmentendpointslist[sidx2 * 2 + 1]; if ((far_pi == far_ei) || (far_pj == far_ei)) { // Create a Steiner point at the intersection of the segment // [far_ei, far_ej] and the sphere centered at far_ei with // radius |far_ei - refpt|. L = distance(far_ei, far_ej); L1 = distance(far_ei, refpt); t = L1 / L; for (i = 0; i < 3; i++) { steinpt[i] = far_ei[i] + t * (far_ej[i] - far_ei[i]); } adjflag = 1; } else if ((far_pi == far_ej) || (far_pj == far_ej)) { L = distance(far_ei, far_ej); L1 = distance(far_ej, refpt); t = L1 / L; for (i = 0; i < 3; i++) { steinpt[i] = far_ej[i] + t * (far_ei[i] - far_ej[i]); } adjflag = 1; } else { // Cut the segment by the projection point of refpt. projpt2edge(refpt, ei, ej, steinpt); } } else { // Cut the segment by the projection point of refpt. projpt2edge(refpt, ei, ej, steinpt); } // Make sure that steinpt is not too close to ei and ej. L = distance(ei, ej); L1 = distance(steinpt, ei); t = L1 / L; if ((t < 0.2) || (t > 0.8)) { // Split the point at the middle. for (i = 0; i < 3; i++) { steinpt[i] = ei[i] + 0.5 * (ej[i] - ei[i]); } } } else { // Split the point at the middle. for (i = 0; i < 3; i++) { steinpt[i] = ei[i] + 0.5 * (ej[i] - ei[i]); } } return adjflag; } /////////////////////////////////////////////////////////////////////////////// // // // delaunizesegments() Recover segments in a DT. // // // // All segments need to be recovered are in 'subsegstack' (Q). They will be // // be recovered one by one (in a random order). // // // // Given a segment s in the Q, this routine first queries s in the DT, if s // // matches an edge in DT, it is 'locked' at the edge. Otherwise, s is split // // by inserting a new point p in both the DT and itself. The two new subseg- // // ments of s are queued in Q. The process continues until Q is empty. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::delaunizesegments() { triface searchtet, spintet; face searchsh; face sseg, *psseg; point refpt, newpt; enum interresult dir; insertvertexflags ivf; int t1ver; ivf.bowywat = 1; // Use Bowyer-Watson insertion. ivf.sloc = (int)ONEDGE; // on 'sseg'. ivf.sbowywat = 1; // Use Bowyer-Watson insertion. ivf.assignmeshsize = b->metric; ivf.smlenflag = useinsertradius; // Return the closet mesh vertex. // Loop until 'subsegstack' is empty. while (subsegstack->objects > 0l) { // seglist is used as a stack. subsegstack->objects--; psseg = (face*)fastlookup(subsegstack, subsegstack->objects); sseg = *psseg; // Check if this segment has been recovered. sstpivot1(sseg, searchtet); if (searchtet.tet != NULL) { continue; // Not a missing segment. } // Search the segment. dir = scoutsegment(sorg(sseg), sdest(sseg), &sseg, &searchtet, &refpt, NULL); if (dir == SHAREEDGE) { // Found this segment, insert it. // Let the segment remember an adjacent tet. sstbond1(sseg, searchtet); // Bond the segment to all tets containing it. spintet = searchtet; do { tssbond1(spintet, sseg); fnextself(spintet); } while (spintet.tet != searchtet.tet); } else { if ((dir == ACROSSFACE) || (dir == ACROSSEDGE)) { // The segment is missing. Split it. // Create a new point. makepoint(&newpt, FREESEGVERTEX); // setpointtype(newpt, FREESEGVERTEX); getsteinerptonsegment(&sseg, refpt, newpt); // Start searching from 'searchtet'. ivf.iloc = (int)OUTSIDE; // Insert the new point into the tetrahedralization T. // Missing segments and subfaces are queued for recovery. // Note that T is convex (nonconvex = 0). if (insertpoint(newpt, &searchtet, &searchsh, &sseg, &ivf)) { // The new point has been inserted. st_segref_count++; if (steinerleft > 0) steinerleft--; if (useinsertradius) { save_segmentpoint_insradius(newpt, ivf.parentpt, ivf.smlen); } } else { if (ivf.iloc == (int)NEARVERTEX) { // The new point (in the segment) is very close to an existing // vertex -- a small feature is detected. point nearpt = org(searchtet); if (pointtype(nearpt) == FREESEGVERTEX) { face parentseg; sdecode(point2sh(nearpt), parentseg); point p1 = farsorg(sseg); point p2 = farsdest(sseg); point p3 = farsorg(parentseg); point p4 = farsdest(parentseg); printf("Two segments are very close to each other.\n"); printf(" Segment 1: [%d, %d] #%d\n", pointmark(p1), pointmark(p2), shellmark(sseg)); printf(" Segment 2: [%d, %d] #%d\n", pointmark(p3), pointmark(p4), shellmark(parentseg)); terminatetetgen(this, 4); } else { terminatetetgen(this, 2); } } else if (ivf.iloc == (int)ONVERTEX) { // The new point (in the segment) is coincident with an existing // vertex -- a self-intersection is detected. eprevself(searchtet); report_selfint_edge(sorg(sseg), sdest(sseg), &sseg, &searchtet, ACROSSVERT); } else { // An unknown case. Report a bug. terminatetetgen(this, 2); } } } else { // An unknown case. Report a bug. terminatetetgen(this, 2); } } } // while } /////////////////////////////////////////////////////////////////////////////// // // // scoutsubface() Search subface in the tetrahedralization. // // // // 'searchsh' is searched in T. If it exists, it is 'locked' at the face in // // T. 'searchtet' refers to the face. Otherwise, it is missing. // // // // The parameter 'shflag' indicates whether 'searchsh' is a boundary face or // // not. It is possible that 'searchsh' is a temporarily subface that is used // // as a cavity boundary face. // // // /////////////////////////////////////////////////////////////////////////////// int tetgenmesh::scoutsubface(face* searchsh, triface* searchtet, int shflag) { point pa = sorg(*searchsh); point pb = sdest(*searchsh); // Get a tet whose origin is a. point2tetorg(pa, *searchtet); // Search the edge [a,b]. enum interresult dir = finddirection(searchtet, pb); if (dir == ACROSSVERT) { // Check validity of a PLC. if (dest(*searchtet) != pb) { if (shflag) { // A vertex lies on the search edge. report_selfint_edge(pa, pb, searchsh, searchtet, dir); } else { terminatetetgen(this, 2); } } int t1ver; // The edge exists. Check if the face exists. point pc = sapex(*searchsh); // Searchtet holds edge [a,b]. Search a face with apex c. triface spintet = *searchtet; while (1) { if (apex(spintet) == pc) { // Found a face matching to 'searchsh'! if (!issubface(spintet)) { // Insert 'searchsh'. tsbond(spintet, *searchsh); fsymself(spintet); sesymself(*searchsh); tsbond(spintet, *searchsh); *searchtet = spintet; return 1; } else { terminatetetgen(this, 2); } } fnextself(spintet); if (spintet.tet == searchtet->tet) break; } } return 0; } /////////////////////////////////////////////////////////////////////////////// // // // formregion() Form the missing region of a missing subface. // // // // 'missh' is a missing subface. From it we form a missing region R which is // // a connected region formed by a set of missing subfaces of a facet. // // Comment: There should be no segment inside R. // // // // 'missingshs' returns the list of subfaces in R. All subfaces in this list // // are oriented as the 'missh'. 'missingshbds' returns the list of boundary // // edges (tetrahedral handles) of R. 'missingshverts' returns all vertices // // of R. They are all pmarktested. // // // // Except the first one (which is 'missh') in 'missingshs', each subface in // // this list represents an internal edge of R, i.e., it is missing in the // // tetrahedralization. Since R may contain interior vertices, not all miss- // // ing edges can be found by this way. // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::formregion(face* missh, arraypool* missingshs, arraypool* missingshbds, arraypool* missingshverts) { triface searchtet, spintet; face neighsh, *parysh; face neighseg, fakeseg; point pa, pb, *parypt; enum interresult dir; int t1ver; int i, j; smarktest(*missh); missingshs->newindex((void**)&parysh); *parysh = *missh; // Incrementally find other missing subfaces. for (i = 0; i < missingshs->objects; i++) { missh = (face*)fastlookup(missingshs, i); for (j = 0; j < 3; j++) { pa = sorg(*missh); pb = sdest(*missh); point2tetorg(pa, searchtet); dir = finddirection(&searchtet, pb); if (dir != ACROSSVERT) { // This edge is missing. Its neighbor is a missing subface. spivot(*missh, neighsh); if (!smarktested(neighsh)) { // Adjust the face orientation. if (sorg(neighsh) != pb) sesymself(neighsh); smarktest(neighsh); missingshs->newindex((void**)&parysh); *parysh = neighsh; } } else { if (dest(searchtet) != pb) { // Report a PLC problem. report_selfint_edge(pa, pb, missh, &searchtet, dir); } } // Collect the vertices of R. if (!pmarktested(pa)) { pmarktest(pa); missingshverts->newindex((void**)&parypt); *parypt = pa; } senextself(*missh); } // j } // i // Get the boundary edges of R. for (i = 0; i < missingshs->objects; i++) { missh = (face*)fastlookup(missingshs, i); for (j = 0; j < 3; j++) { spivot(*missh, neighsh); if ((neighsh.sh == NULL) || !smarktested(neighsh)) { // A boundary edge of R. // Let the segment point to the adjacent tet. point2tetorg(sorg(*missh), searchtet); finddirection(&searchtet, sdest(*missh)); missingshbds->newindex((void**)&parysh); *parysh = *missh; // Check if this edge is a segment. sspivot(*missh, neighseg); if (neighseg.sh == NULL) { // Temporarily create a segment at this edge. makeshellface(subsegs, &fakeseg); setsorg(fakeseg, sorg(*missh)); setsdest(fakeseg, sdest(*missh)); sinfect(fakeseg); // Mark it as faked. // Connect it to all tets at this edge. spintet = searchtet; while (1) { tssbond1(spintet, fakeseg); fnextself(spintet); if (spintet.tet == searchtet.tet) break; } neighseg = fakeseg; } // Let the segment and the boundary edge point to each other. ssbond(*missh, neighseg); sstbond1(neighseg, searchtet); } senextself(*missh); } // j } // i // Unmarktest collected missing subfaces. for (i = 0; i < missingshs->objects; i++) { parysh = (face*)fastlookup(missingshs, i); sunmarktest(*parysh); } } /////////////////////////////////////////////////////////////////////////////// // // // scoutcrossedge() Search an edge that crosses the missing region. // // // // Return 1 if a crossing edge is found. It is returned by 'crosstet'. More- // // over, the edge is oriented such that its origin lies below R. Return 0 // // if no such edge is found. // // // // Assumption: All vertices of the missing region are marktested. // // // /////////////////////////////////////////////////////////////////////////////// int tetgenmesh::scoutcrossedge(triface& crosstet, arraypool* missingshbds, arraypool* missingshs) { triface searchtet, spintet, neightet; face oldsh, searchsh, *parysh; face neighseg; point pa, pb, pc, pd, pe; REAL ori; int types[2], poss[4]; int searchflag, interflag; int t1ver; int i, j; searchflag = 0; // Search the first new subface to fill the region. for (i = 0; i < missingshbds->objects && !searchflag; i++) { parysh = (face*)fastlookup(missingshbds, i); sspivot(*parysh, neighseg); sstpivot1(neighseg, searchtet); if (org(searchtet) != sorg(*parysh)) { esymself(searchtet); } spintet = searchtet; while (1) { if (pmarktested(apex(spintet))) { // A possible interior face. neightet = spintet; oldsh = *parysh; // Try to recover an interior edge. for (j = 0; j < 2; j++) { enextself(neightet); if (!issubseg(neightet)) { if (j == 0) { senext(oldsh, searchsh); } else { senext2(oldsh, searchsh); sesymself(searchsh); esymself(neightet); } // Calculate a lifted point. pa = sorg(searchsh); pb = sdest(searchsh); pc = sapex(searchsh); pd = dest(neightet); calculateabovepoint4(pa, pb, pc, pd); // The lifted point must lie above 'searchsh'. ori = orient3d(pa, pb, pc, dummypoint); if (ori > 0) { sesymself(searchsh); senextself(searchsh); } else if (ori == 0) { terminatetetgen(this, 2); } if (sscoutsegment(&searchsh, dest(neightet), 0, 0, 1) == SHAREEDGE) { // Insert a temp segment to protect the recovered edge. face tmpseg; makeshellface(subsegs, &tmpseg); ssbond(searchsh, tmpseg); spivotself(searchsh); ssbond(searchsh, tmpseg); // Recover locally Delaunay edges. lawsonflip(); // Delete the tmp segment. spivot(tmpseg, searchsh); ssdissolve(searchsh); spivotself(searchsh); ssdissolve(searchsh); shellfacedealloc(subsegs, tmpseg.sh); searchflag = 1; } else { // Undo the performed flips. if (flipstack != NULL) { lawsonflip(); } } break; } // if (!issubseg(neightet)) } // j if (searchflag) break; } // if (pmarktested(apex(spintet))) fnextself(spintet); if (spintet.tet == searchtet.tet) break; } } // i if (searchflag) { // Remove faked segments. face checkseg; // Remark: We should not use the array 'missingshbds', since the flips may // change the subfaces. We search them from the subfaces in R. for (i = 0; i < missingshs->objects; i++) { parysh = (face*)fastlookup(missingshs, i); oldsh = *parysh; for (j = 0; j < 3; j++) { if (isshsubseg(oldsh)) { sspivot(oldsh, checkseg); if (sinfected(checkseg)) { // It's a faked segment. Delete it. sstpivot1(checkseg, searchtet); spintet = searchtet; while (1) { tssdissolve1(spintet); fnextself(spintet); if (spintet.tet == searchtet.tet) break; } shellfacedealloc(subsegs, checkseg.sh); ssdissolve(oldsh); } } senextself(oldsh); } // j } fillregioncount++; return 0; } // if (i < missingshbds->objects) searchflag = -1; for (j = 0; j < missingshbds->objects && (searchflag == -1); j++) { parysh = (face*)fastlookup(missingshbds, j); sspivot(*parysh, neighseg); sstpivot1(neighseg, searchtet); interflag = 0; // Let 'spintet' be [#,#,d,e] where [#,#] is the boundary edge of R. spintet = searchtet; while (1) { pd = apex(spintet); pe = oppo(spintet); // Skip a hull edge. if ((pd != dummypoint) && (pe != dummypoint)) { // Skip an edge containing a vertex of R. if (!pmarktested(pd) && !pmarktested(pe)) { // Check if [d,e] intersects R. for (i = 0; i < missingshs->objects && !interflag; i++) { parysh = (face*)fastlookup(missingshs, i); pa = sorg(*parysh); pb = sdest(*parysh); pc = sapex(*parysh); interflag = tri_edge_test(pa, pb, pc, pd, pe, NULL, 1, types, poss); if (interflag > 0) { if (interflag == 2) { // They intersect at a single point. if ((types[0] == (int)ACROSSFACE) || (types[0] == (int)ACROSSEDGE)) { // Go to the crossing edge [d,e,#,#]. edestoppo(spintet, crosstet); // // [d,e,#,#]. if (issubseg(crosstet)) { // It is a segment. Report a PLC problem. report_selfint_face(pa, pb, pc, parysh, &crosstet, interflag, types, poss); } else { triface chkface = crosstet; while (1) { if (issubface(chkface)) break; fsymself(chkface); if (chkface.tet == crosstet.tet) break; } if (issubface(chkface)) { // Two subfaces are intersecting. report_selfint_face(pa, pb, pc, parysh, &chkface, interflag, types, poss); } } // Adjust the edge such that d lies below [a,b,c]. ori = orient3d(pa, pb, pc, pd); if (ori < 0) { esymself(crosstet); } searchflag = 1; } else { // An improper intersection type, ACROSSVERT, TOUCHFACE, // TOUCHEDGE, SHAREVERT, ... // Maybe it is due to a PLC problem. report_selfint_face(pa, pb, pc, parysh, &crosstet, interflag, types, poss); } } break; } // if (interflag > 0) } } } // Leave search at this bdry edge if an intersection is found. if (interflag > 0) break; // Go to the next tetrahedron. fnextself(spintet); if (spintet.tet == searchtet.tet) break; } // while (1) } // j return searchflag; } /////////////////////////////////////////////////////////////////////////////// // // // formcavity() Form the cavity of a missing region. // // // // The missing region R is formed by a set of missing subfaces 'missingshs'. // // In the following, we assume R is horizontal and oriented. (All subfaces // // of R are oriented in the same way.) 'searchtet' is a tetrahedron [d,e,#, // // #] which intersects R in its interior, where the edge [d,e] intersects R, // // and d lies below R. // // // // 'crosstets' returns the set of crossing tets. Every tet in it has the // // form [d,e,#,#] where [d,e] is a crossing edge, and d lies below R. The // // set of tets form the cavity C, which is divided into two parts by R, one // // at top and one at bottom. 'topfaces' and 'botfaces' return the upper and // // lower boundary faces of C. 'toppoints' contains vertices of 'crosstets' // // in the top part of C, and so does 'botpoints'. Both 'toppoints' and // // 'botpoints' contain vertices of R. // // // // Important: This routine assumes all vertices of the facet containing this // // subface are marked, i.e., pmarktested(p) returns true. // // // /////////////////////////////////////////////////////////////////////////////// bool tetgenmesh::formcavity(triface* searchtet, arraypool* missingshs, arraypool* crosstets, arraypool* topfaces, arraypool* botfaces, arraypool* toppoints, arraypool* botpoints) { arraypool* crossedges; triface spintet, neightet, chkface, *parytet; face* parysh = NULL; point pa, pd, pe, *parypt; bool testflag, invalidflag; int intflag, types[2], poss[4]; int t1ver; int i, j, k; // Temporarily re-use 'topfaces' for all crossing edges. crossedges = topfaces; if (b->verbose > 2) { printf(" Form the cavity of a missing region.\n"); } // Mark this edge to avoid testing it later. markedge(*searchtet); crossedges->newindex((void**)&parytet); *parytet = *searchtet; invalidflag = 0; // Collect all crossing tets. Each cross tet is saved in the standard // form [d,e,#,#], where [d,e] is a crossing edge, d lies below R. // NEITHER d NOR e is a vertex of R (!pmarktested). for (i = 0; i < crossedges->objects && !invalidflag; i++) { // Get a crossing edge [d,e,#,#]. searchtet = (triface*)fastlookup(crossedges, i); // Sort vertices into the bottom and top arrays. pd = org(*searchtet); if (!pinfected(pd)) { pinfect(pd); botpoints->newindex((void**)&parypt); *parypt = pd; } pe = dest(*searchtet); if (!pinfected(pe)) { pinfect(pe); toppoints->newindex((void**)&parypt); *parypt = pe; } // All tets sharing this edge are crossing tets. spintet = *searchtet; while (1) { if (!infected(spintet)) { infect(spintet); crosstets->newindex((void**)&parytet); *parytet = spintet; } // Go to the next crossing tet. fnextself(spintet); if (spintet.tet == searchtet->tet) break; } // while (1) // Detect new crossing edges. spintet = *searchtet; while (1) { // spintet is [d,e,a,#], where d lies below R, and e lies above R. pa = apex(spintet); if (pa != dummypoint) { if (!pmarktested(pa)) { // There exists a crossing edge, either [e,a] or [a,d]. First check // if the crossing edge has already be added, i.e.,to check if one // of the tetrahedron at this edge has been marked. testflag = true; for (j = 0; j < 2 && testflag; j++) { if (j == 0) { enext(spintet, neightet); } else { eprev(spintet, neightet); } while (1) { if (edgemarked(neightet)) { // This crossing edge has already been tested. Skip it. testflag = false; break; } fnextself(neightet); if (neightet.tet == spintet.tet) break; } } // j if (testflag) { // Test if [e,a] or [a,d] intersects R. // Do a brute-force search in the set of subfaces of R. Slow! // Need to be improved! pd = org(spintet); pe = dest(spintet); for (k = 0; k < missingshs->objects; k++) { parysh = (face*)fastlookup(missingshs, k); intflag = tri_edge_test(sorg(*parysh), sdest(*parysh), sapex(*parysh), pe, pa, NULL, 1, types, poss); if (intflag > 0) { // Found intersection. 'a' lies below R. if (intflag == 2) { enext(spintet, neightet); if ((types[0] == (int)ACROSSFACE) || (types[0] == (int)ACROSSEDGE)) { // Only this case is valid. } else { // A non-valid intersection. Maybe a PLC problem. invalidflag = 1; } } else { // Coplanar intersection. Maybe a PLC problem. invalidflag = 1; } break; } intflag = tri_edge_test(sorg(*parysh), sdest(*parysh), sapex(*parysh), pa, pd, NULL, 1, types, poss); if (intflag > 0) { // Found intersection. 'a' lies above R. if (intflag == 2) { eprev(spintet, neightet); if ((types[0] == (int)ACROSSFACE) || (types[0] == (int)ACROSSEDGE)) { // Only this case is valid. } else { // A non-valid intersection. Maybe a PLC problem. invalidflag = 1; } } else { // Coplanar intersection. Maybe a PLC problem. invalidflag = 1; } break; } } // k if (k < missingshs->objects) { // Found a pair of triangle - edge intersection. if (invalidflag) { break; // the while (1) loop } // Adjust the edge direction, so that its origin lies below R, // and its destination lies above R. esymself(neightet); // This edge may be a segment. if (issubseg(neightet)) { report_selfint_face(sorg(*parysh), sdest(*parysh), sapex(*parysh), parysh, &neightet, intflag, types, poss); } // Check if it is an edge of a subface. chkface = neightet; while (1) { if (issubface(chkface)) break; fsymself(chkface); if (chkface.tet == neightet.tet) break; } if (issubface(chkface)) { // Two subfaces are intersecting. report_selfint_face(sorg(*parysh), sdest(*parysh), sapex(*parysh), parysh, &chkface, intflag, types, poss); } // Mark this edge to avoid testing it again. markedge(neightet); crossedges->newindex((void**)&parytet); *parytet = neightet; } else { // No intersection is found. It may be a PLC problem. invalidflag = 1; break; // the while (1) loop } // if (k == missingshs->objects) } // if (testflag) } } // if (pa != dummypoint) // Go to the next crossing tet. fnextself(spintet); if (spintet.tet == searchtet->tet) break; } // while (1) } // i // Unmark all marked edges. for (i = 0; i < crossedges->objects; i++) { searchtet = (triface*)fastlookup(crossedges, i); unmarkedge(*searchtet); } crossedges->restart(); if (invalidflag) { // Unmark all collected tets. for (i = 0; i < crosstets->objects; i++) { searchtet = (triface*)fastlookup(crosstets, i); uninfect(*searchtet); } // Unmark all collected vertices. for (i = 0; i < botpoints->objects; i++) { parypt = (point*)fastlookup(botpoints, i); puninfect(*parypt); } for (i = 0; i < toppoints->objects; i++) { parypt = (point*)fastlookup(toppoints, i); puninfect(*parypt); } crosstets->restart(); botpoints->restart(); toppoints->restart(); // Randomly split an interior edge of R. i = randomnation(missingshs->objects - 1); recentsh = *(face*)fastlookup(missingshs, i); return false; } if (b->verbose > 2) { printf(" Formed cavity: %ld (%ld) cross tets (edges).\n", crosstets->objects, crossedges->objects); } // Collect the top and bottom faces and the middle vertices. Since all top // and bottom vertices have been infected. Uninfected vertices must be // middle vertices (i.e., the vertices of R). // NOTE 1: Hull tets may be collected. Process them as a normal one. // NOTE 2: Some previously recovered subfaces may be completely inside the // cavity. In such case, we remove these subfaces from the cavity and put // them into 'subfacstack'. They will be recovered later. // NOTE 3: Some segments may be completely inside the cavity, e.g., they // attached to a subface which is inside the cavity. Such segments are // put in 'subsegstack'. They will be recovered later. // NOTE4 : The interior subfaces and segments mentioned in NOTE 2 and 3 // are identified in the routine "carvecavity()". for (i = 0; i < crosstets->objects; i++) { searchtet = (triface*)fastlookup(crosstets, i); // searchtet is [d,e,a,b]. eorgoppo(*searchtet, spintet); fsym(spintet, neightet); // neightet is [a,b,e,#] if (!infected(neightet)) { // A top face. topfaces->newindex((void**)&parytet); *parytet = neightet; } edestoppo(*searchtet, spintet); fsym(spintet, neightet); // neightet is [b,a,d,#] if (!infected(neightet)) { // A bottom face. botfaces->newindex((void**)&parytet); *parytet = neightet; } // Add middle vertices if there are (skip dummypoint). pa = org(neightet); if (!pinfected(pa)) { if (pa != dummypoint) { pinfect(pa); botpoints->newindex((void**)&parypt); *parypt = pa; toppoints->newindex((void**)&parypt); *parypt = pa; } } pa = dest(neightet); if (!pinfected(pa)) { if (pa != dummypoint) { pinfect(pa); botpoints->newindex((void**)&parypt); *parypt = pa; toppoints->newindex((void**)&parypt); *parypt = pa; } } } // i // Uninfect all collected top, bottom, and middle vertices. for (i = 0; i < toppoints->objects; i++) { parypt = (point*)fastlookup(toppoints, i); puninfect(*parypt); } for (i = 0; i < botpoints->objects; i++) { parypt = (point*)fastlookup(botpoints, i); puninfect(*parypt); } cavitycount++; return true; } /////////////////////////////////////////////////////////////////////////////// // // // delaunizecavity() Fill a cavity by Delaunay tetrahedra. // // // // The cavity C to be tetrahedralized is the top or bottom part of a whole // // cavity. 'cavfaces' contains the boundary faces of C. NOTE: faces in 'cav- // // faces' do not form a closed polyhedron. The "open" side are subfaces of // // the missing facet. These faces will be recovered later in fillcavity(). // // // // This routine first constructs the DT of the vertices. Then it identifies // // the half boundary faces of the cavity in DT. Possiblely the cavity C will // // be enlarged. // // // // The DT is returned in 'newtets'. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::delaunizecavity(arraypool* cavpoints, arraypool* cavfaces, arraypool* cavshells, arraypool* newtets, arraypool* crosstets, arraypool* misfaces) { triface searchtet, neightet, *parytet, *parytet1; face tmpsh, *parysh; point pa, pb, pc, pd, pt[3], *parypt; insertvertexflags ivf; REAL ori; long baknum, bakhullsize; int bakchecksubsegflag, bakchecksubfaceflag; int t1ver; int i, j; if (b->verbose > 2) { printf(" Delaunizing cavity: %ld points, %ld faces.\n", cavpoints->objects, cavfaces->objects); } // Remember the current number of crossing tets. It may be enlarged later. baknum = crosstets->objects; bakhullsize = hullsize; bakchecksubsegflag = checksubsegflag; bakchecksubfaceflag = checksubfaceflag; hullsize = 0l; checksubsegflag = 0; checksubfaceflag = 0; b->verbose--; // Suppress informations for creating Delaunay tetra. b->plc = 0; // Do not check near vertices. ivf.bowywat = 1; // Use Bowyer-Watson algorithm. // Get four non-coplanar points (no dummypoint). pa = pb = pc = NULL; for (i = 0; i < cavfaces->objects; i++) { parytet = (triface*)fastlookup(cavfaces, i); parytet->ver = epivot[parytet->ver]; if (apex(*parytet) != dummypoint) { pa = org(*parytet); pb = dest(*parytet); pc = apex(*parytet); break; } } pd = NULL; for (; i < cavfaces->objects; i++) { parytet = (triface*)fastlookup(cavfaces, i); pt[0] = org(*parytet); pt[1] = dest(*parytet); pt[2] = apex(*parytet); for (j = 0; j < 3; j++) { if (pt[j] != dummypoint) { // Do not include a hull point. ori = orient3d(pa, pb, pc, pt[j]); if (ori != 0) { pd = pt[j]; if (ori > 0) { // Swap pa and pb. pt[j] = pa; pa = pb; pb = pt[j]; } break; } } } if (pd != NULL) break; } // Create an init DT. initialdelaunay(pa, pb, pc, pd); // Incrementally insert the vertices (duplicated vertices are ignored). for (i = 0; i < cavpoints->objects; i++) { pt[0] = *(point*)fastlookup(cavpoints, i); searchtet = recenttet; ivf.iloc = (int)OUTSIDE; insertpoint(pt[0], &searchtet, NULL, NULL, &ivf); } if (b->verbose > 2) { printf(" Identifying %ld boundary faces of the cavity.\n", cavfaces->objects); } while (1) { // Identify boundary faces. Mark interior tets. Save missing faces. for (i = 0; i < cavfaces->objects; i++) { parytet = (triface*)fastlookup(cavfaces, i); // Skip an interior face (due to the enlargement of the cavity). if (infected(*parytet)) continue; parytet->ver = epivot[parytet->ver]; pt[0] = org(*parytet); pt[1] = dest(*parytet); pt[2] = apex(*parytet); // Create a temp subface. makeshellface(subfaces, &tmpsh); setshvertices(tmpsh, pt[0], pt[1], pt[2]); // Insert tmpsh in DT. searchtet.tet = NULL; if (scoutsubface(&tmpsh, &searchtet, 0)) { // shflag = 0 // Inserted! 'tmpsh' must face toward the inside of the cavity. // Remember the boundary tet (outside the cavity) in tmpsh // (use the adjacent tet slot). tmpsh.sh[0] = (shellface)encode(*parytet); // Save this subface. cavshells->newindex((void**)&parysh); *parysh = tmpsh; } else { // This boundary face is missing. shellfacedealloc(subfaces, tmpsh.sh); // Save this face in list. misfaces->newindex((void**)&parytet1); *parytet1 = *parytet; } } // i if (misfaces->objects > 0) { if (b->verbose > 2) { printf(" Enlarging the cavity. %ld missing bdry faces\n", misfaces->objects); } // Removing all temporary subfaces. for (i = 0; i < cavshells->objects; i++) { parysh = (face*)fastlookup(cavshells, i); stpivot(*parysh, neightet); tsdissolve(neightet); // Detach it from adj. tets. fsymself(neightet); tsdissolve(neightet); shellfacedealloc(subfaces, parysh->sh); } cavshells->restart(); // Infect the points which are of the cavity. for (i = 0; i < cavpoints->objects; i++) { pt[0] = *(point*)fastlookup(cavpoints, i); pinfect(pt[0]); // Mark it as inserted. } // Enlarge the cavity. for (i = 0; i < misfaces->objects; i++) { // Get a missing face. parytet = (triface*)fastlookup(misfaces, i); if (!infected(*parytet)) { // Put it into crossing tet list. infect(*parytet); crosstets->newindex((void**)&parytet1); *parytet1 = *parytet; // Insert the opposite point if it is not in DT. pd = oppo(*parytet); if (!pinfected(pd)) { searchtet = recenttet; ivf.iloc = (int)OUTSIDE; insertpoint(pd, &searchtet, NULL, NULL, &ivf); pinfect(pd); cavpoints->newindex((void**)&parypt); *parypt = pd; } // Add three opposite faces into the boundary list. for (j = 0; j < 3; j++) { esym(*parytet, neightet); fsymself(neightet); if (!infected(neightet)) { cavfaces->newindex((void**)&parytet1); *parytet1 = neightet; } enextself(*parytet); } // j } // if (!infected(parytet)) } // i // Uninfect the points which are of the cavity. for (i = 0; i < cavpoints->objects; i++) { pt[0] = *(point*)fastlookup(cavpoints, i); puninfect(pt[0]); } misfaces->restart(); continue; } // if (misfaces->objects > 0) break; } // while (1) // Collect all tets of the DT. All new tets are marktested. marktest(recenttet); newtets->newindex((void**)&parytet); *parytet = recenttet; for (i = 0; i < newtets->objects; i++) { searchtet = *(triface*)fastlookup(newtets, i); for (j = 0; j < 4; j++) { decode(searchtet.tet[j], neightet); if (!marktested(neightet)) { marktest(neightet); newtets->newindex((void**)&parytet); *parytet = neightet; } } } cavpoints->restart(); cavfaces->restart(); if (crosstets->objects > baknum) { // The cavity has been enlarged. cavityexpcount++; } // Restore the original values. hullsize = bakhullsize; checksubsegflag = bakchecksubsegflag; checksubfaceflag = bakchecksubfaceflag; b->verbose++; b->plc = 1; } /////////////////////////////////////////////////////////////////////////////// // // // fillcavity() Fill new tets into the cavity. // // // // The new tets are stored in two disjoint sets(which share the same facet). // // 'topfaces' and 'botfaces' are the boundaries of these two sets, respect- // // ively. 'midfaces' is empty on input, and will store faces in the facet. // // // // Important: This routine assumes all vertices of the missing region R are // // marktested, i.e., pmarktested(p) returns true. // // // /////////////////////////////////////////////////////////////////////////////// bool tetgenmesh::fillcavity(arraypool* topshells, arraypool* botshells, arraypool* midfaces, arraypool* missingshs, arraypool* topnewtets, arraypool* botnewtets, triface* crossedge) { arraypool* cavshells; triface bdrytet, neightet, *parytet; triface searchtet, spintet; face* parysh; face checkseg; point pa, pb, pc; bool mflag; int t1ver; int i, j; // Connect newtets to tets outside the cavity. These connections are needed // for identifying the middle faces (which belong to R). for (j = 0; j < 2; j++) { cavshells = (j == 0 ? topshells : botshells); if (cavshells != NULL) { for (i = 0; i < cavshells->objects; i++) { // Get a temp subface. parysh = (face*)fastlookup(cavshells, i); // Get the boundary tet outside the cavity (saved in sh[0]). decode(parysh->sh[0], bdrytet); pa = org(bdrytet); pb = dest(bdrytet); pc = apex(bdrytet); // Get the adjacent new tet inside the cavity. stpivot(*parysh, neightet); // Mark neightet as an interior tet of this cavity. infect(neightet); // Connect the two tets (the old connections are replaced). bond(bdrytet, neightet); tsdissolve(neightet); // Clear the pointer to tmpsh. // Update the point-to-tets map. setpoint2tet(pa, (tetrahedron)neightet.tet); setpoint2tet(pb, (tetrahedron)neightet.tet); setpoint2tet(pc, (tetrahedron)neightet.tet); } // i } // if (cavshells != NULL) } // j if (crossedge != NULL) { // Glue top and bottom tets at their common facet. triface toptet, bottet, spintet, *midface; point pd, pe; REAL ori; int types[2], poss[4]; int interflag; int bflag; mflag = false; pd = org(*crossedge); pe = dest(*crossedge); // Search the first (middle) face in R. // Since R may be non-convex, we must make sure that the face is in the // interior of R. We search a face in 'topnewtets' whose three vertices // are on R and it intersects 'crossedge' in its interior. Then search // a matching face in 'botnewtets'. for (i = 0; i < topnewtets->objects && !mflag; i++) { searchtet = *(triface*)fastlookup(topnewtets, i); for (searchtet.ver = 0; searchtet.ver < 4 && !mflag; searchtet.ver++) { pa = org(searchtet); if (pmarktested(pa)) { pb = dest(searchtet); if (pmarktested(pb)) { pc = apex(searchtet); if (pmarktested(pc)) { // Check if this face intersects [d,e]. interflag = tri_edge_test(pa, pb, pc, pd, pe, NULL, 1, types, poss); if (interflag == 2) { // They intersect at a single point. Found. toptet = searchtet; // The face lies in the interior of R. // Get the tet (in topnewtets) which lies above R. ori = orient3d(pa, pb, pc, pd); if (ori < 0) { fsymself(toptet); pa = org(toptet); pb = dest(toptet); } else if (ori == 0) { terminatetetgen(this, 2); } // Search the face [b,a,c] in 'botnewtets'. for (j = 0; j < botnewtets->objects; j++) { neightet = *(triface*)fastlookup(botnewtets, j); // Is neightet contains 'b'. if ((point)neightet.tet[4] == pb) { neightet.ver = 11; } else if ((point)neightet.tet[5] == pb) { neightet.ver = 3; } else if ((point)neightet.tet[6] == pb) { neightet.ver = 7; } else if ((point)neightet.tet[7] == pb) { neightet.ver = 0; } else { continue; } // Is the 'neightet' contains edge [b,a]. if (dest(neightet) == pa) { // 'neightet' is just the edge. } else if (apex(neightet) == pa) { eprevesymself(neightet); } else if (oppo(neightet) == pa) { esymself(neightet); enextself(neightet); } else { continue; } // Is 'neightet' the face [b,a,c]. if (apex(neightet) == pc) { bottet = neightet; mflag = true; break; } } // j } // if (interflag == 2) } // pc } // pb } // pa } // toptet.ver } // i if (mflag) { // Found a pair of matched faces in 'toptet' and 'bottet'. bond(toptet, bottet); // Both are interior tets. infect(toptet); infect(bottet); // Add this face into search list. markface(toptet); midfaces->newindex((void**)&parytet); *parytet = toptet; } else { // No pair of 'toptet' and 'bottet'. toptet.tet = NULL; // Randomly split an interior edge of R. i = randomnation(missingshs->objects - 1); recentsh = *(face*)fastlookup(missingshs, i); } // Find other middle faces, connect top and bottom tets. for (i = 0; i < midfaces->objects && mflag; i++) { // Get a matched middle face [a, b, c] midface = (triface*)fastlookup(midfaces, i); // Check the neighbors at the edges of this face. for (j = 0; j < 3 && mflag; j++) { toptet = *midface; bflag = false; while (1) { // Go to the next face in the same tet. esymself(toptet); pc = apex(toptet); if (pmarktested(pc)) { break; // Find a subface. } if (pc == dummypoint) { terminatetetgen(this, 2); // Check this case. break; // Find a subface. } // Go to the adjacent tet. fsymself(toptet); // Do we walk outside the cavity? if (!marktested(toptet)) { // Yes, the adjacent face is not a middle face. bflag = true; break; } } if (!bflag) { if (!facemarked(toptet)) { fsym(*midface, bottet); spintet = bottet; while (1) { esymself(bottet); pd = apex(bottet); if (pd == pc) break; // Face matched. fsymself(bottet); if (bottet.tet == spintet.tet) { // Not found a matched bottom face. mflag = false; break; } } // while (1) if (mflag) { if (marktested(bottet)) { // Connect two tets together. bond(toptet, bottet); // Both are interior tets. infect(toptet); infect(bottet); // Add this face into list. markface(toptet); midfaces->newindex((void**)&parytet); *parytet = toptet; } else { // The 'bottet' is not inside the cavity! terminatetetgen(this, 2); // Check this case } } else { // mflag == false // Adjust 'toptet' and 'bottet' to be the crossing edges. fsym(*midface, bottet); spintet = bottet; while (1) { esymself(bottet); pd = apex(bottet); if (pmarktested(pd)) { // assert(pd != pc); // Let 'toptet' be [a,b,c,#], and 'bottet' be [b,a,d,*]. // Adjust 'toptet' and 'bottet' to be the crossing edges. // Test orient3d(b,c,#,d). ori = orient3d(dest(toptet), pc, oppo(toptet), pd); if (ori < 0) { // Edges [a,d] and [b,c] cross each other. enextself(toptet); // [b,c] enextself(bottet); // [a,d] } else if (ori > 0) { // Edges [a,c] and [b,d] cross each other. eprevself(toptet); // [c,a] eprevself(bottet); // [d,b] } else { // b,c,#,and d are coplanar!. terminatetetgen(this, 2); // assert(0); } break; // Not matched } fsymself(bottet); } } // if (!mflag) } // if (!facemarked(toptet)) } // if (!bflag) enextself(*midface); } // j } // i if (mflag) { if (b->verbose > 2) { printf(" Found %ld middle subfaces.\n", midfaces->objects); } face oldsh, newsh, casout, casin, neighsh; oldsh = *(face*)fastlookup(missingshs, 0); // Create new subfaces to fill the region R. for (i = 0; i < midfaces->objects; i++) { // Get a matched middle face [a, b, c] midface = (triface*)fastlookup(midfaces, i); unmarkface(*midface); makeshellface(subfaces, &newsh); setsorg(newsh, org(*midface)); setsdest(newsh, dest(*midface)); setsapex(newsh, apex(*midface)); // The new subface gets its markers from the old one. setshellmark(newsh, shellmark(oldsh)); if (checkconstraints) { setareabound(newsh, areabound(oldsh)); } if (useinsertradius) { setfacetindex(newsh, getfacetindex(oldsh)); } // Connect the new subface to adjacent tets. tsbond(*midface, newsh); fsym(*midface, neightet); sesymself(newsh); tsbond(neightet, newsh); } // Connect new subfaces together and to the bdry of R. // Delete faked segments. for (i = 0; i < midfaces->objects; i++) { // Get a matched middle face [a, b, c] midface = (triface*)fastlookup(midfaces, i); for (j = 0; j < 3; j++) { tspivot(*midface, newsh); spivot(newsh, casout); if (casout.sh == NULL) { // Search its neighbor. fnext(*midface, searchtet); while (1) { // (1) First check if this side is a bdry edge of R. tsspivot1(searchtet, checkseg); if (checkseg.sh != NULL) { // It's a bdry edge of R. // Get the old subface. checkseg.shver = 0; spivot(checkseg, oldsh); if (sinfected(checkseg)) { // It's a faked segment. Delete it. spintet = searchtet; while (1) { tssdissolve1(spintet); fnextself(spintet); if (spintet.tet == searchtet.tet) break; } shellfacedealloc(subsegs, checkseg.sh); ssdissolve(oldsh); checkseg.sh = NULL; } spivot(oldsh, casout); if (casout.sh != NULL) { casin = casout; if (checkseg.sh != NULL) { // Make sure that the subface has the right ori at the // segment. checkseg.shver = 0; if (sorg(newsh) != sorg(checkseg)) { sesymself(newsh); } spivot(casin, neighsh); while (neighsh.sh != oldsh.sh) { casin = neighsh; spivot(casin, neighsh); } } sbond1(newsh, casout); sbond1(casin, newsh); } if (checkseg.sh != NULL) { ssbond(newsh, checkseg); } break; } // if (checkseg.sh != NULL) // (2) Second check if this side is an interior edge of R. tspivot(searchtet, neighsh); if (neighsh.sh != NULL) { // Found an adjacent subface of newsh (an interior edge). sbond(newsh, neighsh); break; } fnextself(searchtet); } // while (1) } // if (casout.sh == NULL) enextself(*midface); } // j } // i // Delete old subfaces. for (i = 0; i < missingshs->objects; i++) { parysh = (face*)fastlookup(missingshs, i); shellfacedealloc(subfaces, parysh->sh); } } else { if (toptet.tet != NULL) { // Faces at top and bottom are not matched. // Choose a Steiner point in R. // Split one of the crossing edges. pa = org(toptet); pb = dest(toptet); pc = org(bottet); pd = dest(bottet); // Search an edge in R which is either [a,b] or [c,d]. // Reminder: Subfaces in this list 'missingshs', except the first // one, represents an interior edge of R. parysh = NULL; // Avoid a warning in MSVC for (i = 1; i < missingshs->objects; i++) { parysh = (face*)fastlookup(missingshs, i); if (((sorg(*parysh) == pa) && (sdest(*parysh) == pb)) || ((sorg(*parysh) == pb) && (sdest(*parysh) == pa))) break; if (((sorg(*parysh) == pc) && (sdest(*parysh) == pd)) || ((sorg(*parysh) == pd) && (sdest(*parysh) == pc))) break; } if (i < missingshs->objects) { // Found. Return it. recentsh = *parysh; } else { terminatetetgen(this, 2); // assert(0); } } else { // terminatetetgen(this, 2); // Report a bug } } midfaces->restart(); } else { mflag = true; } // Delete the temp subfaces. for (j = 0; j < 2; j++) { cavshells = (j == 0 ? topshells : botshells); if (cavshells != NULL) { for (i = 0; i < cavshells->objects; i++) { parysh = (face*)fastlookup(cavshells, i); shellfacedealloc(subfaces, parysh->sh); } } } topshells->restart(); if (botshells != NULL) { botshells->restart(); } return mflag; } /////////////////////////////////////////////////////////////////////////////// // // // carvecavity() Delete old tets and outer new tets of the cavity. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::carvecavity(arraypool* crosstets, arraypool* topnewtets, arraypool* botnewtets) { arraypool* newtets; shellface *sptr, *ssptr; triface *parytet, *pnewtet, newtet, neightet, spintet; face checksh, *parysh; face checkseg, *paryseg; int t1ver; int i, j; if (b->verbose > 2) { printf(" Carve cavity: %ld old tets.\n", crosstets->objects); } // First process subfaces and segments which are adjacent to the cavity. // They must be re-connected to new tets in the cavity. // Comment: It is possible that some subfaces and segments are completely // inside the cavity. This can happen even if the cavity is not enlarged. // Before deleting the old tets, find and queue all interior subfaces // and segments. They will be recovered later. 2010-05-06. // Collect all subfaces and segments which attached to the old tets. for (i = 0; i < crosstets->objects; i++) { parytet = (triface*)fastlookup(crosstets, i); if ((sptr = (shellface*)parytet->tet[9]) != NULL) { for (j = 0; j < 4; j++) { if (sptr[j]) { sdecode(sptr[j], checksh); if (!sinfected(checksh)) { sinfect(checksh); cavetetshlist->newindex((void**)&parysh); *parysh = checksh; } } } // j } if ((ssptr = (shellface*)parytet->tet[8]) != NULL) { for (j = 0; j < 6; j++) { if (ssptr[j]) { sdecode(ssptr[j], checkseg); // Skip a deleted segment (was a faked segment) if (checkseg.sh[3] != NULL) { if (!sinfected(checkseg)) { sinfect(checkseg); cavetetseglist->newindex((void**)&paryseg); *paryseg = checkseg; } } } } // j } } // i // Uninfect collected subfaces. for (i = 0; i < cavetetshlist->objects; i++) { parysh = (face*)fastlookup(cavetetshlist, i); suninfect(*parysh); } // Uninfect collected segments. for (i = 0; i < cavetetseglist->objects; i++) { paryseg = (face*)fastlookup(cavetetseglist, i); suninfect(*paryseg); } // Connect subfaces to new tets. for (i = 0; i < cavetetshlist->objects; i++) { parysh = (face*)fastlookup(cavetetshlist, i); // Get an adjacent tet at this subface. stpivot(*parysh, neightet); // Does this tet lie inside the cavity. if (infected(neightet)) { // Yes. Get the other adjacent tet at this subface. sesymself(*parysh); stpivot(*parysh, neightet); // Does this tet lie inside the cavity. if (infected(neightet)) { checksh = *parysh; stdissolve(checksh); caveencshlist->newindex((void**)&parysh); *parysh = checksh; } } if (!infected(neightet)) { // Found an outside tet. Re-connect this subface to a new tet. fsym(neightet, newtet); sesymself(*parysh); tsbond(newtet, *parysh); } } // i for (i = 0; i < cavetetseglist->objects; i++) { checkseg = *(face*)fastlookup(cavetetseglist, i); // Check if the segment is inside the cavity. sstpivot1(checkseg, neightet); spintet = neightet; while (1) { if (!infected(spintet)) { // This segment is on the boundary of the cavity. break; } fnextself(spintet); if (spintet.tet == neightet.tet) { sstdissolve1(checkseg); caveencseglist->newindex((void**)&paryseg); *paryseg = checkseg; break; } } if (!infected(spintet)) { // A boundary segment. Connect this segment to the new tets. sstbond1(checkseg, spintet); neightet = spintet; while (1) { tssbond1(spintet, checkseg); fnextself(spintet); if (spintet.tet == neightet.tet) break; } } } // i cavetetshlist->restart(); cavetetseglist->restart(); // Delete the old tets in cavity. for (i = 0; i < crosstets->objects; i++) { parytet = (triface*)fastlookup(crosstets, i); if (ishulltet(*parytet)) { hullsize--; } tetrahedrondealloc(parytet->tet); } crosstets->restart(); // crosstets will be re-used. // Collect new tets in cavity. Some new tets have already been found // (and infected) in the fillcavity(). We first collect them. for (j = 0; j < 2; j++) { newtets = (j == 0 ? topnewtets : botnewtets); if (newtets != NULL) { for (i = 0; i < newtets->objects; i++) { parytet = (triface*)fastlookup(newtets, i); if (infected(*parytet)) { crosstets->newindex((void**)&pnewtet); *pnewtet = *parytet; } } // i } } // j // Now we collect all new tets in cavity. for (i = 0; i < crosstets->objects; i++) { parytet = (triface*)fastlookup(crosstets, i); for (j = 0; j < 4; j++) { decode(parytet->tet[j], neightet); if (marktested(neightet)) { // Is it a new tet? if (!infected(neightet)) { // Find an interior tet. // assert((point) neightet.tet[7] != dummypoint); // SELF_CHECK infect(neightet); crosstets->newindex((void**)&pnewtet); *pnewtet = neightet; } } } // j } // i parytet = (triface*)fastlookup(crosstets, 0); recenttet = *parytet; // Remember a live handle. // Delete outer new tets. for (j = 0; j < 2; j++) { newtets = (j == 0 ? topnewtets : botnewtets); if (newtets != NULL) { for (i = 0; i < newtets->objects; i++) { parytet = (triface*)fastlookup(newtets, i); if (infected(*parytet)) { // This is an interior tet. uninfect(*parytet); unmarktest(*parytet); if (ishulltet(*parytet)) { hullsize++; } } else { // An outer tet. Delete it. tetrahedrondealloc(parytet->tet); } } } } crosstets->restart(); topnewtets->restart(); if (botnewtets != NULL) { botnewtets->restart(); } } /////////////////////////////////////////////////////////////////////////////// // // // restorecavity() Reconnect old tets and delete new tets of the cavity. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::restorecavity(arraypool* crosstets, arraypool* topnewtets, arraypool* botnewtets, arraypool* missingshbds) { triface *parytet, neightet, spintet; face* parysh; face checkseg; point* ppt; int t1ver; int i, j; // Reconnect crossing tets to cavity boundary. for (i = 0; i < crosstets->objects; i++) { parytet = (triface*)fastlookup(crosstets, i); parytet->ver = 0; for (parytet->ver = 0; parytet->ver < 4; parytet->ver++) { fsym(*parytet, neightet); if (!infected(neightet)) { // Restore the old connections of tets. bond(*parytet, neightet); } } // Update the point-to-tet map. parytet->ver = 0; ppt = (point*)&(parytet->tet[4]); for (j = 0; j < 4; j++) { setpoint2tet(ppt[j], encode(*parytet)); } } // Uninfect all crossing tets. for (i = 0; i < crosstets->objects; i++) { parytet = (triface*)fastlookup(crosstets, i); uninfect(*parytet); } // Remember a live handle. if (crosstets->objects > 0) { recenttet = *(triface*)fastlookup(crosstets, 0); } // Delete faked segments. for (i = 0; i < missingshbds->objects; i++) { parysh = (face*)fastlookup(missingshbds, i); sspivot(*parysh, checkseg); if (checkseg.sh[3] != NULL) { if (sinfected(checkseg)) { // It's a faked segment. Delete it. sstpivot1(checkseg, neightet); spintet = neightet; while (1) { tssdissolve1(spintet); fnextself(spintet); if (spintet.tet == neightet.tet) break; } shellfacedealloc(subsegs, checkseg.sh); ssdissolve(*parysh); // checkseg.sh = NULL; } } } // i // Delete new tets. for (i = 0; i < topnewtets->objects; i++) { parytet = (triface*)fastlookup(topnewtets, i); tetrahedrondealloc(parytet->tet); } if (botnewtets != NULL) { for (i = 0; i < botnewtets->objects; i++) { parytet = (triface*)fastlookup(botnewtets, i); tetrahedrondealloc(parytet->tet); } } crosstets->restart(); topnewtets->restart(); if (botnewtets != NULL) { botnewtets->restart(); } } /////////////////////////////////////////////////////////////////////////////// // // // flipcertify() Insert a crossing face into priority queue. // // // // A crossing face of a facet must have at least one top and one bottom ver- // // tex of the facet. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::flipcertify(triface* chkface, badface** pqueue, point plane_pa, point plane_pb, point plane_pc) { badface *parybf, *prevbf, *nextbf; triface neightet; face checksh; point p[5]; REAL w[5]; REAL insph, ori4; int topi, boti; int i; // Compute the flip time \tau. fsym(*chkface, neightet); p[0] = org(*chkface); p[1] = dest(*chkface); p[2] = apex(*chkface); p[3] = oppo(*chkface); p[4] = oppo(neightet); // Check if the face is a crossing face. topi = boti = 0; for (i = 0; i < 3; i++) { if (pmarktest2ed(p[i])) topi++; if (pmarktest3ed(p[i])) boti++; } if ((topi == 0) || (boti == 0)) { // It is not a crossing face. // return; for (i = 3; i < 5; i++) { if (pmarktest2ed(p[i])) topi++; if (pmarktest3ed(p[i])) boti++; } if ((topi == 0) || (boti == 0)) { // The two tets sharing at this face are on one side of the facet. // Check if this face is locally Delaunay (due to rounding error). if ((p[3] != dummypoint) && (p[4] != dummypoint)) { // Do not check it if it is a subface. tspivot(*chkface, checksh); if (checksh.sh == NULL) { insph = insphere_s(p[1], p[0], p[2], p[3], p[4]); if (insph > 0) { // Add the face into queue. if (b->verbose > 2) { printf(" A locally non-Delanay face (%d, %d, %d)-%d,%d\n", pointmark(p[0]), pointmark(p[1]), pointmark(p[2]), pointmark(p[3]), pointmark(p[4])); } parybf = (badface*)flippool->alloc(); parybf->key = 0.; // tau = 0, do immediately. parybf->tt = *chkface; parybf->forg = p[0]; parybf->fdest = p[1]; parybf->fapex = p[2]; parybf->foppo = p[3]; parybf->noppo = p[4]; // Add it at the top of the priority queue. if (*pqueue == NULL) { *pqueue = parybf; parybf->nextitem = NULL; } else { parybf->nextitem = *pqueue; *pqueue = parybf; } } // if (insph > 0) } // if (checksh.sh == NULL) } } return; // Test: omit this face. } // Decide the "height" for each point. for (i = 0; i < 5; i++) { if (pmarktest2ed(p[i])) { // A top point has a positive weight. w[i] = orient3dfast(plane_pa, plane_pb, plane_pc, p[i]); if (w[i] < 0) w[i] = -w[i]; } else { w[i] = 0; } } insph = insphere(p[1], p[0], p[2], p[3], p[4]); ori4 = orient4d(p[1], p[0], p[2], p[3], p[4], w[1], w[0], w[2], w[3], w[4]); if (ori4 > 0) { // Add the face into queue. if (b->verbose > 2) { printf(" Insert face (%d, %d, %d) - %d, %d\n", pointmark(p[0]), pointmark(p[1]), pointmark(p[2]), pointmark(p[3]), pointmark(p[4])); } parybf = (badface*)flippool->alloc(); parybf->key = -insph / ori4; parybf->tt = *chkface; parybf->forg = p[0]; parybf->fdest = p[1]; parybf->fapex = p[2]; parybf->foppo = p[3]; parybf->noppo = p[4]; // Push the face into priority queue. // pq.push(bface); if (*pqueue == NULL) { *pqueue = parybf; parybf->nextitem = NULL; } else { // Search an item whose key is larger or equal to current key. prevbf = NULL; nextbf = *pqueue; // if (!b->flipinsert_random) { // Default use a priority queue. // Insert the item into priority queue. while (nextbf != NULL) { if (nextbf->key < parybf->key) { prevbf = nextbf; nextbf = nextbf->nextitem; } else { break; } } //} // if (!b->flipinsert_random) // Insert the new item between prev and next items. if (prevbf == NULL) { *pqueue = parybf; } else { prevbf->nextitem = parybf; } parybf->nextitem = nextbf; } } else if (ori4 == 0) { } } /////////////////////////////////////////////////////////////////////////////// // // // flipinsertfacet() Insert a facet into a CDT by flips. // // // // The algorithm is described in Shewchuk's paper "Updating and Constructing // // Constrained Delaunay and Constrained Regular Triangulations by Flips", in // // Proc. 19th Ann. Symp. on Comput. Geom., 86--95, 2003. // // // // 'crosstets' contains the set of crossing tetrahedra (infected) of the // // facet. 'toppoints' and 'botpoints' are points lies above and below the // // facet, not on the facet. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::flipinsertfacet(arraypool* crosstets, arraypool* toppoints, arraypool* botpoints, arraypool* midpoints) { arraypool *crossfaces, *bfacearray; triface fliptets[6], baktets[2], fliptet, newface; triface neightet, *parytet; badface* pqueue; badface *popbf, bface; point plane_pa, plane_pb, plane_pc; point p1, p2, pd, pe; point* parypt; flipconstraints fc; REAL ori[3]; int convcount, copcount; int flipflag, fcount; int n, i; long f23count, f32count, f44count; long totalfcount; f23count = flip23count; f32count = flip32count; f44count = flip44count; // Get three affinely independent vertices in the missing region R. calculateabovepoint(midpoints, &plane_pa, &plane_pb, &plane_pc); // Mark top and bottom points. Do not mark midpoints. for (i = 0; i < toppoints->objects; i++) { parypt = (point*)fastlookup(toppoints, i); if (!pmarktested(*parypt)) { pmarktest2(*parypt); } } for (i = 0; i < botpoints->objects; i++) { parypt = (point*)fastlookup(botpoints, i); if (!pmarktested(*parypt)) { pmarktest3(*parypt); } } // Collect crossing faces. crossfaces = cavetetlist; // Re-use array 'cavetetlist'. // Each crossing face contains at least one bottom vertex and // one top vertex. for (i = 0; i < crosstets->objects; i++) { parytet = (triface*)fastlookup(crosstets, i); fliptet = *parytet; for (fliptet.ver = 0; fliptet.ver < 4; fliptet.ver++) { fsym(fliptet, neightet); if (infected(neightet)) { // It is an interior face. if (!marktested(neightet)) { // It is an unprocessed face. crossfaces->newindex((void**)&parytet); *parytet = fliptet; } } } marktest(fliptet); } if (b->verbose > 1) { printf(" Found %ld crossing faces.\n", crossfaces->objects); } for (i = 0; i < crosstets->objects; i++) { parytet = (triface*)fastlookup(crosstets, i); unmarktest(*parytet); uninfect(*parytet); } // Initialize the priority queue. pqueue = NULL; for (i = 0; i < crossfaces->objects; i++) { parytet = (triface*)fastlookup(crossfaces, i); flipcertify(parytet, &pqueue, plane_pa, plane_pb, plane_pc); } crossfaces->restart(); // The list for temporarily storing unflipable faces. bfacearray = new arraypool(sizeof(triface), 4); fcount = 0; // Count the number of flips. // Flip insert the facet. while (pqueue != NULL) { // Pop a face from the priority queue. popbf = pqueue; bface = *popbf; // Update the queue. pqueue = pqueue->nextitem; // Delete the popped item from the pool. flippool->dealloc((void*)popbf); if (!isdeadtet(bface.tt)) { if ((org(bface.tt) == bface.forg) && (dest(bface.tt) == bface.fdest) && (apex(bface.tt) == bface.fapex) && (oppo(bface.tt) == bface.foppo)) { // It is still a crossing face of R. fliptet = bface.tt; fsym(fliptet, neightet); if (oppo(neightet) == bface.noppo) { pd = oppo(fliptet); pe = oppo(neightet); if (b->verbose > 2) { printf(" Get face (%d, %d, %d) - %d, %d, tau = %.17g\n", pointmark(bface.forg), pointmark(bface.fdest), pointmark(bface.fapex), pointmark(bface.foppo), pointmark(bface.noppo), bface.key); } flipflag = 0; // Check for which type of flip can we do. convcount = 3; copcount = 0; for (i = 0; i < 3; i++) { p1 = org(fliptet); p2 = dest(fliptet); ori[i] = orient3d(p1, p2, pd, pe); if (ori[i] < 0) { convcount--; // break; } else if (ori[i] == 0) { convcount--; // Possible 4-to-4 flip. copcount++; // break; } enextself(fliptet); } if (convcount == 3) { // A 2-to-3 flip is found. fliptets[0] = fliptet; // abcd, d may be the new vertex. fliptets[1] = neightet; // bace. flip23(fliptets, 1, &fc); // Put the link faces into check list. for (i = 0; i < 3; i++) { eprevesym(fliptets[i], newface); crossfaces->newindex((void**)&parytet); *parytet = newface; } for (i = 0; i < 3; i++) { enextesym(fliptets[i], newface); crossfaces->newindex((void**)&parytet); *parytet = newface; } flipflag = 1; } else if (convcount == 2) { // if (copcount <= 1) { // A 3-to-2 or 4-to-4 may be possible. // Get the edge which is locally non-convex or flat. for (i = 0; i < 3; i++) { if (ori[i] <= 0) break; enextself(fliptet); } // Collect tets sharing at this edge. esym(fliptet, fliptets[0]); // [b,a,d,c] n = 0; do { p1 = apex(fliptets[n]); if (!(pmarktested(p1) || pmarktest2ed(p1) || pmarktest3ed(p1))) { // This apex is not on the cavity. Hence the face does not // lie inside the cavity. Do not flip this edge. n = 1000; break; } fnext(fliptets[n], fliptets[n + 1]); n++; } while ((fliptets[n].tet != fliptet.tet) && (n < 5)); if (n == 3) { // Found a 3-to-2 flip. flip32(fliptets, 1, &fc); // Put the link faces into check list. for (i = 0; i < 3; i++) { esym(fliptets[0], newface); crossfaces->newindex((void**)&parytet); *parytet = newface; enextself(fliptets[0]); } for (i = 0; i < 3; i++) { esym(fliptets[1], newface); crossfaces->newindex((void**)&parytet); *parytet = newface; enextself(fliptets[1]); } flipflag = 1; } else if (n == 4) { if (copcount == 1) { // Found a 4-to-4 flip. // Let the six vertices are: a,b,c,d,e,f, where // fliptets[0] = [b,a,d,c] // [1] = [b,a,c,e] // [2] = [b,a,e,f] // [3] = [b,a,f,d] // After the 4-to-4 flip, edge [a,b] is flipped, edge [e,d] // is created. // First do a 2-to-3 flip. // Comment: This flip temporarily creates a degenerated // tet (whose volume is zero). It will be removed by the // followed 3-to-2 flip. fliptets[0] = fliptet; // = [a,b,c,d], d is the new vertex. // fliptets[1]; // = [b,a,c,e]. baktets[0] = fliptets[2]; // = [b,a,e,f] baktets[1] = fliptets[3]; // = [b,a,f,d] // The flip may involve hull tets. flip23(fliptets, 1, &fc); // Put the "outer" link faces into check list. // fliptets[0] = [e,d,a,b] => will be flipped, so // [a,b,d] and [a,b,e] are not "outer" link faces. for (i = 1; i < 3; i++) { eprevesym(fliptets[i], newface); crossfaces->newindex((void**)&parytet); *parytet = newface; } for (i = 1; i < 3; i++) { enextesym(fliptets[i], newface); crossfaces->newindex((void**)&parytet); *parytet = newface; } // Then do a 3-to-2 flip. enextesymself(fliptets[0]); // fliptets[0] is [e,d,a,b]. eprevself(fliptets[0]); // = [b,a,d,c], d is the new vertex. fliptets[1] = baktets[0]; // = [b,a,e,f] fliptets[2] = baktets[1]; // = [b,a,f,d] flip32(fliptets, 1, &fc); // Put the "outer" link faces into check list. // fliptets[0] = [d,e,f,a] // fliptets[1] = [e,d,f,b] // Faces [a,b,d] and [a,b,e] are not "outer" link faces. enextself(fliptets[0]); for (i = 1; i < 3; i++) { esym(fliptets[0], newface); crossfaces->newindex((void**)&parytet); *parytet = newface; enextself(fliptets[0]); } enextself(fliptets[1]); for (i = 1; i < 3; i++) { esym(fliptets[1], newface); crossfaces->newindex((void**)&parytet); *parytet = newface; enextself(fliptets[1]); } flip23count--; flip32count--; flip44count++; flipflag = 1; } } } else { // There are more than 1 non-convex or coplanar cases. flipflag = -1; // Ignore this face. if (b->verbose > 2) { printf(" Ignore face (%d, %d, %d) - %d, %d, tau = %.17g\n", pointmark(bface.forg), pointmark(bface.fdest), pointmark(bface.fapex), pointmark(bface.foppo), pointmark(bface.noppo), bface.key); } } // if (convcount == 1) if (flipflag == 1) { // Update the priority queue. for (i = 0; i < crossfaces->objects; i++) { parytet = (triface*)fastlookup(crossfaces, i); flipcertify(parytet, &pqueue, plane_pa, plane_pb, plane_pc); } crossfaces->restart(); if (1) { // if (!b->flipinsert_random) { // Insert all queued unflipped faces. for (i = 0; i < bfacearray->objects; i++) { parytet = (triface*)fastlookup(bfacearray, i); // This face may be changed. if (!isdeadtet(*parytet)) { flipcertify(parytet, &pqueue, plane_pa, plane_pb, plane_pc); } } bfacearray->restart(); } fcount++; } else if (flipflag == 0) { // Queue an unflippable face. To process it later. bfacearray->newindex((void**)&parytet); *parytet = fliptet; } } // if (pe == bface.noppo) } // if ((pa == bface.forg) && ...) } // if (bface.tt != NULL) } // while (pqueue != NULL) if (bfacearray->objects > 0) { if (fcount == 0) { printf("!! No flip is found in %ld faces.\n", bfacearray->objects); terminatetetgen(this, 2); // assert(0); } } delete bfacearray; // Un-mark top and bottom points. for (i = 0; i < toppoints->objects; i++) { parypt = (point*)fastlookup(toppoints, i); punmarktest2(*parypt); } for (i = 0; i < botpoints->objects; i++) { parypt = (point*)fastlookup(botpoints, i); punmarktest3(*parypt); } f23count = flip23count - f23count; f32count = flip32count - f32count; f44count = flip44count - f44count; totalfcount = f23count + f32count + f44count; if (b->verbose > 2) { printf(" Total %ld flips. f23(%ld), f32(%ld), f44(%ld).\n", totalfcount, f23count, f32count, f44count); } } /////////////////////////////////////////////////////////////////////////////// // // // insertpoint_cdt() Insert a new point into a CDT. // // // /////////////////////////////////////////////////////////////////////////////// int tetgenmesh::insertpoint_cdt(point newpt, triface* searchtet, face* splitsh, face* splitseg, insertvertexflags* ivf, arraypool* cavpoints, arraypool* cavfaces, arraypool* cavshells, arraypool* newtets, arraypool* crosstets, arraypool* misfaces) { triface neightet, *parytet; face checksh, *parysh, *parysh1; face *paryseg, *paryseg1; point* parypt; int t1ver; int i; if (b->verbose > 2) { printf(" Insert point %d into CDT\n", pointmark(newpt)); } if (!insertpoint(newpt, searchtet, NULL, NULL, ivf)) { // Point is not inserted. Check ivf->iloc for reason. return 0; } for (i = 0; i < cavetetvertlist->objects; i++) { cavpoints->newindex((void**)&parypt); *parypt = *(point*)fastlookup(cavetetvertlist, i); } // Add the new point into the point list. cavpoints->newindex((void**)&parypt); *parypt = newpt; for (i = 0; i < cavebdrylist->objects; i++) { cavfaces->newindex((void**)&parytet); *parytet = *(triface*)fastlookup(cavebdrylist, i); } for (i = 0; i < caveoldtetlist->objects; i++) { crosstets->newindex((void**)&parytet); *parytet = *(triface*)fastlookup(caveoldtetlist, i); } cavetetvertlist->restart(); cavebdrylist->restart(); caveoldtetlist->restart(); // Insert the point using the cavity algorithm. delaunizecavity(cavpoints, cavfaces, cavshells, newtets, crosstets, misfaces); fillcavity(cavshells, NULL, NULL, NULL, NULL, NULL, NULL); carvecavity(crosstets, newtets, NULL); if ((splitsh != NULL) || (splitseg != NULL)) { // Insert the point into the surface mesh. sinsertvertex(newpt, splitsh, splitseg, ivf->sloc, ivf->sbowywat, 0); // Put all new subfaces into stack. for (i = 0; i < caveshbdlist->objects; i++) { // Get an old subface at edge [a, b]. parysh = (face*)fastlookup(caveshbdlist, i); spivot(*parysh, checksh); // The new subface [a, b, p]. // Do not recover a deleted new face (degenerated). if (checksh.sh[3] != NULL) { subfacstack->newindex((void**)&parysh); *parysh = checksh; } } if (splitseg != NULL) { // Queue two new subsegments in C(p) for recovery. for (i = 0; i < cavesegshlist->objects; i++) { paryseg = (face*)fastlookup(cavesegshlist, i); subsegstack->newindex((void**)&paryseg1); *paryseg1 = *paryseg; } } // if (splitseg != NULL) // Delete the old subfaces in sC(p). for (i = 0; i < caveshlist->objects; i++) { parysh = (face*)fastlookup(caveshlist, i); if (checksubfaceflag) { // It is possible that this subface still connects to adjacent // tets which are not in C(p). If so, clear connections in the // adjacent tets at this subface. stpivot(*parysh, neightet); if (neightet.tet != NULL) { if (neightet.tet[4] != NULL) { // Found an adjacent tet. It must be not in C(p). tsdissolve(neightet); fsymself(neightet); tsdissolve(neightet); } } } shellfacedealloc(subfaces, parysh->sh); } if (splitseg != NULL) { // Delete the old segment in sC(p). shellfacedealloc(subsegs, splitseg->sh); } // Clear working lists. caveshlist->restart(); caveshbdlist->restart(); cavesegshlist->restart(); } // if ((splitsh != NULL) || (splitseg != NULL)) // Put all interior subfaces into stack for recovery. // They were collected in carvecavity(). // Note: Some collected subfaces may be deleted by sinsertvertex(). for (i = 0; i < caveencshlist->objects; i++) { parysh = (face*)fastlookup(caveencshlist, i); if (parysh->sh[3] != NULL) { subfacstack->newindex((void**)&parysh1); *parysh1 = *parysh; } } // Put all interior segments into stack for recovery. // They were collected in carvecavity(). // Note: Some collected segments may be deleted by sinsertvertex(). for (i = 0; i < caveencseglist->objects; i++) { paryseg = (face*)fastlookup(caveencseglist, i); if (paryseg->sh[3] != NULL) { subsegstack->newindex((void**)&paryseg1); *paryseg1 = *paryseg; } } caveencshlist->restart(); caveencseglist->restart(); return 1; } /////////////////////////////////////////////////////////////////////////////// // // // refineregion() Refine a missing region by inserting points. // // // // 'splitsh' represents an edge of the facet to be split. It must be not a // // segment. // // // Assumption: The current mesh is a CDT and is convex. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::refineregion(face& splitsh, arraypool* cavpoints, arraypool* cavfaces, arraypool* cavshells, arraypool* newtets, arraypool* crosstets, arraypool* misfaces) { triface searchtet, spintet; face splitseg, *paryseg; point steinpt, pa, pb, refpt; insertvertexflags ivf; enum interresult dir; long baknum = points->items; int t1ver; int i; // Do not split a segment. for (i = 0; i < 3; i++) { sspivot(splitsh, splitseg); if (splitseg.sh == NULL) break; senextself(splitsh); } if (b->verbose > 2) { printf(" Refining region at edge (%d, %d, %d).\n", pointmark(sorg(splitsh)), pointmark(sdest(splitsh)), pointmark(sapex(splitsh))); } // Add the Steiner point at the barycenter of the face. pa = sorg(splitsh); pb = sdest(splitsh); // Create a new point. makepoint(&steinpt, FREEFACETVERTEX); for (i = 0; i < 3; i++) { steinpt[i] = 0.5 * (pa[i] + pb[i]); } ivf.bowywat = 1; // Use the Bowyer-Watson algorrithm. ivf.cdtflag = 1; // Only create the initial cavity. ivf.sloc = (int)ONEDGE; ivf.sbowywat = 1; ivf.assignmeshsize = b->metric; ivf.smlenflag = useinsertradius; // Return the closet mesh vertex. point2tetorg(pa, searchtet); // Start location from it. ivf.iloc = (int)OUTSIDE; ivf.rejflag = 1; // Reject it if it encroaches upon any segment. if (!insertpoint_cdt(steinpt, &searchtet, &splitsh, NULL, &ivf, cavpoints, cavfaces, cavshells, newtets, crosstets, misfaces)) { if (ivf.iloc == (int)ENCSEGMENT) { pointdealloc(steinpt); // Split an encroached segment. i = randomnation(encseglist->objects); paryseg = (face*)fastlookup(encseglist, i); splitseg = *paryseg; encseglist->restart(); // Split the segment. pa = sorg(splitseg); pb = sdest(splitseg); // Create a new point. makepoint(&steinpt, FREESEGVERTEX); for (i = 0; i < 3; i++) { steinpt[i] = 0.5 * (pa[i] + pb[i]); } point2tetorg(pa, searchtet); ivf.iloc = (int)OUTSIDE; ivf.rejflag = 0; if (!insertpoint_cdt(steinpt, &searchtet, &splitsh, &splitseg, &ivf, cavpoints, cavfaces, cavshells, newtets, crosstets, misfaces)) { terminatetetgen(this, 2); } if (useinsertradius) { save_segmentpoint_insradius(steinpt, ivf.parentpt, ivf.smlen); } st_segref_count++; if (steinerleft > 0) steinerleft--; } else { terminatetetgen(this, 2); // assert(0); } } else { if (useinsertradius) { save_facetpoint_insradius(steinpt, ivf.parentpt, ivf.smlen); } st_facref_count++; if (steinerleft > 0) steinerleft--; } while (subsegstack->objects > 0l) { // seglist is used as a stack. subsegstack->objects--; paryseg = (face*)fastlookup(subsegstack, subsegstack->objects); splitseg = *paryseg; // Check if this segment has been recovered. sstpivot1(splitseg, searchtet); if (searchtet.tet != NULL) continue; // Search the segment. dir = scoutsegment(sorg(splitseg), sdest(splitseg), &splitseg, &searchtet, &refpt, NULL); if (dir == SHAREEDGE) { // Found this segment, insert it. // Let the segment remember an adjacent tet. sstbond1(splitseg, searchtet); // Bond the segment to all tets containing it. spintet = searchtet; do { tssbond1(spintet, splitseg); fnextself(spintet); } while (spintet.tet != searchtet.tet); } else { if ((dir == ACROSSFACE) || (dir == ACROSSEDGE)) { // Split the segment. makepoint(&steinpt, FREESEGVERTEX); getsteinerptonsegment(&splitseg, refpt, steinpt); ivf.iloc = (int)OUTSIDE; ivf.rejflag = 0; if (!insertpoint_cdt(steinpt, &searchtet, &splitsh, &splitseg, &ivf, cavpoints, cavfaces, cavshells, newtets, crosstets, misfaces)) { terminatetetgen(this, 2); } if (useinsertradius) { save_segmentpoint_insradius(steinpt, ivf.parentpt, ivf.smlen); } st_segref_count++; if (steinerleft > 0) steinerleft--; } else { terminatetetgen(this, 2); } } } // while if (b->verbose > 2) { printf(" Added %ld Steiner points.\n", points->items - baknum); } } /////////////////////////////////////////////////////////////////////////////// // // // constrainedfacets() Recover constrained facets in a CDT. // // // // All unrecovered subfaces are queued in 'subfacestack'. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::constrainedfacets() { arraypool *tg_crosstets, *tg_topnewtets, *tg_botnewtets; arraypool *tg_topfaces, *tg_botfaces, *tg_midfaces; arraypool *tg_topshells, *tg_botshells, *tg_facfaces; arraypool *tg_toppoints, *tg_botpoints; arraypool *tg_missingshs, *tg_missingshbds, *tg_missingshverts; triface searchtet, neightet, crossedge; face searchsh, *parysh, *parysh1; face* paryseg; point* parypt; enum interresult dir; int facetcount; int success; int t1ver; int i, j; // Initialize arrays. tg_crosstets = new arraypool(sizeof(triface), 10); tg_topnewtets = new arraypool(sizeof(triface), 10); tg_botnewtets = new arraypool(sizeof(triface), 10); tg_topfaces = new arraypool(sizeof(triface), 10); tg_botfaces = new arraypool(sizeof(triface), 10); tg_midfaces = new arraypool(sizeof(triface), 10); tg_toppoints = new arraypool(sizeof(point), 8); tg_botpoints = new arraypool(sizeof(point), 8); tg_facfaces = new arraypool(sizeof(face), 10); tg_topshells = new arraypool(sizeof(face), 10); tg_botshells = new arraypool(sizeof(face), 10); tg_missingshs = new arraypool(sizeof(face), 10); tg_missingshbds = new arraypool(sizeof(face), 10); tg_missingshverts = new arraypool(sizeof(point), 8); // This is a global array used by refineregion(). encseglist = new arraypool(sizeof(face), 4); facetcount = 0; while (subfacstack->objects > 0l) { subfacstack->objects--; parysh = (face*)fastlookup(subfacstack, subfacstack->objects); searchsh = *parysh; if (searchsh.sh[3] == NULL) continue; // It is dead. if (isshtet(searchsh)) continue; // It is recovered. // Collect all unrecovered subfaces which are co-facet. smarktest(searchsh); tg_facfaces->newindex((void**)&parysh); *parysh = searchsh; for (i = 0; i < tg_facfaces->objects; i++) { parysh = (face*)fastlookup(tg_facfaces, i); for (j = 0; j < 3; j++) { if (!isshsubseg(*parysh)) { spivot(*parysh, searchsh); if (!smarktested(searchsh)) { if (!isshtet(searchsh)) { smarktest(searchsh); tg_facfaces->newindex((void**)&parysh1); *parysh1 = searchsh; } } } senextself(*parysh); } // j } // i // Have found all facet subfaces. Unmark them. for (i = 0; i < tg_facfaces->objects; i++) { parysh = (face*)fastlookup(tg_facfaces, i); sunmarktest(*parysh); } if (b->verbose > 1) { printf(" Recovering facet #%d: %ld subfaces.\n", facetcount + 1, tg_facfaces->objects); } facetcount++; while (tg_facfaces->objects > 0l) { tg_facfaces->objects--; parysh = (face*)fastlookup(tg_facfaces, tg_facfaces->objects); searchsh = *parysh; if (searchsh.sh[3] == NULL) continue; // It is dead. if (isshtet(searchsh)) continue; // It is recovered. searchtet.tet = NULL; if (scoutsubface(&searchsh, &searchtet, 1)) continue; // The subface is missing. Form the missing region. // Re-use 'tg_crosstets' for 'adjtets'. formregion(&searchsh, tg_missingshs, tg_missingshbds, tg_missingshverts); int searchflag = scoutcrossedge(searchtet, tg_missingshbds, tg_missingshs); if (searchflag > 0) { // Save this crossing edge, will be used by fillcavity(). crossedge = searchtet; // Form a cavity of crossing tets. success = formcavity(&searchtet, tg_missingshs, tg_crosstets, tg_topfaces, tg_botfaces, tg_toppoints, tg_botpoints); if (success) { if (!b->flipinsert) { // Tetrahedralize the top part. Re-use 'tg_midfaces'. delaunizecavity(tg_toppoints, tg_topfaces, tg_topshells, tg_topnewtets, tg_crosstets, tg_midfaces); // Tetrahedralize the bottom part. Re-use 'tg_midfaces'. delaunizecavity(tg_botpoints, tg_botfaces, tg_botshells, tg_botnewtets, tg_crosstets, tg_midfaces); // Fill the cavity with new tets. success = fillcavity(tg_topshells, tg_botshells, tg_midfaces, tg_missingshs, tg_topnewtets, tg_botnewtets, &crossedge); if (success) { // Cavity is remeshed. Delete old tets and outer new tets. carvecavity(tg_crosstets, tg_topnewtets, tg_botnewtets); } else { restorecavity(tg_crosstets, tg_topnewtets, tg_botnewtets, tg_missingshbds); } } else { // Use the flip algorithm of Shewchuk to recover the subfaces. flipinsertfacet(tg_crosstets, tg_toppoints, tg_botpoints, tg_missingshverts); // Put all subfaces in R back to tg_facfaces. for (i = 0; i < tg_missingshs->objects; i++) { parysh = (face*)fastlookup(tg_missingshs, i); tg_facfaces->newindex((void**)&parysh1); *parysh1 = *parysh; } success = 1; // Clear working lists. tg_crosstets->restart(); tg_topfaces->restart(); tg_botfaces->restart(); tg_toppoints->restart(); tg_botpoints->restart(); } // b->flipinsert if (success) { // Recover interior subfaces. for (i = 0; i < caveencshlist->objects; i++) { parysh = (face*)fastlookup(caveencshlist, i); if (!scoutsubface(parysh, &searchtet, 1)) { // Add this face at the end of the list, so it will be // processed immediately. tg_facfaces->newindex((void**)&parysh1); *parysh1 = *parysh; } } caveencshlist->restart(); // Recover interior segments. This should always be recovered. for (i = 0; i < caveencseglist->objects; i++) { paryseg = (face*)fastlookup(caveencseglist, i); dir = scoutsegment(sorg(*paryseg), sdest(*paryseg), paryseg, &searchtet, NULL, NULL); if (dir != SHAREEDGE) { terminatetetgen(this, 2); } // Insert this segment. // Let the segment remember an adjacent tet. sstbond1(*paryseg, searchtet); // Bond the segment to all tets containing it. neightet = searchtet; do { tssbond1(neightet, *paryseg); fnextself(neightet); } while (neightet.tet != searchtet.tet); } caveencseglist->restart(); } // success - remesh cavity } // success - form cavity else { terminatetetgen(this, 2); // Report a bug. } // Not success - form cavity } else { // Put all subfaces in R back to tg_facfaces. for (i = 0; i < tg_missingshs->objects; i++) { parysh = (face*)fastlookup(tg_missingshs, i); tg_facfaces->newindex((void**)&parysh1); *parysh1 = *parysh; } if (searchflag != -1) { // Some edge(s) in the missing regions were flipped. success = 1; } else { restorecavity(tg_crosstets, tg_topnewtets, tg_botnewtets, tg_missingshbds); // Only remove fake segments. // Choose an edge to split (set in recentsh) recentsh = searchsh; success = 0; // Do refineregion(); } } // if (scoutcrossedge) // Unmarktest all points of the missing region. for (i = 0; i < tg_missingshverts->objects; i++) { parypt = (point*)fastlookup(tg_missingshverts, i); punmarktest(*parypt); } tg_missingshverts->restart(); tg_missingshbds->restart(); tg_missingshs->restart(); if (!success) { // The missing region can not be recovered. Refine it. refineregion(recentsh, tg_toppoints, tg_topfaces, tg_topshells, tg_topnewtets, tg_crosstets, tg_midfaces); } } // while (tg_facfaces->objects) } // while ((subfacstack->objects) // Accumulate the dynamic memory. totalworkmemory += (tg_crosstets->totalmemory + tg_topnewtets->totalmemory + tg_botnewtets->totalmemory + tg_topfaces->totalmemory + tg_botfaces->totalmemory + tg_midfaces->totalmemory + tg_toppoints->totalmemory + tg_botpoints->totalmemory + tg_facfaces->totalmemory + tg_topshells->totalmemory + tg_botshells->totalmemory + tg_missingshs->totalmemory + tg_missingshbds->totalmemory + tg_missingshverts->totalmemory + encseglist->totalmemory); // Delete arrays. delete tg_crosstets; delete tg_topnewtets; delete tg_botnewtets; delete tg_topfaces; delete tg_botfaces; delete tg_midfaces; delete tg_toppoints; delete tg_botpoints; delete tg_facfaces; delete tg_topshells; delete tg_botshells; delete tg_missingshs; delete tg_missingshbds; delete tg_missingshverts; delete encseglist; encseglist = NULL; } /////////////////////////////////////////////////////////////////////////////// // // // constraineddelaunay() Create a constrained Delaunay tetrahedralization.// // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::constraineddelaunay(clock_t& tv) { face searchsh, *parysh; face searchseg, *paryseg; int s, i; // Statistics. long bakfillregioncount; long bakcavitycount, bakcavityexpcount; long bakseg_ref_count; if (!b->quiet) { printf("Constrained Delaunay...\n"); } makesegmentendpointsmap(); makefacetverticesmap(); if (b->verbose) { printf(" Delaunizing segments.\n"); } checksubsegflag = 1; // Put all segments into the list (in random order). subsegs->traversalinit(); for (i = 0; i < subsegs->items; i++) { s = randomnation(i + 1); // Move the s-th seg to the i-th. subsegstack->newindex((void**)&paryseg); *paryseg = *(face*)fastlookup(subsegstack, s); // Put i-th seg to be the s-th. searchseg.sh = shellfacetraverse(subsegs); // sinfect(searchseg); // Only save it once. paryseg = (face*)fastlookup(subsegstack, s); *paryseg = searchseg; } // Recover non-Delaunay segments. delaunizesegments(); if (b->verbose) { printf(" Inserted %ld Steiner points.\n", st_segref_count); } tv = clock(); if (b->verbose) { printf(" Constraining facets.\n"); } // Subfaces will be introduced. checksubfaceflag = 1; bakfillregioncount = fillregioncount; bakcavitycount = cavitycount; bakcavityexpcount = cavityexpcount; bakseg_ref_count = st_segref_count; // Randomly order the subfaces. subfaces->traversalinit(); for (i = 0; i < subfaces->items; i++) { s = randomnation(i + 1); // Move the s-th subface to the i-th. subfacstack->newindex((void**)&parysh); *parysh = *(face*)fastlookup(subfacstack, s); // Put i-th subface to be the s-th. searchsh.sh = shellfacetraverse(subfaces); parysh = (face*)fastlookup(subfacstack, s); *parysh = searchsh; } // Recover facets. constrainedfacets(); if (b->verbose) { if (fillregioncount > bakfillregioncount) { printf(" Remeshed %ld regions.\n", fillregioncount - bakfillregioncount); } if (cavitycount > bakcavitycount) { printf(" Remeshed %ld cavities", cavitycount - bakcavitycount); if (cavityexpcount - bakcavityexpcount) { printf(" (%ld enlarged)", cavityexpcount - bakcavityexpcount); } printf(".\n"); } if (st_segref_count + st_facref_count - bakseg_ref_count > 0) { printf(" Inserted %ld (%ld, %ld) refine points.\n", st_segref_count + st_facref_count - bakseg_ref_count, st_segref_count - bakseg_ref_count, st_facref_count); } } } //// //// //// //// //// constrained_cxx ////////////////////////////////////////////////////////// //// steiner_cxx ////////////////////////////////////////////////////////////// //// //// //// //// /////////////////////////////////////////////////////////////////////////////// // // // checkflipeligibility() A call back function for boundary recovery. // // // // 'fliptype' indicates which elementary flip will be performed: 1 : 2-to-3, // // and 2 : 3-to-2, respectively. // // // // 'pa, ..., pe' are the vertices involved in this flip, where [a,b,c] is // // the flip face, and [d,e] is the flip edge. NOTE: 'pc' may be 'dummypoint',// // other points must not be 'dummypoint'. // // // /////////////////////////////////////////////////////////////////////////////// int tetgenmesh::checkflipeligibility(int fliptype, point pa, point pb, point pc, point pd, point pe, int level, int edgepivot, flipconstraints* fc) { point tmppts[3]; enum interresult dir; int types[2], poss[4]; int intflag; int rejflag = 0; int i; if (fc->seg[0] != NULL) { // A constraining edge is given (e.g., for edge recovery). if (fliptype == 1) { // A 2-to-3 flip: [a,b,c] => [e,d,a], [e,d,b], [e,d,c]. tmppts[0] = pa; tmppts[1] = pb; tmppts[2] = pc; for (i = 0; i < 3 && !rejflag; i++) { if (tmppts[i] != dummypoint) { // Test if the face [e,d,#] intersects the edge. intflag = tri_edge_test(pe, pd, tmppts[i], fc->seg[0], fc->seg[1], NULL, 1, types, poss); if (intflag == 2) { // They intersect at a single point. dir = (enum interresult)types[0]; if (dir == ACROSSFACE) { // The interior of [e,d,#] intersect the segment. rejflag = 1; } else if (dir == ACROSSEDGE) { if (poss[0] == 0) { // The interior of [e,d] intersect the segment. // Since [e,d] is the newly created edge. Reject this flip. rejflag = 1; } } } else if (intflag == 4) { // They may intersect at either a point or a line segment. dir = (enum interresult)types[0]; if (dir == ACROSSEDGE) { if (poss[0] == 0) { // The interior of [e,d] intersect the segment. // Since [e,d] is the newly created edge. Reject this flip. rejflag = 1; } } } } // if (tmppts[0] != dummypoint) } // i } else if (fliptype == 2) { // A 3-to-2 flip: [e,d,a], [e,d,b], [e,d,c] => [a,b,c] if (pc != dummypoint) { // Check if the new face [a,b,c] intersect the edge in its interior. intflag = tri_edge_test(pa, pb, pc, fc->seg[0], fc->seg[1], NULL, 1, types, poss); if (intflag == 2) { // They intersect at a single point. dir = (enum interresult)types[0]; if (dir == ACROSSFACE) { // The interior of [a,b,c] intersect the segment. rejflag = 1; // Do not flip. } } else if (intflag == 4) { // [a,b,c] is coplanar with the edge. dir = (enum interresult)types[0]; if (dir == ACROSSEDGE) { // The boundary of [a,b,c] intersect the segment. rejflag = 1; // Do not flip. } } } // if (pc != dummypoint) } } // if (fc->seg[0] != NULL) if ((fc->fac[0] != NULL) && !rejflag) { // A constraining face is given (e.g., for face recovery). if (fliptype == 1) { // A 2-to-3 flip. // Test if the new edge [e,d] intersects the face. intflag = tri_edge_test(fc->fac[0], fc->fac[1], fc->fac[2], pe, pd, NULL, 1, types, poss); if (intflag == 2) { // They intersect at a single point. dir = (enum interresult)types[0]; if (dir == ACROSSFACE) { rejflag = 1; } else if (dir == ACROSSEDGE) { rejflag = 1; } } else if (intflag == 4) { // The edge [e,d] is coplanar with the face. // There may be two intersections. for (i = 0; i < 2 && !rejflag; i++) { dir = (enum interresult)types[i]; if (dir == ACROSSFACE) { rejflag = 1; } else if (dir == ACROSSEDGE) { rejflag = 1; } } } } // if (fliptype == 1) } // if (fc->fac[0] != NULL) if ((fc->remvert != NULL) && !rejflag) { // The vertex is going to be removed. Do not create a new edge which // contains this vertex. if (fliptype == 1) { // A 2-to-3 flip. if ((pd == fc->remvert) || (pe == fc->remvert)) { rejflag = 1; } } } if (fc->remove_large_angle && !rejflag) { // Remove a large dihedral angle. Do not create a new small angle. REAL cosmaxd = 0, diff; if (fliptype == 1) { // We assume that neither 'a' nor 'b' is dummypoint. // A 2-to-3 flip: [a,b,c] => [e,d,a], [e,d,b], [e,d,c]. // The new tet [e,d,a,b] will be flipped later. Only two new tets: // [e,d,b,c] and [e,d,c,a] need to be checked. if ((pc != dummypoint) && (pe != dummypoint) && (pd != dummypoint)) { // Get the largest dihedral angle of [e,d,b,c]. tetalldihedral(pe, pd, pb, pc, NULL, &cosmaxd, NULL); diff = cosmaxd - fc->cosdihed_in; if (fabs(diff / fc->cosdihed_in) < b->epsilon) diff = 0.0; // Rounding. if (diff <= 0) { // if (cosmaxd <= fc->cosdihed_in) { rejflag = 1; } else { // Record the largest new angle. if (cosmaxd < fc->cosdihed_out) { fc->cosdihed_out = cosmaxd; } // Get the largest dihedral angle of [e,d,c,a]. tetalldihedral(pe, pd, pc, pa, NULL, &cosmaxd, NULL); diff = cosmaxd - fc->cosdihed_in; if (fabs(diff / fc->cosdihed_in) < b->epsilon) diff = 0.0; // Rounding. if (diff <= 0) { // if (cosmaxd <= fc->cosdihed_in) { rejflag = 1; } else { // Record the largest new angle. if (cosmaxd < fc->cosdihed_out) { fc->cosdihed_out = cosmaxd; } } } } // if (pc != dummypoint && ...) } else if (fliptype == 2) { // A 3-to-2 flip: [e,d,a], [e,d,b], [e,d,c] => [a,b,c] // We assume that neither 'e' nor 'd' is dummypoint. if (level == 0) { // Both new tets [a,b,c,d] and [b,a,c,e] are new tets. if ((pa != dummypoint) && (pb != dummypoint) && (pc != dummypoint)) { // Get the largest dihedral angle of [a,b,c,d]. tetalldihedral(pa, pb, pc, pd, NULL, &cosmaxd, NULL); diff = cosmaxd - fc->cosdihed_in; if (fabs(diff / fc->cosdihed_in) < b->epsilon) diff = 0.0; // Rounding if (diff <= 0) { // if (cosmaxd <= fc->cosdihed_in) { rejflag = 1; } else { // Record the largest new angle. if (cosmaxd < fc->cosdihed_out) { fc->cosdihed_out = cosmaxd; } // Get the largest dihedral angle of [b,a,c,e]. tetalldihedral(pb, pa, pc, pe, NULL, &cosmaxd, NULL); diff = cosmaxd - fc->cosdihed_in; if (fabs(diff / fc->cosdihed_in) < b->epsilon) diff = 0.0; // Rounding if (diff <= 0) { // if (cosmaxd <= fc->cosdihed_in) { rejflag = 1; } else { // Record the largest new angle. if (cosmaxd < fc->cosdihed_out) { fc->cosdihed_out = cosmaxd; } } } } } else { // level > 0 if (edgepivot == 1) { // The new tet [a,b,c,d] will be flipped. Only check [b,a,c,e]. if ((pa != dummypoint) && (pb != dummypoint) && (pc != dummypoint)) { // Get the largest dihedral angle of [b,a,c,e]. tetalldihedral(pb, pa, pc, pe, NULL, &cosmaxd, NULL); diff = cosmaxd - fc->cosdihed_in; if (fabs(diff / fc->cosdihed_in) < b->epsilon) diff = 0.0; // Rounding if (diff <= 0) { // if (cosmaxd <= fc->cosdihed_in) { rejflag = 1; } else { // Record the largest new angle. if (cosmaxd < fc->cosdihed_out) { fc->cosdihed_out = cosmaxd; } } } } else { // The new tet [b,a,c,e] will be flipped. Only check [a,b,c,d]. if ((pa != dummypoint) && (pb != dummypoint) && (pc != dummypoint)) { // Get the largest dihedral angle of [b,a,c,e]. tetalldihedral(pa, pb, pc, pd, NULL, &cosmaxd, NULL); diff = cosmaxd - fc->cosdihed_in; if (fabs(diff / fc->cosdihed_in) < b->epsilon) diff = 0.0; // Rounding if (diff <= 0) { // if (cosmaxd <= fc->cosdihed_in) { rejflag = 1; } else { // Record the largest new angle. if (cosmaxd < fc->cosdihed_out) { fc->cosdihed_out = cosmaxd; } } } } // edgepivot } // level } } return rejflag; } /////////////////////////////////////////////////////////////////////////////// // // // removeedgebyflips() Attempt to remove an edge by flips. // // // // 'flipedge' is a non-convex or flat edge [a,b,#,#] to be removed. // // // // The return value is a positive integer, it indicates whether the edge is // // removed or not. A value "2" means the edge is removed, otherwise, the // // edge is not removed and the value (must >= 3) is the current number of // // tets in the edge star. // // // /////////////////////////////////////////////////////////////////////////////// int tetgenmesh::removeedgebyflips(triface* flipedge, flipconstraints* fc) { triface *abtets, spintet; int t1ver; int n, nn, i; if (checksubsegflag) { // Do not flip a segment. if (issubseg(*flipedge)) { if (fc->collectencsegflag) { face checkseg, *paryseg; tsspivot1(*flipedge, checkseg); if (!sinfected(checkseg)) { // Queue this segment in list. sinfect(checkseg); caveencseglist->newindex((void**)&paryseg); *paryseg = checkseg; } } return 0; } } // Count the number of tets at edge [a,b]. n = 0; spintet = *flipedge; while (1) { n++; fnextself(spintet); if (spintet.tet == flipedge->tet) break; } if (n < 3) { // It is only possible when the mesh contains inverted tetrahedra. terminatetetgen(this, 2); // Report a bug } if ((b->flipstarsize > 0) && (n > b->flipstarsize)) { // The star size exceeds the limit. return 0; // Do not flip it. } // Allocate spaces. abtets = new triface[n]; // Collect the tets at edge [a,b]. spintet = *flipedge; i = 0; while (1) { abtets[i] = spintet; setelemcounter(abtets[i], 1); i++; fnextself(spintet); if (spintet.tet == flipedge->tet) break; } // Try to flip the edge (level = 0, edgepivot = 0). nn = flipnm(abtets, n, 0, 0, fc); if (nn > 2) { // Edge is not flipped. Unmarktest the remaining tets in Star(ab). for (i = 0; i < nn; i++) { setelemcounter(abtets[i], 0); } // Restore the input edge (needed by Lawson's flip). *flipedge = abtets[0]; } // Release the temporary allocated spaces. // NOTE: fc->unflip must be 0. int bakunflip = fc->unflip; fc->unflip = 0; flipnm_post(abtets, n, nn, 0, fc); fc->unflip = bakunflip; delete[] abtets; return nn; } /////////////////////////////////////////////////////////////////////////////// // // // removefacebyflips() Remove a face by flips. // // // // Return 1 if the face is removed. Otherwise, return 0. // // // // ASSUMPTIONS: // // - 'flipface' must not be a subface. // // - 'flipface' must not be a hull face. // // // /////////////////////////////////////////////////////////////////////////////// int tetgenmesh::removefacebyflips(triface* flipface, flipconstraints* fc) { triface fliptets[3], flipedge; point pa, pb, pc, pd, pe; REAL ori; int reducflag = 0; fliptets[0] = *flipface; fsym(*flipface, fliptets[1]); pa = org(fliptets[0]); pb = dest(fliptets[0]); pc = apex(fliptets[0]); pd = oppo(fliptets[0]); pe = oppo(fliptets[1]); ori = orient3d(pa, pb, pd, pe); if (ori > 0) { ori = orient3d(pb, pc, pd, pe); if (ori > 0) { ori = orient3d(pc, pa, pd, pe); if (ori > 0) { // Found a 2-to-3 flip. reducflag = 1; } else { eprev(*flipface, flipedge); // [c,a] } } else { enext(*flipface, flipedge); // [b,c] } } else { flipedge = *flipface; // [a,b] } if (reducflag) { // A 2-to-3 flip is found. flip23(fliptets, 0, fc); return 1; } else { // Try to flip the selected edge of this face. if (removeedgebyflips(&flipedge, fc) == 2) { return 1; } } // Face is not removed. return 0; } /////////////////////////////////////////////////////////////////////////////// // // // recoveredge() Recover an edge in current tetrahedralization. // // // // If the edge is recovered, 'searchtet' returns a tet containing the edge. // // // // This edge may intersect a set of faces and edges in the mesh. All these // // faces or edges are needed to be removed. // // // // If the parameter 'fullsearch' is set, it tries to flip any face or edge // // that intersects the recovering edge. Otherwise, only the face or edge // // which is visible by 'startpt' is tried. // // // // The parameter 'sedge' is used to report self-intersection. If it is not // // a NULL, it is EITHER a segment OR a subface that contains this edge. // // // // Note that this routine assumes that the tetrahedralization is convex. // // // /////////////////////////////////////////////////////////////////////////////// int tetgenmesh::recoveredgebyflips(point startpt, point endpt, face* sedge, triface* searchtet, int fullsearch) { flipconstraints fc; enum interresult dir; fc.seg[0] = startpt; fc.seg[1] = endpt; fc.checkflipeligibility = 1; // The mainloop of the edge reocvery. while (1) { // Loop I // Search the edge from 'startpt'. point2tetorg(startpt, *searchtet); dir = finddirection(searchtet, endpt); if (dir == ACROSSVERT) { if (dest(*searchtet) == endpt) { return 1; // Edge is recovered. } else { if (sedge) { return report_selfint_edge(startpt, endpt, sedge, searchtet, dir); } else { return 0; } } } // The edge is missing. // Try to remove the first intersecting face/edge. enextesymself(*searchtet); // Go to the opposite face. if (dir == ACROSSFACE) { if (checksubfaceflag) { if (issubface(*searchtet)) { if (sedge) { return report_selfint_edge(startpt, endpt, sedge, searchtet, dir); } else { return 0; // Cannot flip a subface. } } } // Try to flip a crossing face. if (removefacebyflips(searchtet, &fc)) { continue; } } else if (dir == ACROSSEDGE) { if (checksubsegflag) { if (issubseg(*searchtet)) { if (sedge) { return report_selfint_edge(startpt, endpt, sedge, searchtet, dir); } else { return 0; // Cannot flip a segment. } } } // Try to flip an intersecting edge. if (removeedgebyflips(searchtet, &fc) == 2) { continue; } } // The edge is missing. if (fullsearch) { // Try to flip one of the faces/edges which intersects the edge. triface neightet, spintet; point pa, pb, pc, pd; badface bakface; enum interresult dir1; int types[2], poss[4], pos = 0; int success = 0; int t1ver; int i, j; // Loop through the sequence of intersecting faces/edges from // 'startpt' to 'endpt'. point2tetorg(startpt, *searchtet); dir = finddirection(searchtet, endpt); // Go to the face/edge intersecting the searching edge. enextesymself(*searchtet); // Go to the opposite face. // This face/edge has been tried in previous step. while (1) { // Loop I-I // Find the next intersecting face/edge. fsymself(*searchtet); if (dir == ACROSSFACE) { neightet = *searchtet; j = (neightet.ver & 3); // j is the current face number. for (i = j + 1; i < j + 4; i++) { neightet.ver = (i % 4); pa = org(neightet); pb = dest(neightet); pc = apex(neightet); pd = oppo(neightet); // The above point. if (tri_edge_test(pa, pb, pc, startpt, endpt, pd, 1, types, poss)) { dir = (enum interresult)types[0]; pos = poss[0]; break; } else { dir = DISJOINT; pos = 0; } } // i // There must be an intersection face/edge. if (dir == DISJOINT) { terminatetetgen(this, 2); } } else if (dir == ACROSSEDGE) { while (1) { // Loop I-I-I // Check the two opposite faces (of the edge) in 'searchtet'. for (i = 0; i < 2; i++) { if (i == 0) { enextesym(*searchtet, neightet); } else { eprevesym(*searchtet, neightet); } pa = org(neightet); pb = dest(neightet); pc = apex(neightet); pd = oppo(neightet); // The above point. if (tri_edge_test(pa, pb, pc, startpt, endpt, pd, 1, types, poss)) { dir = (enum interresult)types[0]; pos = poss[0]; break; // for loop } else { dir = DISJOINT; pos = 0; } } // i if (dir != DISJOINT) { // Find an intersection face/edge. break; // Loop I-I-I } // No intersection. Rotate to the next tet at the edge. fnextself(*searchtet); } // while (1) // Loop I-I-I } else { terminatetetgen(this, 2); // Report a bug } // Adjust to the intersecting edge/vertex. for (i = 0; i < pos; i++) { enextself(neightet); } if (dir == SHAREVERT) { // Check if we have reached the 'endpt'. pd = org(neightet); if (pd == endpt) { // Failed to recover the edge. break; // Loop I-I } else { terminatetetgen(this, 2); // Report a bug } } // The next to be flipped face/edge. *searchtet = neightet; // Bakup this face (tetrahedron). bakface.forg = org(*searchtet); bakface.fdest = dest(*searchtet); bakface.fapex = apex(*searchtet); bakface.foppo = oppo(*searchtet); // Try to flip this intersecting face/edge. if (dir == ACROSSFACE) { if (checksubfaceflag) { if (issubface(*searchtet)) { if (sedge) { return report_selfint_edge(startpt, endpt, sedge, searchtet, dir); } else { return 0; // Cannot flip a subface. } } } if (removefacebyflips(searchtet, &fc)) { success = 1; break; // Loop I-I } } else if (dir == ACROSSEDGE) { if (checksubsegflag) { if (issubseg(*searchtet)) { if (sedge) { return report_selfint_edge(startpt, endpt, sedge, searchtet, dir); } else { return 0; // Cannot flip a segment. } } } if (removeedgebyflips(searchtet, &fc) == 2) { success = 1; break; // Loop I-I } } else if (dir == ACROSSVERT) { if (sedge) { // return report_selfint_edge(startpt, endpt, sedge, searchtet, dir); terminatetetgen(this, 2); } else { return 0; } } else { terminatetetgen(this, 2); } // The face/edge is not flipped. if ((searchtet->tet == NULL) || (org(*searchtet) != bakface.forg) || (dest(*searchtet) != bakface.fdest) || (apex(*searchtet) != bakface.fapex) || (oppo(*searchtet) != bakface.foppo)) { // 'searchtet' was flipped. We must restore it. point2tetorg(bakface.forg, *searchtet); dir1 = finddirection(searchtet, bakface.fdest); if (dir1 == ACROSSVERT) { if (dest(*searchtet) == bakface.fdest) { spintet = *searchtet; while (1) { if (apex(spintet) == bakface.fapex) { // Found the face. *searchtet = spintet; break; } fnextself(spintet); if (spintet.tet == searchtet->tet) { searchtet->tet = NULL; break; // Not find. } } // while (1) if (searchtet->tet != NULL) { if (oppo(*searchtet) != bakface.foppo) { fsymself(*searchtet); if (oppo(*searchtet) != bakface.foppo) { // The original (intersecting) tet has been flipped. searchtet->tet = NULL; break; // Not find. } } } } else { searchtet->tet = NULL; // Not find. } } else { searchtet->tet = NULL; // Not find. } if (searchtet->tet == NULL) { success = 0; // This face/edge has been destroyed. break; // Loop I-I } } } // while (1) // Loop I-I if (success) { // One of intersecting faces/edges is flipped. continue; } } // if (fullsearch) // The edge is missing. break; // Loop I } // while (1) // Loop I return 0; } /////////////////////////////////////////////////////////////////////////////// // // // add_steinerpt_in_schoenhardtpoly() Insert a Steiner point in a Schoen- // // hardt polyhedron. // // // // 'abtets' is an array of n tets which all share at the edge [a,b]. Let the // // tets are [a,b,p0,p1], [a,b,p1,p2], ..., [a,b,p_(n-2),p_(n-1)]. Moreover, // // the edge [p0,p_(n-1)] intersects all of the tets in 'abtets'. A special // // case is that the edge [p0,p_(n-1)] is coplanar with the edge [a,b]. // // Such set of tets arises when we want to recover an edge from 'p0' to 'p_ // // (n-1)', and the number of tets at [a,b] can not be reduced by any flip. // // // /////////////////////////////////////////////////////////////////////////////// int tetgenmesh::add_steinerpt_in_schoenhardtpoly(triface* abtets, int n, int chkencflag) { triface worktet, *parytet; triface faketet1, faketet2; point pc, pd, steinerpt; insertvertexflags ivf; optparameters opm; REAL vcd[3], sampt[3], smtpt[3]; REAL maxminvol = 0.0, minvol = 0.0, ori; int success, maxidx = 0; int it, i; pc = apex(abtets[0]); // pc = p0 pd = oppo(abtets[n - 1]); // pd = p_(n-1) // Find an optimial point in edge [c,d]. It is visible by all outer faces // of 'abtets', and it maxmizes the min volume. // initialize the list of 2n boundary faces. for (i = 0; i < n; i++) { edestoppo(abtets[i], worktet); // [p_i,p_i+1,a] cavetetlist->newindex((void**)&parytet); *parytet = worktet; eorgoppo(abtets[i], worktet); // [p_i+1,p_i,b] cavetetlist->newindex((void**)&parytet); *parytet = worktet; } int N = 100; REAL stepi = 0.01; // Search the point along the edge [c,d]. for (i = 0; i < 3; i++) vcd[i] = pd[i] - pc[i]; // Sample N points in edge [c,d]. for (it = 1; it < N; it++) { for (i = 0; i < 3; i++) { sampt[i] = pc[i] + (stepi * (double)it) * vcd[i]; } for (i = 0; i < cavetetlist->objects; i++) { parytet = (triface*)fastlookup(cavetetlist, i); ori = orient3d(dest(*parytet), org(*parytet), apex(*parytet), sampt); if (i == 0) { minvol = ori; } else { if (minvol > ori) minvol = ori; } } // i if (it == 1) { maxminvol = minvol; maxidx = it; } else { if (maxminvol < minvol) { maxminvol = minvol; maxidx = it; } } } // it if (maxminvol <= 0) { cavetetlist->restart(); return 0; } for (i = 0; i < 3; i++) { smtpt[i] = pc[i] + (stepi * (double)maxidx) * vcd[i]; } // Create two faked tets to hold the two non-existing boundary faces: // [d,c,a] and [c,d,b]. maketetrahedron(&faketet1); setvertices(faketet1, pd, pc, org(abtets[0]), dummypoint); cavetetlist->newindex((void**)&parytet); *parytet = faketet1; maketetrahedron(&faketet2); setvertices(faketet2, pc, pd, dest(abtets[0]), dummypoint); cavetetlist->newindex((void**)&parytet); *parytet = faketet2; // Point smooth options. opm.max_min_volume = 1; opm.numofsearchdirs = 20; opm.searchstep = 0.001; opm.maxiter = 100; // Limit the maximum iterations. opm.initval = 0.0; // Initial volume is zero. // Try to relocate the point into the inside of the polyhedron. success = smoothpoint(smtpt, cavetetlist, 1, &opm); if (success) { while (opm.smthiter == 100) { // It was relocated and the prescribed maximum iteration reached. // Try to increase the search stepsize. opm.searchstep *= 10.0; // opm.maxiter = 100; // Limit the maximum iterations. opm.initval = opm.imprval; opm.smthiter = 0; // Init. smoothpoint(smtpt, cavetetlist, 1, &opm); } } // if (success) // Delete the two faked tets. tetrahedrondealloc(faketet1.tet); tetrahedrondealloc(faketet2.tet); cavetetlist->restart(); if (!success) { return 0; } // Insert the Steiner point. makepoint(&steinerpt, FREEVOLVERTEX); for (i = 0; i < 3; i++) steinerpt[i] = smtpt[i]; // Insert the created Steiner point. for (i = 0; i < n; i++) { infect(abtets[i]); caveoldtetlist->newindex((void**)&parytet); *parytet = abtets[i]; } worktet = abtets[0]; // No need point location. ivf.iloc = (int)INSTAR; ivf.chkencflag = chkencflag; ivf.assignmeshsize = b->metric; if (ivf.assignmeshsize) { // Search the tet containing 'steinerpt' for size interpolation. locate(steinerpt, &(abtets[0])); worktet = abtets[0]; } // Insert the new point into the tetrahedralization T. // Note that T is convex (nonconvex = 0). if (insertpoint(steinerpt, &worktet, NULL, NULL, &ivf)) { // The vertex has been inserted. st_volref_count++; if (steinerleft > 0) steinerleft--; return 1; } else { // Not inserted. pointdealloc(steinerpt); return 0; } } /////////////////////////////////////////////////////////////////////////////// // // // add_steinerpt_in_segment() Add a Steiner point inside a segment. // // // /////////////////////////////////////////////////////////////////////////////// int tetgenmesh::add_steinerpt_in_segment(face* misseg, int searchlevel) { triface searchtet; face *paryseg, candseg; point startpt, endpt, pc, pd; flipconstraints fc; enum interresult dir; REAL P[3], Q[3], tp, tq; REAL len, smlen = 0, split = 0, split_q = 0; int success; int i; startpt = sorg(*misseg); endpt = sdest(*misseg); fc.seg[0] = startpt; fc.seg[1] = endpt; fc.checkflipeligibility = 1; fc.collectencsegflag = 1; point2tetorg(startpt, searchtet); dir = finddirection(&searchtet, endpt); // Try to flip the first intersecting face/edge. enextesymself(searchtet); // Go to the opposite face. int bak_fliplinklevel = b->fliplinklevel; b->fliplinklevel = searchlevel; if (dir == ACROSSFACE) { // A face is intersected with the segment. Try to flip it. success = removefacebyflips(&searchtet, &fc); } else if (dir == ACROSSEDGE) { // An edge is intersected with the segment. Try to flip it. success = removeedgebyflips(&searchtet, &fc); } split = 0; for (i = 0; i < caveencseglist->objects; i++) { paryseg = (face*)fastlookup(caveencseglist, i); suninfect(*paryseg); // Calculate the shortest edge between the two lines. pc = sorg(*paryseg); pd = sdest(*paryseg); tp = tq = 0; if (linelineint(startpt, endpt, pc, pd, P, Q, &tp, &tq)) { // Does the shortest edge lie between the two segments? // Round tp and tq. if ((tp > 0) && (tq < 1)) { if (tp < 0.5) { if (tp < (b->epsilon * 1e+3)) tp = 0.0; } else { if ((1.0 - tp) < (b->epsilon * 1e+3)) tp = 1.0; } } if ((tp <= 0) || (tp >= 1)) continue; if ((tq > 0) && (tq < 1)) { if (tq < 0.5) { if (tq < (b->epsilon * 1e+3)) tq = 0.0; } else { if ((1.0 - tq) < (b->epsilon * 1e+3)) tq = 1.0; } } if ((tq <= 0) || (tq >= 1)) continue; // It is a valid shortest edge. Calculate its length. len = distance(P, Q); if (split == 0) { smlen = len; split = tp; split_q = tq; candseg = *paryseg; } else { if (len < smlen) { smlen = len; split = tp; split_q = tq; candseg = *paryseg; } } } } caveencseglist->restart(); b->fliplinklevel = bak_fliplinklevel; if (split == 0) { // Found no crossing segment. return 0; } face splitsh; face splitseg; point steinerpt, *parypt; insertvertexflags ivf; if (b->addsteiner_algo == 1) { // Split the segment at the closest point to a near segment. makepoint(&steinerpt, FREESEGVERTEX); for (i = 0; i < 3; i++) { steinerpt[i] = startpt[i] + split * (endpt[i] - startpt[i]); } } else { // b->addsteiner_algo == 2 for (i = 0; i < 3; i++) { P[i] = startpt[i] + split * (endpt[i] - startpt[i]); } pc = sorg(candseg); pd = sdest(candseg); for (i = 0; i < 3; i++) { Q[i] = pc[i] + split_q * (pd[i] - pc[i]); } makepoint(&steinerpt, FREEVOLVERTEX); for (i = 0; i < 3; i++) { steinerpt[i] = 0.5 * (P[i] + Q[i]); } } // We need to locate the point. Start searching from 'searchtet'. if (split < 0.5) { point2tetorg(startpt, searchtet); } else { point2tetorg(endpt, searchtet); } if (b->addsteiner_algo == 1) { splitseg = *misseg; spivot(*misseg, splitsh); } else { splitsh.sh = NULL; splitseg.sh = NULL; } ivf.iloc = (int)OUTSIDE; ivf.bowywat = 1; ivf.lawson = 0; ivf.rejflag = 0; ivf.chkencflag = 0; ivf.sloc = (int)ONEDGE; ivf.sbowywat = 1; ivf.splitbdflag = 0; ivf.validflag = 1; ivf.respectbdflag = 1; ivf.assignmeshsize = b->metric; if (!insertpoint(steinerpt, &searchtet, &splitsh, &splitseg, &ivf)) { pointdealloc(steinerpt); return 0; } if (b->addsteiner_algo == 1) { // Save this Steiner point (for removal). // Re-use the array 'subvertstack'. subvertstack->newindex((void**)&parypt); *parypt = steinerpt; st_segref_count++; } else { // b->addsteiner_algo == 2 // Queue the segment for recovery. subsegstack->newindex((void**)&paryseg); *paryseg = *misseg; st_volref_count++; } if (steinerleft > 0) steinerleft--; return 1; } /////////////////////////////////////////////////////////////////////////////// // // // addsteiner4recoversegment() Add a Steiner point for recovering a seg. // // // /////////////////////////////////////////////////////////////////////////////// int tetgenmesh::addsteiner4recoversegment(face* misseg, int splitsegflag) { triface *abtets, searchtet, spintet; face splitsh; face* paryseg; point startpt, endpt; point pa, pb, pd, steinerpt, *parypt; enum interresult dir; insertvertexflags ivf; int types[2], poss[4]; int n, endi, success; int t1ver; int i; startpt = sorg(*misseg); if (pointtype(startpt) == FREESEGVERTEX) { sesymself(*misseg); startpt = sorg(*misseg); } endpt = sdest(*misseg); // Try to recover the edge by adding Steiner points. point2tetorg(startpt, searchtet); dir = finddirection(&searchtet, endpt); enextself(searchtet); if (dir == ACROSSFACE) { // The segment is crossing at least 3 faces. Find the common edge of // the first 3 crossing faces. esymself(searchtet); fsym(searchtet, spintet); pd = oppo(spintet); for (i = 0; i < 3; i++) { pa = org(spintet); pb = dest(spintet); if (tri_edge_test(pa, pb, pd, startpt, endpt, NULL, 1, types, poss)) { break; // Found the edge. } enextself(spintet); eprevself(searchtet); } esymself(searchtet); } spintet = searchtet; n = 0; endi = -1; while (1) { // Check if the endpt appears in the star. if (apex(spintet) == endpt) { endi = n; // Remember the position of endpt. } n++; // Count a tet in the star. fnextself(spintet); if (spintet.tet == searchtet.tet) break; } if (endi > 0) { // endpt is also in the edge star // Get all tets in the edge star. abtets = new triface[n]; spintet = searchtet; for (i = 0; i < n; i++) { abtets[i] = spintet; fnextself(spintet); } success = 0; if (dir == ACROSSFACE) { // Find a Steiner points inside the polyhedron. if (add_steinerpt_in_schoenhardtpoly(abtets, endi, 0)) { success = 1; } } else if (dir == ACROSSEDGE) { // PLC check. if (issubseg(searchtet)) { terminatetetgen(this, 2); } if (n > 4) { // In this case, 'abtets' is separated by the plane (containing the // two intersecting edges) into two parts, P1 and P2, where P1 // consists of 'endi' tets: abtets[0], abtets[1], ..., // abtets[endi-1], and P2 consists of 'n - endi' tets: // abtets[endi], abtets[endi+1], abtets[n-1]. if (endi > 2) { // P1 // There are at least 3 tets in the first part. if (add_steinerpt_in_schoenhardtpoly(abtets, endi, 0)) { success++; } } if ((n - endi) > 2) { // P2 // There are at least 3 tets in the first part. if (add_steinerpt_in_schoenhardtpoly(&(abtets[endi]), n - endi, 0)) { success++; } } } else { // In this case, a 4-to-4 flip should be re-cover the edge [c,d]. // However, there will be invalid tets (either zero or negtive // volume). Otherwise, [c,d] should already be recovered by the // recoveredge() function. terminatetetgen(this, 2); } } else { terminatetetgen(this, 2); } delete[] abtets; if (success) { // Add the missing segment back to the recovering list. subsegstack->newindex((void**)&paryseg); *paryseg = *misseg; return 1; } } // if (endi > 0) if (!splitsegflag) { return 0; } if (b->verbose > 2) { printf(" Splitting segment (%d, %d)\n", pointmark(startpt), pointmark(endpt)); } steinerpt = NULL; if (b->addsteiner_algo > 0) { // -Y/1 or -Y/2 if (add_steinerpt_in_segment(misseg, 3)) { return 1; } sesymself(*misseg); if (add_steinerpt_in_segment(misseg, 3)) { return 1; } sesymself(*misseg); } if (steinerpt == NULL) { // Split the segment at its midpoint. makepoint(&steinerpt, FREESEGVERTEX); for (i = 0; i < 3; i++) { steinerpt[i] = 0.5 * (startpt[i] + endpt[i]); } // We need to locate the point. spivot(*misseg, splitsh); ivf.iloc = (int)OUTSIDE; ivf.bowywat = 1; ivf.lawson = 0; ivf.rejflag = 0; ivf.chkencflag = 0; ivf.sloc = (int)ONEDGE; ivf.sbowywat = 1; ivf.splitbdflag = 0; ivf.validflag = 1; ivf.respectbdflag = 1; ivf.assignmeshsize = b->metric; if (!insertpoint(steinerpt, &searchtet, &splitsh, misseg, &ivf)) { terminatetetgen(this, 2); } } // if (endi > 0) // Save this Steiner point (for removal). // Re-use the array 'subvertstack'. subvertstack->newindex((void**)&parypt); *parypt = steinerpt; st_segref_count++; if (steinerleft > 0) steinerleft--; return 1; } /////////////////////////////////////////////////////////////////////////////// // // // recoversegments() Recover all segments. // // // // All segments need to be recovered are in 'subsegstack'. // // // // This routine first tries to recover each segment by only using flips. If // // no flip is possible, and the flag 'steinerflag' is set, it then tries to // // insert Steiner points near or in the segment. // // // /////////////////////////////////////////////////////////////////////////////// int tetgenmesh::recoversegments(arraypool* misseglist, int fullsearch, int steinerflag) { triface searchtet, spintet; face sseg, *paryseg; point startpt, endpt; int success; int t1ver; long bak_inpoly_count = st_volref_count; long bak_segref_count = st_segref_count; if (b->verbose > 1) { printf(" Recover segments [%s level = %2d] #: %ld.\n", (b->fliplinklevel > 0) ? "fixed" : "auto", (b->fliplinklevel > 0) ? b->fliplinklevel : autofliplinklevel, subsegstack->objects); } // Loop until 'subsegstack' is empty. while (subsegstack->objects > 0l) { // seglist is used as a stack. subsegstack->objects--; paryseg = (face*)fastlookup(subsegstack, subsegstack->objects); sseg = *paryseg; // Check if this segment has been recovered. sstpivot1(sseg, searchtet); if (searchtet.tet != NULL) { continue; // Not a missing segment. } startpt = sorg(sseg); endpt = sdest(sseg); if (b->verbose > 2) { printf(" Recover segment (%d, %d).\n", pointmark(startpt), pointmark(endpt)); } success = 0; if (recoveredgebyflips(startpt, endpt, &sseg, &searchtet, 0)) { success = 1; } else { // Try to recover it from the other direction. if (recoveredgebyflips(endpt, startpt, &sseg, &searchtet, 0)) { success = 1; } } if (!success && fullsearch) { if (recoveredgebyflips(startpt, endpt, &sseg, &searchtet, fullsearch)) { success = 1; } } if (success) { // Segment is recovered. Insert it. // Let the segment remember an adjacent tet. sstbond1(sseg, searchtet); // Bond the segment to all tets containing it. spintet = searchtet; do { tssbond1(spintet, sseg); fnextself(spintet); } while (spintet.tet != searchtet.tet); } else { if (steinerflag > 0) { // Try to recover the segment but do not split it. if (addsteiner4recoversegment(&sseg, 0)) { success = 1; } if (!success && (steinerflag > 1)) { // Split the segment. addsteiner4recoversegment(&sseg, 1); success = 1; } } if (!success) { if (misseglist != NULL) { // Save this segment. misseglist->newindex((void**)&paryseg); *paryseg = sseg; } } } } // while (subsegstack->objects > 0l) if (steinerflag) { if (b->verbose > 1) { // Report the number of added Steiner points. if (st_volref_count > bak_inpoly_count) { printf(" Add %ld Steiner points in volume.\n", st_volref_count - bak_inpoly_count); } if (st_segref_count > bak_segref_count) { printf(" Add %ld Steiner points in segments.\n", st_segref_count - bak_segref_count); } } } return 0; } /////////////////////////////////////////////////////////////////////////////// // // // recoverfacebyflips() Recover a face by flips. // // // // 'pa', 'pb', and 'pc' are the three vertices of this face. This routine // // tries to recover it in the tetrahedral mesh. It is assumed that the three // // edges, i.e., pa->pb, pb->pc, and pc->pa all exist. // // // // If the face is recovered, it is returned by 'searchtet'. // // // // If 'searchsh' is not NULL, it is a subface to be recovered. Its vertices // // must be pa, pb, and pc. It is mainly used to check self-intersections. // // Another use of this subface is to split it when a Steiner point is found // // inside this subface. // // // /////////////////////////////////////////////////////////////////////////////// int tetgenmesh::recoverfacebyflips(point pa, point pb, point pc, face* searchsh, triface* searchtet) { triface spintet, flipedge; point pd, pe; flipconstraints fc; int types[2], poss[4], intflag; int success; int t1ver; int i, j; fc.fac[0] = pa; fc.fac[1] = pb; fc.fac[2] = pc; fc.checkflipeligibility = 1; success = 0; for (i = 0; i < 3 && !success; i++) { while (1) { // Get a tet containing the edge [a,b]. point2tetorg(fc.fac[i], *searchtet); finddirection(searchtet, fc.fac[(i + 1) % 3]); // Search the face [a,b,c] spintet = *searchtet; while (1) { if (apex(spintet) == fc.fac[(i + 2) % 3]) { // Found the face. *searchtet = spintet; // Return the face [a,b,c]. for (j = i; j > 0; j--) { eprevself(*searchtet); } success = 1; break; } fnextself(spintet); if (spintet.tet == searchtet->tet) break; } // while (1) if (success) break; // The face is missing. Try to recover it. flipedge.tet = NULL; // Find a crossing edge of this face. spintet = *searchtet; while (1) { pd = apex(spintet); pe = oppo(spintet); if ((pd != dummypoint) && (pe != dummypoint)) { // Check if [d,e] intersects [a,b,c] intflag = tri_edge_test(pa, pb, pc, pd, pe, NULL, 1, types, poss); if (intflag > 0) { // By the assumption that all edges of the face exist, they can // only intersect at a single point. if (intflag == 2) { // Go to the edge [d,e]. edestoppo(spintet, flipedge); // [d,e,a,b] if (searchsh != NULL) { // Check the intersection type. if ((types[0] == (int)ACROSSFACE) || (types[0] == (int)ACROSSEDGE)) { // Check if [e,d] is a segment. if (issubseg(flipedge)) { return report_selfint_face(pa, pb, pc, searchsh, &flipedge, intflag, types, poss); } else { // Check if [e,d] is an edge of a subface. triface chkface = flipedge; while (1) { if (issubface(chkface)) break; fsymself(chkface); if (chkface.tet == flipedge.tet) break; } if (issubface(chkface)) { // Two subfaces are intersecting. return report_selfint_face(pa, pb, pc, searchsh, &chkface, intflag, types, poss); } } } else if (types[0] == TOUCHFACE) { // This is possible when a Steiner point was added on it. point touchpt, *parypt; if (poss[1] == 0) { touchpt = pd; // pd is a coplanar vertex. } else { touchpt = pe; // pe is a coplanar vertex. } if (pointtype(touchpt) == FREEVOLVERTEX) { // A volume Steiner point was added in this subface. // Split this subface by this point. face checksh, *parysh; int siloc = (int)ONFACE; int sbowat = 0; // Only split this subface. A 1-to-3 flip. setpointtype(touchpt, FREEFACETVERTEX); sinsertvertex(touchpt, searchsh, NULL, siloc, sbowat, 0); st_volref_count--; st_facref_count++; // Queue this vertex for removal. subvertstack->newindex((void**)&parypt); *parypt = touchpt; // Queue new subfaces for recovery. // Put all new subfaces into stack for recovery. for (i = 0; i < caveshbdlist->objects; i++) { // Get an old subface at edge [a, b]. parysh = (face*)fastlookup(caveshbdlist, i); spivot(*parysh, checksh); // The new subface [a, b, p]. // Do not recover a deleted new face (degenerated). if (checksh.sh[3] != NULL) { subfacstack->newindex((void**)&parysh); *parysh = checksh; } } // Delete the old subfaces in sC(p). for (i = 0; i < caveshlist->objects; i++) { parysh = (face*)fastlookup(caveshlist, i); shellfacedealloc(subfaces, parysh->sh); } // Clear working lists. caveshlist->restart(); caveshbdlist->restart(); cavesegshlist->restart(); // We can return this function. searchsh->sh = NULL; // It has been split. return 1; } else { // Other cases may be due to a bug or a PLC error. return report_selfint_face(pa, pb, pc, searchsh, &flipedge, intflag, types, poss); } } else { // The other intersection types: ACROSSVERT, TOUCHEDGE, // SHAREVERTEX should not be possible or due to a PLC error. return report_selfint_face(pa, pb, pc, searchsh, &flipedge, intflag, types, poss); } } // if (searchsh != NULL) } else { // intflag == 4. Coplanar case. terminatetetgen(this, 2); } break; } // if (intflag > 0) } fnextself(spintet); if (spintet.tet == searchtet->tet) { terminatetetgen(this, 2); } } // while (1) // Try to flip the edge [d,e]. if (removeedgebyflips(&flipedge, &fc) == 2) { // A crossing edge is removed. continue; } break; } // while (1) } // i return success; } /////////////////////////////////////////////////////////////////////////////// // // // recoversubfaces() Recover all subfaces. // // // /////////////////////////////////////////////////////////////////////////////// int tetgenmesh::recoversubfaces(arraypool* misshlist, int steinerflag) { triface searchtet, neightet, spintet; face searchsh, neighsh, neineish, *parysh; face bdsegs[3]; point startpt, endpt, apexpt, *parypt; point steinerpt; insertvertexflags ivf; int success; int t1ver; int i, j; if (b->verbose > 1) { printf(" Recover subfaces [%s level = %2d] #: %ld.\n", (b->fliplinklevel > 0) ? "fixed" : "auto", (b->fliplinklevel > 0) ? b->fliplinklevel : autofliplinklevel, subfacstack->objects); } // Loop until 'subfacstack' is empty. while (subfacstack->objects > 0l) { subfacstack->objects--; parysh = (face*)fastlookup(subfacstack, subfacstack->objects); searchsh = *parysh; if (searchsh.sh[3] == NULL) continue; // Skip a dead subface. stpivot(searchsh, neightet); if (neightet.tet != NULL) continue; // Skip a recovered subface. if (b->verbose > 2) { printf(" Recover subface (%d, %d, %d).\n", pointmark(sorg(searchsh)), pointmark(sdest(searchsh)), pointmark(sapex(searchsh))); } // The three edges of the face need to be existed first. for (i = 0; i < 3; i++) { sspivot(searchsh, bdsegs[i]); if (bdsegs[i].sh != NULL) { // The segment must exist. sstpivot1(bdsegs[i], searchtet); if (searchtet.tet == NULL) { terminatetetgen(this, 2); } } else { // This edge is not a segment (due to a Steiner point). // Check whether it exists or not. success = 0; startpt = sorg(searchsh); endpt = sdest(searchsh); point2tetorg(startpt, searchtet); finddirection(&searchtet, endpt); if (dest(searchtet) == endpt) { success = 1; } else { // The edge is missing. Try to recover it. if (recoveredgebyflips(startpt, endpt, &searchsh, &searchtet, 0)) { success = 1; } else { if (recoveredgebyflips(endpt, startpt, &searchsh, &searchtet, 0)) { success = 1; } } } if (success) { // Insert a temporary segment to protect this edge. makeshellface(subsegs, &(bdsegs[i])); setshvertices(bdsegs[i], startpt, endpt, NULL); smarktest2(bdsegs[i]); // It's a temporary segment. // Insert this segment into surface mesh. ssbond(searchsh, bdsegs[i]); spivot(searchsh, neighsh); if (neighsh.sh != NULL) { ssbond(neighsh, bdsegs[i]); } // Insert this segment into tetrahedralization. sstbond1(bdsegs[i], searchtet); // Bond the segment to all tets containing it. spintet = searchtet; do { tssbond1(spintet, bdsegs[i]); fnextself(spintet); } while (spintet.tet != searchtet.tet); } else { // An edge of this subface is missing. Can't recover this subface. // Delete any temporary segment that has been created. for (j = (i - 1); j >= 0; j--) { if (smarktest2ed(bdsegs[j])) { spivot(bdsegs[j], neineish); ssdissolve(neineish); spivot(neineish, neighsh); if (neighsh.sh != NULL) { ssdissolve(neighsh); } sstpivot1(bdsegs[j], searchtet); spintet = searchtet; while (1) { tssdissolve1(spintet); fnextself(spintet); if (spintet.tet == searchtet.tet) break; } shellfacedealloc(subsegs, bdsegs[j].sh); } } // j if (steinerflag) { // Add a Steiner point at the midpoint of this edge. if (b->verbose > 2) { printf(" Add a Steiner point in subedge (%d, %d).\n", pointmark(startpt), pointmark(endpt)); } makepoint(&steinerpt, FREEFACETVERTEX); for (j = 0; j < 3; j++) { steinerpt[j] = 0.5 * (startpt[j] + endpt[j]); } point2tetorg(startpt, searchtet); // Start from 'searchtet'. ivf.iloc = (int)OUTSIDE; // Need point location. ivf.bowywat = 1; ivf.lawson = 0; ivf.rejflag = 0; ivf.chkencflag = 0; ivf.sloc = (int)ONEDGE; ivf.sbowywat = 1; // Allow flips in facet. ivf.splitbdflag = 0; ivf.validflag = 1; ivf.respectbdflag = 1; ivf.assignmeshsize = b->metric; if (!insertpoint(steinerpt, &searchtet, &searchsh, NULL, &ivf)) { terminatetetgen(this, 2); } // Save this Steiner point (for removal). // Re-use the array 'subvertstack'. subvertstack->newindex((void**)&parypt); *parypt = steinerpt; st_facref_count++; if (steinerleft > 0) steinerleft--; } // if (steinerflag) break; } } senextself(searchsh); } // i if (i == 3) { // Recover the subface. startpt = sorg(searchsh); endpt = sdest(searchsh); apexpt = sapex(searchsh); success = recoverfacebyflips(startpt, endpt, apexpt, &searchsh, &searchtet); // Delete any temporary segment that has been created. for (j = 0; j < 3; j++) { if (smarktest2ed(bdsegs[j])) { spivot(bdsegs[j], neineish); ssdissolve(neineish); spivot(neineish, neighsh); if (neighsh.sh != NULL) { ssdissolve(neighsh); } sstpivot1(bdsegs[j], neightet); spintet = neightet; while (1) { tssdissolve1(spintet); fnextself(spintet); if (spintet.tet == neightet.tet) break; } shellfacedealloc(subsegs, bdsegs[j].sh); } } // j if (success) { if (searchsh.sh != NULL) { // Face is recovered. Insert it. tsbond(searchtet, searchsh); fsymself(searchtet); sesymself(searchsh); tsbond(searchtet, searchsh); } } else { if (steinerflag) { // Add a Steiner point at the barycenter of this subface. if (b->verbose > 2) { printf(" Add a Steiner point in subface (%d, %d, %d).\n", pointmark(startpt), pointmark(endpt), pointmark(apexpt)); } makepoint(&steinerpt, FREEFACETVERTEX); for (j = 0; j < 3; j++) { steinerpt[j] = (startpt[j] + endpt[j] + apexpt[j]) / 3.0; } point2tetorg(startpt, searchtet); // Start from 'searchtet'. ivf.iloc = (int)OUTSIDE; // Need point location. ivf.bowywat = 1; ivf.lawson = 0; ivf.rejflag = 0; ivf.chkencflag = 0; ivf.sloc = (int)ONFACE; ivf.sbowywat = 1; // Allow flips in facet. ivf.splitbdflag = 0; ivf.validflag = 1; ivf.respectbdflag = 1; ivf.assignmeshsize = b->metric; if (!insertpoint(steinerpt, &searchtet, &searchsh, NULL, &ivf)) { terminatetetgen(this, 2); } // Save this Steiner point (for removal). // Re-use the array 'subvertstack'. subvertstack->newindex((void**)&parypt); *parypt = steinerpt; st_facref_count++; if (steinerleft > 0) steinerleft--; } // if (steinerflag) } } else { success = 0; } if (!success) { if (misshlist != NULL) { // Save this subface. misshlist->newindex((void**)&parysh); *parysh = searchsh; } } } // while (subfacstack->objects > 0l) return 0; } /////////////////////////////////////////////////////////////////////////////// // // // getvertexstar() Return the star of a vertex. // // // // If the flag 'fullstar' is set, return the complete star of this vertex. // // Otherwise, only a part of the star which is bounded by facets is returned.// // // // 'tetlist' returns the list of tets in the star of the vertex 'searchpt'. // // Every tet in 'tetlist' is at the face opposing to 'searchpt'. // // // // 'vertlist' returns the list of vertices in the star (exclude 'searchpt'). // // // // 'shlist' returns the list of subfaces in the star. Each subface must face // // to the interior of this star. // // // /////////////////////////////////////////////////////////////////////////////// int tetgenmesh::getvertexstar(int fullstar, point searchpt, arraypool* tetlist, arraypool* vertlist, arraypool* shlist) { triface searchtet, neightet, *parytet; face checksh, *parysh; point pt, *parypt; int collectflag; int t1ver; int i, j; point2tetorg(searchpt, searchtet); // Go to the opposite face (the link face) of the vertex. enextesymself(searchtet); // assert(oppo(searchtet) == searchpt); infect(searchtet); // Collect this tet (link face). tetlist->newindex((void**)&parytet); *parytet = searchtet; if (vertlist != NULL) { // Collect three (link) vertices. j = (searchtet.ver & 3); // The current vertex index. for (i = 1; i < 4; i++) { pt = (point)searchtet.tet[4 + ((j + i) % 4)]; pinfect(pt); vertlist->newindex((void**)&parypt); *parypt = pt; } } collectflag = 1; esym(searchtet, neightet); if (issubface(neightet)) { if (shlist != NULL) { tspivot(neightet, checksh); if (!sinfected(checksh)) { // Collect this subface (link edge). sinfected(checksh); shlist->newindex((void**)&parysh); *parysh = checksh; } } if (!fullstar) { collectflag = 0; } } if (collectflag) { fsymself(neightet); // Goto the adj tet of this face. esymself(neightet); // Goto the oppo face of this vertex. // assert(oppo(neightet) == searchpt); infect(neightet); // Collect this tet (link face). tetlist->newindex((void**)&parytet); *parytet = neightet; if (vertlist != NULL) { // Collect its apex. pt = apex(neightet); pinfect(pt); vertlist->newindex((void**)&parypt); *parypt = pt; } } // if (collectflag) // Continue to collect all tets in the star. for (i = 0; i < tetlist->objects; i++) { searchtet = *(triface*)fastlookup(tetlist, i); // Note that 'searchtet' is a face opposite to 'searchpt', and the neighbor // tet at the current edge is already collected. // Check the neighbors at the other two edges of this face. for (j = 0; j < 2; j++) { collectflag = 1; enextself(searchtet); esym(searchtet, neightet); if (issubface(neightet)) { if (shlist != NULL) { tspivot(neightet, checksh); if (!sinfected(checksh)) { // Collect this subface (link edge). sinfected(checksh); shlist->newindex((void**)&parysh); *parysh = checksh; } } if (!fullstar) { collectflag = 0; } } if (collectflag) { fsymself(neightet); if (!infected(neightet)) { esymself(neightet); // Go to the face opposite to 'searchpt'. infect(neightet); tetlist->newindex((void**)&parytet); *parytet = neightet; if (vertlist != NULL) { // Check if a vertex is collected. pt = apex(neightet); if (!pinfected(pt)) { pinfect(pt); vertlist->newindex((void**)&parypt); *parypt = pt; } } } // if (!infected(neightet)) } // if (collectflag) } // j } // i // Uninfect the list of tets and vertices. for (i = 0; i < tetlist->objects; i++) { parytet = (triface*)fastlookup(tetlist, i); uninfect(*parytet); } if (vertlist != NULL) { for (i = 0; i < vertlist->objects; i++) { parypt = (point*)fastlookup(vertlist, i); puninfect(*parypt); } } if (shlist != NULL) { for (i = 0; i < shlist->objects; i++) { parysh = (face*)fastlookup(shlist, i); suninfect(*parysh); } } return (int)tetlist->objects; } /////////////////////////////////////////////////////////////////////////////// // // // getedge() Get a tetrahedron having the two endpoints. // // // // The method here is to search the second vertex in the link faces of the // // first vertex. The global array 'cavetetlist' is re-used for searching. // // // // This function is used for the case when the mesh is non-convex. Otherwise,// // the function finddirection() should be faster than this. // // // /////////////////////////////////////////////////////////////////////////////// int tetgenmesh::getedge(point e1, point e2, triface* tedge) { triface searchtet, neightet, *parytet; point pt; int done; int i, j; if (b->verbose > 2) { printf(" Get edge from %d to %d.\n", pointmark(e1), pointmark(e2)); } // Quickly check if 'tedge' is just this edge. if (!isdeadtet(*tedge)) { if (org(*tedge) == e1) { if (dest(*tedge) == e2) { return 1; } } else if (org(*tedge) == e2) { if (dest(*tedge) == e1) { esymself(*tedge); return 1; } } } // Search for the edge [e1, e2]. point2tetorg(e1, *tedge); finddirection(tedge, e2); if (dest(*tedge) == e2) { return 1; } else { // Search for the edge [e2, e1]. point2tetorg(e2, *tedge); finddirection(tedge, e1); if (dest(*tedge) == e1) { esymself(*tedge); return 1; } } // Go to the link face of e1. point2tetorg(e1, searchtet); enextesymself(searchtet); arraypool* tetlist = cavebdrylist; // Search e2. for (i = 0; i < 3; i++) { pt = apex(searchtet); if (pt == e2) { // Found. 'searchtet' is [#,#,e2,e1]. eorgoppo(searchtet, *tedge); // [e1,e2,#,#]. return 1; } enextself(searchtet); } // Get the adjacent link face at 'searchtet'. fnext(searchtet, neightet); esymself(neightet); // assert(oppo(neightet) == e1); pt = apex(neightet); if (pt == e2) { // Found. 'neightet' is [#,#,e2,e1]. eorgoppo(neightet, *tedge); // [e1,e2,#,#]. return 1; } // Continue searching in the link face of e1. infect(searchtet); tetlist->newindex((void**)&parytet); *parytet = searchtet; infect(neightet); tetlist->newindex((void**)&parytet); *parytet = neightet; done = 0; for (i = 0; (i < tetlist->objects) && !done; i++) { parytet = (triface*)fastlookup(tetlist, i); searchtet = *parytet; for (j = 0; (j < 2) && !done; j++) { enextself(searchtet); fnext(searchtet, neightet); if (!infected(neightet)) { esymself(neightet); pt = apex(neightet); if (pt == e2) { // Found. 'neightet' is [#,#,e2,e1]. eorgoppo(neightet, *tedge); done = 1; } else { infect(neightet); tetlist->newindex((void**)&parytet); *parytet = neightet; } } } // j } // i // Uninfect the list of visited tets. for (i = 0; i < tetlist->objects; i++) { parytet = (triface*)fastlookup(tetlist, i); uninfect(*parytet); } tetlist->restart(); return done; } /////////////////////////////////////////////////////////////////////////////// // // // reduceedgesatvertex() Reduce the number of edges at a given vertex. // // // // 'endptlist' contains the endpoints of edges connecting at the vertex. // // // /////////////////////////////////////////////////////////////////////////////// int tetgenmesh::reduceedgesatvertex(point startpt, arraypool* endptlist) { triface searchtet; point *pendpt, *parypt; enum interresult dir; flipconstraints fc; int reduceflag; int count; int n, i, j; fc.remvert = startpt; fc.checkflipeligibility = 1; while (1) { count = 0; for (i = 0; i < endptlist->objects; i++) { pendpt = (point*)fastlookup(endptlist, i); if (*pendpt == dummypoint) { continue; // Do not reduce a virtual edge. } reduceflag = 0; // Find the edge. if (nonconvex) { if (getedge(startpt, *pendpt, &searchtet)) { dir = ACROSSVERT; } else { // The edge does not exist (was flipped). dir = INTERSECT; } } else { point2tetorg(startpt, searchtet); dir = finddirection(&searchtet, *pendpt); } if (dir == ACROSSVERT) { if (dest(searchtet) == *pendpt) { // Do not flip a segment. if (!issubseg(searchtet)) { n = removeedgebyflips(&searchtet, &fc); if (n == 2) { reduceflag = 1; } } } } else { // The edge has been flipped. reduceflag = 1; } if (reduceflag) { count++; // Move the last vertex into this slot. j = endptlist->objects - 1; parypt = (point*)fastlookup(endptlist, j); *pendpt = *parypt; endptlist->objects--; i--; } } // i if (count == 0) { // No edge is reduced. break; } } // while (1) return (int)endptlist->objects; } /////////////////////////////////////////////////////////////////////////////// // // // removevertexbyflips() Remove a vertex by flips. // // // // This routine attempts to remove the given vertex 'rempt' (p) from the // // tetrahedralization (T) by a sequence of flips. // // // // The algorithm used here is a simple edge reduce method. Suppose there are // // n edges connected at p. We try to reduce the number of edges by flipping // // any edge (not a segment) that is connecting at p. // // // // Unless T is a Delaunay tetrahedralization, there is no guarantee that 'p' // // can be successfully removed. // // // /////////////////////////////////////////////////////////////////////////////// int tetgenmesh::removevertexbyflips(point steinerpt) { triface *fliptets = NULL, wrktets[4]; triface searchtet, spintet, neightet; face parentsh, spinsh, checksh; face leftseg, rightseg, checkseg; point lpt = NULL, rpt = NULL, apexpt; //, *parypt; flipconstraints fc; enum verttype vt; enum locateresult loc; int valence, removeflag; int slawson; int t1ver; int n, i; vt = pointtype(steinerpt); if (vt == FREESEGVERTEX) { sdecode(point2sh(steinerpt), leftseg); leftseg.shver = 0; if (sdest(leftseg) == steinerpt) { senext(leftseg, rightseg); spivotself(rightseg); rightseg.shver = 0; } else { rightseg = leftseg; senext2(rightseg, leftseg); spivotself(leftseg); leftseg.shver = 0; } lpt = sorg(leftseg); rpt = sdest(rightseg); if (b->verbose > 2) { printf(" Removing Steiner point %d in segment (%d, %d).\n", pointmark(steinerpt), pointmark(lpt), pointmark(rpt)); } } else if (vt == FREEFACETVERTEX) { if (b->verbose > 2) { printf(" Removing Steiner point %d in facet.\n", pointmark(steinerpt)); } } else if (vt == FREEVOLVERTEX) { if (b->verbose > 2) { printf(" Removing Steiner point %d in volume.\n", pointmark(steinerpt)); } } else if (vt == VOLVERTEX) { if (b->verbose > 2) { printf(" Removing a point %d in volume.\n", pointmark(steinerpt)); } } else { // It is not a Steiner point. return 0; } // Try to reduce the number of edges at 'p' by flips. getvertexstar(1, steinerpt, cavetetlist, cavetetvertlist, NULL); cavetetlist->restart(); // This list may be re-used. if (cavetetvertlist->objects > 3l) { valence = reduceedgesatvertex(steinerpt, cavetetvertlist); } else { valence = cavetetvertlist->objects; } cavetetvertlist->restart(); removeflag = 0; if (valence == 4) { // Only 4 vertices (4 tets) left! 'p' is inside the convex hull of the 4 // vertices. This case is due to that 'p' is not exactly on the segment. point2tetorg(steinerpt, searchtet); loc = INTETRAHEDRON; removeflag = 1; } else if (valence == 5) { // There are 5 edges. if (vt == FREESEGVERTEX) { sstpivot1(leftseg, searchtet); if (org(searchtet) != steinerpt) { esymself(searchtet); } i = 0; // Count the numbe of tet at the edge [p,lpt]. neightet.tet = NULL; // Init the face. spintet = searchtet; while (1) { i++; if (apex(spintet) == rpt) { // Remember the face containing the edge [lpt, rpt]. neightet = spintet; } fnextself(spintet); if (spintet.tet == searchtet.tet) break; } if (i == 3) { // This case has been checked below. } else if (i == 4) { // There are 4 tets sharing at [p,lpt]. There must be 4 tets sharing // at [p,rpt]. There must be a face [p, lpt, rpt]. if (apex(neightet) == rpt) { // The edge (segment) has been already recovered! // Check if a 6-to-2 flip is possible (to remove 'p'). // Let 'searchtet' be [p,d,a,b] esym(neightet, searchtet); enextself(searchtet); // Check if there are exactly three tets at edge [p,d]. wrktets[0] = searchtet; // [p,d,a,b] for (i = 0; i < 2; i++) { fnext(wrktets[i], wrktets[i + 1]); // [p,d,b,c], [p,d,c,a] } if (apex(wrktets[0]) == oppo(wrktets[2])) { loc = ONFACE; removeflag = 1; } } } } else if (vt == FREEFACETVERTEX) { // It is possible to do a 6-to-2 flip to remove the vertex. point2tetorg(steinerpt, searchtet); // Get the three faces of 'searchtet' which share at p. // All faces has p as origin. wrktets[0] = searchtet; wrktets[1] = searchtet; esymself(wrktets[1]); enextself(wrktets[1]); wrktets[2] = searchtet; eprevself(wrktets[2]); esymself(wrktets[2]); // All internal edges of the six tets have valance either 3 or 4. // Get one edge which has valance 3. searchtet.tet = NULL; for (i = 0; i < 3; i++) { spintet = wrktets[i]; valence = 0; while (1) { valence++; fnextself(spintet); if (spintet.tet == wrktets[i].tet) break; } if (valence == 3) { // Found the edge. searchtet = wrktets[i]; break; } } // Note, we do not detach the three subfaces at p. // They will be removed within a 4-to-1 flip. loc = ONFACE; removeflag = 1; } // removeflag = 1; } if (!removeflag) { if (vt == FREESEGVERTEX) { // Check is it possible to recover the edge [lpt,rpt]. // The condition to check is: Whether each tet containing 'leftseg' is // adjacent to a tet containing 'rightseg'. sstpivot1(leftseg, searchtet); if (org(searchtet) != steinerpt) { esymself(searchtet); } spintet = searchtet; while (1) { // Go to the bottom face of this tet. eprev(spintet, neightet); esymself(neightet); // [steinerpt, p1, p2, lpt] // Get the adjacent tet. fsymself(neightet); // [p1, steinerpt, p2, rpt] if (oppo(neightet) != rpt) { // Found a non-matching adjacent tet. break; } { // [2017-10-15] Check if the tet is inverted? point chkp1 = org(neightet); point chkp2 = apex(neightet); REAL chkori = orient3d(rpt, lpt, chkp1, chkp2); if (chkori >= 0.0) { // Either inverted or degenerated. break; } } fnextself(spintet); if (spintet.tet == searchtet.tet) { // 'searchtet' is [p,d,p1,p2]. loc = ONEDGE; removeflag = 1; break; } } } // if (vt == FREESEGVERTEX) } if (!removeflag) { if (vt == FREESEGVERTEX) { // Check if the edge [lpt, rpt] exists. if (getedge(lpt, rpt, &searchtet)) { // We have recovered this edge. Shift the vertex into the volume. // We can recover this edge if the subfaces are not recovered yet. if (!checksubfaceflag) { // Remove the vertex from the surface mesh. // This will re-create the segment [lpt, rpt] and re-triangulate // all the facets at the segment. // Detach the subsegments from their surrounding tets. for (i = 0; i < 2; i++) { checkseg = (i == 0) ? leftseg : rightseg; sstpivot1(checkseg, neightet); spintet = neightet; while (1) { tssdissolve1(spintet); fnextself(spintet); if (spintet.tet == neightet.tet) break; } sstdissolve1(checkseg); } // i slawson = 1; // Do lawson flip after removal. spivot(rightseg, parentsh); // 'rightseg' has p as its origin. sremovevertex(steinerpt, &parentsh, &rightseg, slawson); // Clear the list for new subfaces. caveshbdlist->restart(); // Insert the new segment. sstbond1(rightseg, searchtet); spintet = searchtet; while (1) { tssbond1(spintet, rightseg); fnextself(spintet); if (spintet.tet == searchtet.tet) break; } // The Steiner point has been shifted into the volume. setpointtype(steinerpt, FREEVOLVERTEX); st_segref_count--; st_volref_count++; return 1; } // if (!checksubfaceflag) } // if (getedge(...)) } // if (vt == FREESEGVERTEX) } // if (!removeflag) if (!removeflag) { return 0; } if (vt == FREESEGVERTEX) { // Detach the subsegments from their surronding tets. for (i = 0; i < 2; i++) { checkseg = (i == 0) ? leftseg : rightseg; sstpivot1(checkseg, neightet); spintet = neightet; while (1) { tssdissolve1(spintet); fnextself(spintet); if (spintet.tet == neightet.tet) break; } sstdissolve1(checkseg); } // i if (checksubfaceflag) { // Detach the subfaces at the subsegments from their attached tets. for (i = 0; i < 2; i++) { checkseg = (i == 0) ? leftseg : rightseg; spivot(checkseg, parentsh); if (parentsh.sh != NULL) { spinsh = parentsh; while (1) { stpivot(spinsh, neightet); if (neightet.tet != NULL) { tsdissolve(neightet); } sesymself(spinsh); stpivot(spinsh, neightet); if (neightet.tet != NULL) { tsdissolve(neightet); } stdissolve(spinsh); spivotself(spinsh); // Go to the next subface. if (spinsh.sh == parentsh.sh) break; } } } // i } // if (checksubfaceflag) } if (loc == INTETRAHEDRON) { // Collect the four tets containing 'p'. fliptets = new triface[4]; fliptets[0] = searchtet; // [p,d,a,b] for (i = 0; i < 2; i++) { fnext(fliptets[i], fliptets[i + 1]); // [p,d,b,c], [p,d,c,a] } eprev(fliptets[0], fliptets[3]); fnextself(fliptets[3]); // it is [a,p,b,c] eprevself(fliptets[3]); esymself(fliptets[3]); // [a,b,c,p]. // Remove p by a 4-to-1 flip. // flip41(fliptets, 1, 0, 0); /* { // Do not flip if there are wrong number of subfaces inside. // Check if there are three subfaces at 'p'. triface newface; face flipshs[3]; int spivot = 0, scount = 0; for (i = 0; i < 3; i++) { fnext(fliptets[3], newface); // [a,b,p,d],[b,c,p,d],[c,a,p,d]. tspivot(newface, flipshs[i]); if (flipshs[i].sh != NULL) { spivot = i; // Remember this subface. scount++; } enextself(fliptets[3]); } if (scount > 0) { // There are three subfaces connecting at p. // Only do flip if a 3-to-1 flip is possible at p at the bottom face. if (scount != 3) { // Wrong number of subfaces. Do not flip. delete [] fliptets; return 0; } // [2018-03-07] an old fix, not 100% safe. // if (scount < 3) { // // The new subface is one of {[a,b,d], [b,c,d], [c,a,d]}. // // assert(scount == 1); // spivot >= 0 // if (scount != 1) { // // Wrong number of subfaces. Do not flip. // delete [] fliptets; // return 0; // } //} } } */ if (vt == FREEFACETVERTEX) { // [2018-03-08] Check if the last 4-to-1 flip is valid. // fliptets[0],[1],[2] are [p,d,a,b],[p,d,b,c],[p,d,c,a] triface checktet, chkface; for (i = 0; i < 3; i++) { enext(fliptets[i], checktet); esymself(checktet); // [a,d,b,p],[b,d,c,p],[c,d,a,p] int scount = 0; int k; for (k = 0; k < 3; k++) { esym(checktet, chkface); if (issubface(chkface)) scount++; enextself(checktet); } if (scount == 3) { break; // Found a tet which support a 3-to-1 flip. } else if (scount == 2) { // This is a strange configuration. Debug it. // Do not do this flip. delete[] fliptets; return 0; } } if (i == 3) { // No tet in [p,d,a,b],[p,d,b,c],[p,d,c,a] support it. int scount = 0; for (i = 0; i < 3; i++) { eprev(fliptets[i], checktet); esymself(checktet); // [p,a,b,d],[p,b,c,d],[p,c,a,d] if (issubface(chkface)) scount++; } if (scount != 3) { // Do not do this flip. delete[] fliptets; return 0; } } } // if (vt == FREEFACETVERTEX) flip41(fliptets, 1, &fc); // recenttet = fliptets[0]; } else if (loc == ONFACE) { // Let the original two tets be [a,b,c,d] and [b,a,c,e]. And p is in // face [a,b,c]. Let 'searchtet' be the tet [p,d,a,b]. // Collect the six tets containing 'p'. fliptets = new triface[6]; fliptets[0] = searchtet; // [p,d,a,b] for (i = 0; i < 2; i++) { fnext(fliptets[i], fliptets[i + 1]); // [p,d,b,c], [p,d,c,a] } eprev(fliptets[0], fliptets[3]); fnextself(fliptets[3]); // [a,p,b,e] esymself(fliptets[3]); // [p,a,e,b] eprevself(fliptets[3]); // [e,p,a,b] for (i = 3; i < 5; i++) { fnext(fliptets[i], fliptets[i + 1]); // [e,p,b,c], [e,p,c,a] } if (vt == FREEFACETVERTEX) { // We need to determine the location of three subfaces at p. valence = 0; // Re-use it. for (i = 3; i < 6; i++) { if (issubface(fliptets[i])) valence++; } if (valence > 0) { // We must do 3-to-2 flip in the upper part. We simply re-arrange // the six tets. for (i = 0; i < 3; i++) { esym(fliptets[i + 3], wrktets[i]); esym(fliptets[i], fliptets[i + 3]); fliptets[i] = wrktets[i]; } // Swap the last two pairs, i.e., [1]<->[[2], and [4]<->[5] wrktets[1] = fliptets[1]; fliptets[1] = fliptets[2]; fliptets[2] = wrktets[1]; wrktets[1] = fliptets[4]; fliptets[4] = fliptets[5]; fliptets[5] = wrktets[1]; } // [2018-03-08] Check if the last 4-to-1 flip is valid. // fliptets[0],[1],[2] are [p,d,a,b],[p,d,b,c],[p,d,c,a] triface checktet, chkface; for (i = 0; i < 3; i++) { enext(fliptets[i], checktet); esymself(checktet); // [a,d,b,p],[b,d,c,p],[c,d,a,p] int scount = 0; int k; for (k = 0; k < 3; k++) { esym(checktet, chkface); if (issubface(chkface)) scount++; enextself(checktet); } if (scount == 3) { break; // Found a tet which support a 3-to-1 flip. } else if (scount == 2) { // This is a strange configuration. Debug it. // Do not do this flip. delete[] fliptets; return 0; } } if (i == 3) { // No tet in [p,d,a,b],[p,d,b,c],[p,d,c,a] support it. int scount = 0; for (i = 0; i < 3; i++) { eprev(fliptets[i], checktet); esymself(checktet); // [p,a,b,d],[p,b,c,d],[p,c,a,d] if (issubface(chkface)) scount++; } if (scount != 3) { // Do not do this flip. delete[] fliptets; return 0; } } } // vt == FREEFACETVERTEX // Remove p by a 6-to-2 flip, which is a combination of two flips: // a 3-to-2 (deletes the edge [e,p]), and // a 4-to-1 (deletes the vertex p). // First do a 3-to-2 flip on [e,p,a,b],[e,p,b,c],[e,p,c,a]. It creates // two new tets: [a,b,c,p] and [b,a,c,e]. The new tet [a,b,c,p] is // degenerate (has zero volume). It will be deleted in the followed // 4-to-1 flip. // flip32(&(fliptets[3]), 1, 0, 0); flip32(&(fliptets[3]), 1, &fc); // Second do a 4-to-1 flip on [p,d,a,b],[p,d,b,c],[p,d,c,a],[a,b,c,p]. // This creates a new tet [a,b,c,d]. // flip41(fliptets, 1, 0, 0); flip41(fliptets, 1, &fc); // recenttet = fliptets[0]; } else if (loc == ONEDGE) { // Let the original edge be [e,d] and p is in [e,d]. Assume there are n // tets sharing at edge [e,d] originally. We number the link vertices // of [e,d]: p_0, p_1, ..., p_n-1. 'searchtet' is [p,d,p_0,p_1]. // Count the number of tets at edge [e,p] and [p,d] (this is n). n = 0; spintet = searchtet; while (1) { n++; fnextself(spintet); if (spintet.tet == searchtet.tet) break; } // Collect the 2n tets containing 'p'. fliptets = new triface[2 * n]; fliptets[0] = searchtet; // [p,b,p_0,p_1] for (i = 0; i < (n - 1); i++) { fnext(fliptets[i], fliptets[i + 1]); // [p,d,p_i,p_i+1]. } eprev(fliptets[0], fliptets[n]); fnextself(fliptets[n]); // [p_0,p,p_1,e] esymself(fliptets[n]); // [p,p_0,e,p_1] eprevself(fliptets[n]); // [e,p,p_0,p_1] for (i = n; i < (2 * n - 1); i++) { fnext(fliptets[i], fliptets[i + 1]); // [e,p,p_i,p_i+1]. } // Remove p by a 2n-to-n flip, it is a sequence of n flips: // - Do a 2-to-3 flip on // [p_0,p_1,p,d] and // [p,p_1,p_0,e]. // This produces: // [e,d,p_0,p_1], // [e,d,p_1,p] (degenerated), and // [e,d,p,p_0] (degenerated). wrktets[0] = fliptets[0]; // [p,d,p_0,p_1] eprevself(wrktets[0]); // [p_0,p,d,p_1] esymself(wrktets[0]); // [p,p_0,p_1,d] enextself(wrktets[0]); // [p_0,p_1,p,d] [0] wrktets[1] = fliptets[n]; // [e,p,p_0,p_1] enextself(wrktets[1]); // [p,p_0,e,p_1] esymself(wrktets[1]); // [p_0,p,p_1,e] eprevself(wrktets[1]); // [p_1,p_0,p,e] [1] // flip23(wrktets, 1, 0, 0); flip23(wrktets, 1, &fc); // Save the new tet [e,d,p,p_0] (degenerated). fliptets[n] = wrktets[2]; // Save the new tet [e,d,p_0,p_1]. fliptets[0] = wrktets[0]; // - Repeat from i = 1 to n-2: (n - 2) flips // - Do a 3-to-2 flip on // [p,p_i,d,e], // [p,p_i,e,p_i+1], and // [p,p_i,p_i+1,d]. // This produces: // [d,e,p_i+1,p_i], and // [e,d,p_i+1,p] (degenerated). for (i = 1; i < (n - 1); i++) { wrktets[0] = wrktets[1]; // [e,d,p_i,p] (degenerated). enextself(wrktets[0]); // [d,p_i,e,p] (...) esymself(wrktets[0]); // [p_i,d,p,e] (...) eprevself(wrktets[0]); // [p,p_i,d,e] (degenerated) [0]. wrktets[1] = fliptets[n + i]; // [e,p,p_i,p_i+1] enextself(wrktets[1]); // [p,p_i,e,p_i+1] [1] wrktets[2] = fliptets[i]; // [p,d,p_i,p_i+1] eprevself(wrktets[2]); // [p_i,p,d,p_i+1] esymself(wrktets[2]); // [p,p_i,p_i+1,d] [2] // flip32(wrktets, 1, 0, 0); flip32(wrktets, 1, &fc); // Save the new tet [e,d,p_i,p_i+1]. // FOR DEBUG ONLY fliptets[i] = wrktets[0]; // [d,e,p_i+1,p_i] // FOR DEBUG ONLY esymself(fliptets[i]); // [e,d,p_i,p_i+1] // FOR DEBUG ONLY } // - Do a 4-to-1 flip on // [p,p_0,e,d], [d,e,p_0,p], // [p,p_0,d,p_n-1], [e,p_n-1,p_0,p], // [p,p_0,p_n-1,e], [p_0,p_n-1,d,p], and // [e,d,p_n-1,p]. // This produces // [e,d,p_n-1,p_0] and // deletes p. wrktets[3] = wrktets[1]; // [e,d,p_n-1,p] (degenerated) [3] wrktets[0] = fliptets[n]; // [e,d,p,p_0] (degenerated) eprevself(wrktets[0]); // [p,e,d,p_0] (...) esymself(wrktets[0]); // [e,p,p_0,d] (...) enextself(wrktets[0]); // [p,p_0,e,d] (degenerated) [0] wrktets[1] = fliptets[n - 1]; // [p,d,p_n-1,p_0] esymself(wrktets[1]); // [d,p,p_0,p_n-1] enextself(wrktets[1]); // [p,p_0,d,p_n-1] [1] wrktets[2] = fliptets[2 * n - 1]; // [e,p,p_n-1,p_0] enextself(wrktets[2]); // [p_p_n-1,e,p_0] esymself(wrktets[2]); // [p_n-1,p,p_0,e] enextself(wrktets[2]); // [p,p_0,p_n-1,e] [2] // flip41(wrktets, 1, 0, 0); flip41(wrktets, 1, &fc); // Save the new tet [e,d,p_n-1,p_0] // FOR DEBUG ONLY fliptets[n - 1] = wrktets[0]; // [e,d,p_n-1,p_0] // FOR DEBUG ONLY // recenttet = fliptets[0]; } delete[] fliptets; if (vt == FREESEGVERTEX) { // Remove the vertex from the surface mesh. // This will re-create the segment [lpt, rpt] and re-triangulate // all the facets at the segment. // Only do lawson flip when subfaces are not recovery yet. slawson = (checksubfaceflag ? 0 : 1); spivot(rightseg, parentsh); // 'rightseg' has p as its origin. sremovevertex(steinerpt, &parentsh, &rightseg, slawson); // The original segment is returned in 'rightseg'. rightseg.shver = 0; // Insert the new segment. point2tetorg(lpt, searchtet); finddirection(&searchtet, rpt); sstbond1(rightseg, searchtet); spintet = searchtet; while (1) { tssbond1(spintet, rightseg); fnextself(spintet); if (spintet.tet == searchtet.tet) break; } if (checksubfaceflag) { // Insert subfaces at segment [lpt,rpt] into the tetrahedralization. spivot(rightseg, parentsh); if (parentsh.sh != NULL) { spinsh = parentsh; while (1) { if (sorg(spinsh) != lpt) { sesymself(spinsh); } apexpt = sapex(spinsh); // Find the adjacent tet of [lpt,rpt,apexpt]; spintet = searchtet; while (1) { if (apex(spintet) == apexpt) { tsbond(spintet, spinsh); sesymself(spinsh); // Get to another side of this face. fsym(spintet, neightet); tsbond(neightet, spinsh); sesymself(spinsh); // Get back to the original side. break; } fnextself(spintet); } spivotself(spinsh); if (spinsh.sh == parentsh.sh) break; } } } // if (checksubfaceflag) // Clear the set of new subfaces. caveshbdlist->restart(); } // if (vt == FREESEGVERTEX) // The point has been removed. if (pointtype(steinerpt) != UNUSEDVERTEX) { setpointtype(steinerpt, UNUSEDVERTEX); unuverts++; } if (vt != VOLVERTEX) { // Update the correspinding counters. if (vt == FREESEGVERTEX) { st_segref_count--; } else if (vt == FREEFACETVERTEX) { st_facref_count--; } else if (vt == FREEVOLVERTEX) { st_volref_count--; } if (steinerleft > 0) steinerleft++; } return 1; } /////////////////////////////////////////////////////////////////////////////// // // // suppressbdrysteinerpoint() Suppress a boundary Steiner point // // // /////////////////////////////////////////////////////////////////////////////// int tetgenmesh::suppressbdrysteinerpoint(point steinerpt) { face parentsh, spinsh, *parysh; face leftseg, rightseg; point lpt = NULL, rpt = NULL; int i; verttype vt = pointtype(steinerpt); if (vt == FREESEGVERTEX) { sdecode(point2sh(steinerpt), leftseg); leftseg.shver = 0; if (sdest(leftseg) == steinerpt) { senext(leftseg, rightseg); spivotself(rightseg); rightseg.shver = 0; } else { rightseg = leftseg; senext2(rightseg, leftseg); spivotself(leftseg); leftseg.shver = 0; } lpt = sorg(leftseg); rpt = sdest(rightseg); if (b->verbose > 2) { printf(" Suppressing Steiner point %d in segment (%d, %d).\n", pointmark(steinerpt), pointmark(lpt), pointmark(rpt)); } // Get all subfaces at the left segment [lpt, steinerpt]. spivot(leftseg, parentsh); if (parentsh.sh != NULL) { // It is not a dangling segment. spinsh = parentsh; while (1) { cavesegshlist->newindex((void**)&parysh); *parysh = spinsh; // Orient the face consistently. if (sorg(*parysh) != sorg(parentsh)) sesymself(*parysh); spivotself(spinsh); if (spinsh.sh == NULL) break; if (spinsh.sh == parentsh.sh) break; } } if (cavesegshlist->objects < 2) { // It is a single segment. Not handle it yet. cavesegshlist->restart(); return 0; } } else if (vt == FREEFACETVERTEX) { if (b->verbose > 2) { printf(" Suppressing Steiner point %d from facet.\n", pointmark(steinerpt)); } sdecode(point2sh(steinerpt), parentsh); // A facet Steiner point. There are exactly two sectors. for (i = 0; i < 2; i++) { cavesegshlist->newindex((void**)&parysh); *parysh = parentsh; sesymself(parentsh); } } else { return 0; } triface searchtet, neightet, *parytet; point pa, pb, pc, pd; REAL v1[3], v2[3], len, u; REAL startpt[3] = { 0, }, samplept[3] = { 0, }, candpt[3] = { 0, }; REAL ori, minvol, smallvol; int samplesize; int it, j, k; int n = (int)cavesegshlist->objects; point* newsteiners = new point[n]; for (i = 0; i < n; i++) newsteiners[i] = NULL; // Search for each sector an interior vertex. for (i = 0; i < cavesegshlist->objects; i++) { parysh = (face*)fastlookup(cavesegshlist, i); stpivot(*parysh, searchtet); // Skip it if it is outside. if (ishulltet(searchtet)) continue; // Get the "half-ball". Tets in 'cavetetlist' all contain 'steinerpt' as // opposite. Subfaces in 'caveshlist' all contain 'steinerpt' as apex. // Moreover, subfaces are oriented towards the interior of the ball. setpoint2tet(steinerpt, encode(searchtet)); getvertexstar(0, steinerpt, cavetetlist, NULL, caveshlist); // Calculate the searching vector. pa = sorg(*parysh); pb = sdest(*parysh); pc = sapex(*parysh); facenormal(pa, pb, pc, v1, 1, NULL); len = sqrt(dot(v1, v1)); v1[0] /= len; v1[1] /= len; v1[2] /= len; if (vt == FREESEGVERTEX) { parysh = (face*)fastlookup(cavesegshlist, (i + 1) % n); pd = sapex(*parysh); facenormal(pb, pa, pd, v2, 1, NULL); len = sqrt(dot(v2, v2)); v2[0] /= len; v2[1] /= len; v2[2] /= len; // Average the two vectors. v1[0] = 0.5 * (v1[0] + v2[0]); v1[1] = 0.5 * (v1[1] + v2[1]); v1[2] = 0.5 * (v1[2] + v2[2]); } // Search the intersection of the ray starting from 'steinerpt' to // the search direction 'v1' and the shell of the half-ball. // - Construct an endpoint. len = distance(pa, pb); v2[0] = steinerpt[0] + len * v1[0]; v2[1] = steinerpt[1] + len * v1[1]; v2[2] = steinerpt[2] + len * v1[2]; for (j = 0; j < cavetetlist->objects; j++) { parytet = (triface*)fastlookup(cavetetlist, j); pa = org(*parytet); pb = dest(*parytet); pc = apex(*parytet); // Test if the ray startpt->v2 lies in the cone: where 'steinerpt' // is the apex, and three sides are defined by the triangle // [pa, pb, pc]. ori = orient3d(steinerpt, pa, pb, v2); if (ori >= 0) { ori = orient3d(steinerpt, pb, pc, v2); if (ori >= 0) { ori = orient3d(steinerpt, pc, pa, v2); if (ori >= 0) { // Found! Calculate the intersection. planelineint(pa, pb, pc, steinerpt, v2, startpt, &u); break; } } } } // j if (j == cavetetlist->objects) { break; // There is no intersection!! Debug is needed. } // Close the ball by adding the subfaces. for (j = 0; j < caveshlist->objects; j++) { parysh = (face*)fastlookup(caveshlist, j); stpivot(*parysh, neightet); cavetetlist->newindex((void**)&parytet); *parytet = neightet; } // Search a best point inside the segment [startpt, steinerpt]. it = 0; samplesize = 100; v1[0] = steinerpt[0] - startpt[0]; v1[1] = steinerpt[1] - startpt[1]; v1[2] = steinerpt[2] - startpt[2]; minvol = -1.0; while (it < 3) { for (j = 1; j < samplesize - 1; j++) { samplept[0] = startpt[0] + ((REAL)j / (REAL)samplesize) * v1[0]; samplept[1] = startpt[1] + ((REAL)j / (REAL)samplesize) * v1[1]; samplept[2] = startpt[2] + ((REAL)j / (REAL)samplesize) * v1[2]; // Find the minimum volume for 'samplept'. smallvol = -1; for (k = 0; k < cavetetlist->objects; k++) { parytet = (triface*)fastlookup(cavetetlist, k); pa = org(*parytet); pb = dest(*parytet); pc = apex(*parytet); ori = orient3d(pb, pa, pc, samplept); { // [2017-10-15] Rounding REAL lab = distance(pa, pb); REAL lbc = distance(pb, pc); REAL lca = distance(pc, pa); REAL lv = (lab + lbc + lca) / 3.0; REAL l3 = lv * lv * lv; if (fabs(ori) / l3 < 1e-8) ori = 0.0; } if (ori <= 0) { break; // An invalid tet. } if (smallvol == -1) { smallvol = ori; } else { if (ori < smallvol) smallvol = ori; } } // k if (k == cavetetlist->objects) { // Found a valid point. Remember it. if (minvol == -1.0) { candpt[0] = samplept[0]; candpt[1] = samplept[1]; candpt[2] = samplept[2]; minvol = smallvol; } else { if (minvol < smallvol) { // It is a better location. Remember it. candpt[0] = samplept[0]; candpt[1] = samplept[1]; candpt[2] = samplept[2]; minvol = smallvol; } else { // No improvement of smallest volume. // Since we are searching along the line [startpt, steinerpy], // The smallest volume can only be decreased later. break; } } } } // j if (minvol > 0) break; samplesize *= 10; it++; } // while (it < 3) if (minvol == -1.0) { // Failed to find a valid point. cavetetlist->restart(); caveshlist->restart(); break; } // Create a new Steiner point inside this section. makepoint(&(newsteiners[i]), FREEVOLVERTEX); newsteiners[i][0] = candpt[0]; newsteiners[i][1] = candpt[1]; newsteiners[i][2] = candpt[2]; cavetetlist->restart(); caveshlist->restart(); } // i if (i < cavesegshlist->objects) { // Failed to suppress the vertex. for (; i > 0; i--) { if (newsteiners[i - 1] != NULL) { pointdealloc(newsteiners[i - 1]); } } delete[] newsteiners; cavesegshlist->restart(); return 0; } // Remove p from the segment or the facet. triface newtet, newface, spintet; face newsh, neighsh; face *splitseg, checkseg; int slawson = 0; // Do not do flip afterword. int t1ver; if (vt == FREESEGVERTEX) { // Detach 'leftseg' and 'rightseg' from their adjacent tets. // These two subsegments will be deleted. sstpivot1(leftseg, neightet); spintet = neightet; while (1) { tssdissolve1(spintet); fnextself(spintet); if (spintet.tet == neightet.tet) break; } sstpivot1(rightseg, neightet); spintet = neightet; while (1) { tssdissolve1(spintet); fnextself(spintet); if (spintet.tet == neightet.tet) break; } } // Loop through all sectors bounded by facets at this segment. // Within each sector, create a new Steiner point 'np', and replace 'p' // by 'np' for all tets in this sector. for (i = 0; i < cavesegshlist->objects; i++) { parysh = (face*)fastlookup(cavesegshlist, i); // 'parysh' is the face [lpt, steinerpt, #]. stpivot(*parysh, neightet); // Get all tets in this sector. setpoint2tet(steinerpt, encode(neightet)); getvertexstar(0, steinerpt, cavetetlist, NULL, caveshlist); if (!ishulltet(neightet)) { // Within each tet in the ball, replace 'p' by 'np'. for (j = 0; j < cavetetlist->objects; j++) { parytet = (triface*)fastlookup(cavetetlist, j); setoppo(*parytet, newsteiners[i]); } // j // Point to a parent tet. parytet = (triface*)fastlookup(cavetetlist, 0); setpoint2tet(newsteiners[i], (tetrahedron)(parytet->tet)); st_volref_count++; if (steinerleft > 0) steinerleft--; } // Disconnect the set of boundary faces. They're temporarily open faces. // They will be connected to the new tets after 'p' is removed. for (j = 0; j < caveshlist->objects; j++) { // Get a boundary face. parysh = (face*)fastlookup(caveshlist, j); stpivot(*parysh, neightet); // assert(apex(neightet) == newpt); // Clear the connection at this face. dissolve(neightet); tsdissolve(neightet); } // Clear the working lists. cavetetlist->restart(); caveshlist->restart(); } // i cavesegshlist->restart(); if (vt == FREESEGVERTEX) { spivot(rightseg, parentsh); // 'rightseg' has p as its origin. splitseg = &rightseg; } else { if (sdest(parentsh) == steinerpt) { senextself(parentsh); } else if (sapex(parentsh) == steinerpt) { senext2self(parentsh); } splitseg = NULL; } sremovevertex(steinerpt, &parentsh, splitseg, slawson); if (vt == FREESEGVERTEX) { // The original segment is returned in 'rightseg'. rightseg.shver = 0; } // For each new subface, create two new tets at each side of it. // Both of the two new tets have its opposite be dummypoint. for (i = 0; i < caveshbdlist->objects; i++) { parysh = (face*)fastlookup(caveshbdlist, i); sinfect(*parysh); // Mark it for connecting new tets. newsh = *parysh; pa = sorg(newsh); pb = sdest(newsh); pc = sapex(newsh); maketetrahedron(&newtet); maketetrahedron(&neightet); setvertices(newtet, pa, pb, pc, dummypoint); setvertices(neightet, pb, pa, pc, dummypoint); bond(newtet, neightet); tsbond(newtet, newsh); sesymself(newsh); tsbond(neightet, newsh); } // Temporarily increase the hullsize. hullsize += (caveshbdlist->objects * 2l); if (vt == FREESEGVERTEX) { // Connecting new tets at the recovered segment. spivot(rightseg, parentsh); spinsh = parentsh; while (1) { if (sorg(spinsh) != lpt) sesymself(spinsh); // Get the new tet at this subface. stpivot(spinsh, newtet); tssbond1(newtet, rightseg); // Go to the other face at this segment. spivot(spinsh, neighsh); if (sorg(neighsh) != lpt) sesymself(neighsh); sesymself(neighsh); stpivot(neighsh, neightet); tssbond1(neightet, rightseg); sstbond1(rightseg, neightet); // Connecting two adjacent tets at this segment. esymself(newtet); esymself(neightet); // Connect the two tets (at rightseg) together. bond(newtet, neightet); // Go to the next subface. spivotself(spinsh); if (spinsh.sh == parentsh.sh) break; } } // Connecting new tets at new subfaces together. for (i = 0; i < caveshbdlist->objects; i++) { parysh = (face*)fastlookup(caveshbdlist, i); newsh = *parysh; // assert(sinfected(newsh)); // Each new subface contains two new tets. for (k = 0; k < 2; k++) { stpivot(newsh, newtet); for (j = 0; j < 3; j++) { // Check if this side is open. esym(newtet, newface); if (newface.tet[newface.ver & 3] == NULL) { // An open face. Connect it to its adjacent tet. sspivot(newsh, checkseg); if (checkseg.sh != NULL) { // A segment. It must not be the recovered segment. tssbond1(newtet, checkseg); sstbond1(checkseg, newtet); } spivot(newsh, neighsh); if (neighsh.sh != NULL) { // The adjacent subface exists. It's not a dangling segment. if (sorg(neighsh) != sdest(newsh)) sesymself(neighsh); stpivot(neighsh, neightet); if (sinfected(neighsh)) { esymself(neightet); } else { // Search for an open face at this edge. spintet = neightet; while (1) { esym(spintet, searchtet); fsym(searchtet, spintet); if (spintet.tet == NULL) break; } // Found an open face at 'searchtet'. neightet = searchtet; } } else { // The edge (at 'newsh') is a dangling segment. // Get an adjacent tet at this segment. sstpivot1(checkseg, neightet); if (org(neightet) != sdest(newsh)) esymself(neightet); // Search for an open face at this edge. spintet = neightet; while (1) { esym(spintet, searchtet); fsym(searchtet, spintet); if (spintet.tet == NULL) break; } // Found an open face at 'searchtet'. neightet = searchtet; } pc = apex(newface); if (apex(neightet) == steinerpt) { // Exterior case. The 'neightet' is a hull tet which contain // 'steinerpt'. It will be deleted after 'steinerpt' is removed. caveoldtetlist->newindex((void**)&parytet); *parytet = neightet; // Connect newface to the adjacent hull tet of 'neightet', which // has the same edge as 'newface', and does not has 'steinerpt'. fnextself(neightet); } else { if (pc == dummypoint) { if (apex(neightet) != dummypoint) { setapex(newface, apex(neightet)); // A hull tet has turned into an interior tet. hullsize--; // Must update the hullsize. } } } bond(newface, neightet); } // if (newface.tet[newface.ver & 3] == NULL) enextself(newtet); senextself(newsh); } // j sesymself(newsh); } // k } // i // Unmark all new subfaces. for (i = 0; i < caveshbdlist->objects; i++) { parysh = (face*)fastlookup(caveshbdlist, i); suninfect(*parysh); } caveshbdlist->restart(); if (caveoldtetlist->objects > 0l) { // Delete hull tets which contain 'steinerpt'. for (i = 0; i < caveoldtetlist->objects; i++) { parytet = (triface*)fastlookup(caveoldtetlist, i); tetrahedrondealloc(parytet->tet); } // Must update the hullsize. hullsize -= caveoldtetlist->objects; caveoldtetlist->restart(); } setpointtype(steinerpt, UNUSEDVERTEX); unuverts++; if (vt == FREESEGVERTEX) { st_segref_count--; } else { // vt == FREEFACETVERTEX st_facref_count--; } if (steinerleft > 0) steinerleft++; // We've removed a Steiner points. point* parypt; int steinercount = 0; int bak_fliplinklevel = b->fliplinklevel; b->fliplinklevel = 100000; // Unlimited flip level. // Try to remove newly added Steiner points. for (i = 0; i < n; i++) { if (newsteiners[i] != NULL) { if (!removevertexbyflips(newsteiners[i])) { if (b->supsteiner_level > 0) { // Not -Y/0 // Save it in subvertstack for removal. subvertstack->newindex((void**)&parypt); *parypt = newsteiners[i]; } steinercount++; } } } b->fliplinklevel = bak_fliplinklevel; if (steinercount > 0) { if (b->verbose > 2) { printf(" Added %d interior Steiner points.\n", steinercount); } } delete[] newsteiners; return 1; } /////////////////////////////////////////////////////////////////////////////// // // // suppresssteinerpoints() Suppress Steiner points. // // // // All Steiner points have been saved in 'subvertstack' in the routines // // carveholes() and suppresssteinerpoint(). // // Each Steiner point is either removed or shifted into the interior. // // // /////////////////////////////////////////////////////////////////////////////// int tetgenmesh::suppresssteinerpoints() { if (!b->quiet) { printf("Suppressing Steiner points ...\n"); } point rempt, *parypt; int bak_fliplinklevel = b->fliplinklevel; b->fliplinklevel = 100000; // Unlimited flip level. int suppcount = 0, remcount = 0; int i; // Try to suppress boundary Steiner points. for (i = 0; i < subvertstack->objects; i++) { parypt = (point*)fastlookup(subvertstack, i); rempt = *parypt; if (pointtype(rempt) != UNUSEDVERTEX) { if ((pointtype(rempt) == FREESEGVERTEX) || (pointtype(rempt) == FREEFACETVERTEX)) { if (suppressbdrysteinerpoint(rempt)) { suppcount++; } } } } // i if (suppcount > 0) { if (b->verbose) { printf(" Suppressed %d boundary Steiner points.\n", suppcount); } } if (b->supsteiner_level > 0) { // -Y/1 for (i = 0; i < subvertstack->objects; i++) { parypt = (point*)fastlookup(subvertstack, i); rempt = *parypt; if (pointtype(rempt) != UNUSEDVERTEX) { if (pointtype(rempt) == FREEVOLVERTEX) { if (removevertexbyflips(rempt)) { remcount++; } } } } } if (remcount > 0) { if (b->verbose) { printf(" Removed %d interior Steiner points.\n", remcount); } } b->fliplinklevel = bak_fliplinklevel; if (b->supsteiner_level > 1) { // -Y/2 // Smooth interior Steiner points. optparameters opm; triface* parytet; point* ppt; REAL ori; int smtcount, count, ivcount; int nt, j; // Point smooth options. opm.max_min_volume = 1; opm.numofsearchdirs = 20; opm.searchstep = 0.001; opm.maxiter = 30; // Limit the maximum iterations. smtcount = 0; do { nt = 0; while (1) { count = 0; ivcount = 0; // Clear the inverted count. for (i = 0; i < subvertstack->objects; i++) { parypt = (point*)fastlookup(subvertstack, i); rempt = *parypt; if (pointtype(rempt) == FREEVOLVERTEX) { getvertexstar(1, rempt, cavetetlist, NULL, NULL); // Calculate the initial smallest volume (maybe zero or negative). for (j = 0; j < cavetetlist->objects; j++) { parytet = (triface*)fastlookup(cavetetlist, j); ppt = (point*)&(parytet->tet[4]); ori = orient3dfast(ppt[1], ppt[0], ppt[2], ppt[3]); if (j == 0) { opm.initval = ori; } else { if (opm.initval > ori) opm.initval = ori; } } if (smoothpoint(rempt, cavetetlist, 1, &opm)) { count++; } if (opm.imprval <= 0.0) { ivcount++; // The mesh contains inverted elements. } cavetetlist->restart(); } } // i smtcount += count; if (count == 0) { // No point has been smoothed. break; } nt++; if (nt > 2) { break; // Already three iterations. } } // while if (ivcount > 0) { // There are inverted elements! if (opm.maxiter > 0) { // Set unlimited smoothing steps. Try again. opm.numofsearchdirs = 30; opm.searchstep = 0.0001; opm.maxiter = -1; continue; } } break; } while (1); // Additional loop for (ivcount > 0) if (ivcount > 0) { printf("BUG Report! The mesh contain inverted elements.\n"); } if (b->verbose) { if (smtcount > 0) { printf(" Smoothed %d Steiner points.\n", smtcount); } } } // -Y2 subvertstack->restart(); return 1; } /////////////////////////////////////////////////////////////////////////////// // // // recoverboundary() Recover segments and facets. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::recoverboundary(clock_t& tv) { arraypool *misseglist, *misshlist; arraypool* bdrysteinerptlist; face searchsh, *parysh; face searchseg, *paryseg; point rempt, *parypt; long ms; // The number of missing segments/subfaces. int nit; // The number of iterations. int s, i; // Counters. long bak_segref_count, bak_facref_count, bak_volref_count; if (!b->quiet) { printf("Recovering boundaries...\n"); } if (b->verbose) { printf(" Recovering segments.\n"); } // Segments will be introduced. checksubsegflag = 1; misseglist = new arraypool(sizeof(face), 8); bdrysteinerptlist = new arraypool(sizeof(point), 8); // In random order. subsegs->traversalinit(); for (i = 0; i < subsegs->items; i++) { s = randomnation(i + 1); // Move the s-th seg to the i-th. subsegstack->newindex((void**)&paryseg); *paryseg = *(face*)fastlookup(subsegstack, s); // Put i-th seg to be the s-th. searchseg.sh = shellfacetraverse(subsegs); paryseg = (face*)fastlookup(subsegstack, s); *paryseg = searchseg; } // The init number of missing segments. ms = subsegs->items; nit = 0; if (b->fliplinklevel < 0) { autofliplinklevel = 1; // Init value. } // First, trying to recover segments by only doing flips. while (1) { recoversegments(misseglist, 0, 0); if (misseglist->objects > 0) { if (b->fliplinklevel >= 0) { break; } else { if (misseglist->objects >= ms) { nit++; if (nit >= 3) { // break; // Do the last round with unbounded flip link level. b->fliplinklevel = 100000; } } else { ms = misseglist->objects; if (nit > 0) { nit--; } } for (i = 0; i < misseglist->objects; i++) { subsegstack->newindex((void**)&paryseg); *paryseg = *(face*)fastlookup(misseglist, i); } misseglist->restart(); autofliplinklevel += b->fliplinklevelinc; } } else { // All segments are recovered. break; } } // while (1) if (b->verbose) { printf(" %ld (%ld) segments are recovered (missing).\n", subsegs->items - misseglist->objects, misseglist->objects); } if (misseglist->objects > 0) { // Second, trying to recover segments by doing more flips (fullsearch). while (misseglist->objects > 0) { ms = misseglist->objects; for (i = 0; i < misseglist->objects; i++) { subsegstack->newindex((void**)&paryseg); *paryseg = *(face*)fastlookup(misseglist, i); } misseglist->restart(); recoversegments(misseglist, 1, 0); if (misseglist->objects < ms) { // The number of missing segments is reduced. continue; } else { break; } } if (b->verbose) { printf(" %ld (%ld) segments are recovered (missing).\n", subsegs->items - misseglist->objects, misseglist->objects); } } if (misseglist->objects > 0) { // Third, trying to recover segments by doing more flips (fullsearch) // and adding Steiner points in the volume. while (misseglist->objects > 0) { ms = misseglist->objects; for (i = 0; i < misseglist->objects; i++) { subsegstack->newindex((void**)&paryseg); *paryseg = *(face*)fastlookup(misseglist, i); } misseglist->restart(); recoversegments(misseglist, 1, 1); if (misseglist->objects < ms) { // The number of missing segments is reduced. continue; } else { break; } } if (b->verbose) { printf(" Added %ld Steiner points in volume.\n", st_volref_count); } } if (misseglist->objects > 0) { // Last, trying to recover segments by doing more flips (fullsearch), // and adding Steiner points in the volume, and splitting segments. long bak_inpoly_count = st_volref_count; // st_inpoly_count; for (i = 0; i < misseglist->objects; i++) { subsegstack->newindex((void**)&paryseg); *paryseg = *(face*)fastlookup(misseglist, i); } misseglist->restart(); recoversegments(misseglist, 1, 2); if (b->verbose) { printf(" Added %ld Steiner points in segments.\n", st_segref_count); if (st_volref_count > bak_inpoly_count) { printf(" Added another %ld Steiner points in volume.\n", st_volref_count - bak_inpoly_count); } } } if (st_segref_count > 0) { // Try to remove the Steiner points added in segments. bak_segref_count = st_segref_count; bak_volref_count = st_volref_count; for (i = 0; i < subvertstack->objects; i++) { // Get the Steiner point. parypt = (point*)fastlookup(subvertstack, i); rempt = *parypt; if (!removevertexbyflips(rempt)) { // Save it in list. bdrysteinerptlist->newindex((void**)&parypt); *parypt = rempt; } } if (b->verbose) { if (st_segref_count < bak_segref_count) { if (bak_volref_count < st_volref_count) { printf(" Suppressed %ld Steiner points in segments.\n", st_volref_count - bak_volref_count); } if ((st_segref_count + (st_volref_count - bak_volref_count)) < bak_segref_count) { printf(" Removed %ld Steiner points in segments.\n", bak_segref_count - (st_segref_count + (st_volref_count - bak_volref_count))); } } } subvertstack->restart(); } tv = clock(); if (b->verbose) { printf(" Recovering facets.\n"); } // Subfaces will be introduced. checksubfaceflag = 1; misshlist = new arraypool(sizeof(face), 8); // Randomly order the subfaces. subfaces->traversalinit(); for (i = 0; i < subfaces->items; i++) { s = randomnation(i + 1); // Move the s-th subface to the i-th. subfacstack->newindex((void**)&parysh); *parysh = *(face*)fastlookup(subfacstack, s); // Put i-th subface to be the s-th. searchsh.sh = shellfacetraverse(subfaces); parysh = (face*)fastlookup(subfacstack, s); *parysh = searchsh; } ms = subfaces->items; nit = 0; b->fliplinklevel = -1; // Init. if (b->fliplinklevel < 0) { autofliplinklevel = 1; // Init value. } while (1) { recoversubfaces(misshlist, 0); if (misshlist->objects > 0) { if (b->fliplinklevel >= 0) { break; } else { if (misshlist->objects >= ms) { nit++; if (nit >= 3) { // break; // Do the last round with unbounded flip link level. b->fliplinklevel = 100000; } } else { ms = misshlist->objects; if (nit > 0) { nit--; } } for (i = 0; i < misshlist->objects; i++) { subfacstack->newindex((void**)&parysh); *parysh = *(face*)fastlookup(misshlist, i); } misshlist->restart(); autofliplinklevel += b->fliplinklevelinc; } } else { // All subfaces are recovered. break; } } // while (1) if (b->verbose) { printf(" %ld (%ld) subfaces are recovered (missing).\n", subfaces->items - misshlist->objects, misshlist->objects); } if (misshlist->objects > 0) { // There are missing subfaces. Add Steiner points. for (i = 0; i < misshlist->objects; i++) { subfacstack->newindex((void**)&parysh); *parysh = *(face*)fastlookup(misshlist, i); } misshlist->restart(); recoversubfaces(NULL, 1); if (b->verbose) { printf(" Added %ld Steiner points in facets.\n", st_facref_count); } } if (st_facref_count > 0) { // Try to remove the Steiner points added in facets. bak_facref_count = st_facref_count; for (i = 0; i < subvertstack->objects; i++) { // Get the Steiner point. parypt = (point*)fastlookup(subvertstack, i); rempt = *parypt; if (!removevertexbyflips(*parypt)) { // Save it in list. bdrysteinerptlist->newindex((void**)&parypt); *parypt = rempt; } } if (b->verbose) { if (st_facref_count < bak_facref_count) { printf(" Removed %ld Steiner points in facets.\n", bak_facref_count - st_facref_count); } } subvertstack->restart(); } if (bdrysteinerptlist->objects > 0) { if (b->verbose) { printf(" %ld Steiner points remained in boundary.\n", bdrysteinerptlist->objects); } } // if // Accumulate the dynamic memory. totalworkmemory += (misseglist->totalmemory + misshlist->totalmemory + bdrysteinerptlist->totalmemory); delete bdrysteinerptlist; delete misseglist; delete misshlist; } //// //// //// //// //// steiner_cxx ////////////////////////////////////////////////////////////// //// reconstruct_cxx ////////////////////////////////////////////////////////// //// //// //// //// /////////////////////////////////////////////////////////////////////////////// // // // carveholes() Remove tetrahedra not in the mesh domain. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::carveholes() { arraypool *tetarray, *hullarray; triface tetloop, neightet, *parytet, *parytet1; triface* regiontets = NULL; face checksh, *parysh; face checkseg; point ptloop, *parypt; int t1ver; int i, j, k; if (!b->quiet) { if (b->convex) { printf("Marking exterior tetrahedra ...\n"); } else { printf("Removing exterior tetrahedra ...\n"); } } // Initialize the pool of exterior tets. tetarray = new arraypool(sizeof(triface), 10); hullarray = new arraypool(sizeof(triface), 10); // Collect unprotected tets and hull tets. tetrahedrons->traversalinit(); tetloop.ver = 11; // The face opposite to dummypoint. tetloop.tet = alltetrahedrontraverse(); while (tetloop.tet != (tetrahedron*)NULL) { if (ishulltet(tetloop)) { // Is this side protected by a subface? if (!issubface(tetloop)) { // Collect an unprotected hull tet and tet. infect(tetloop); hullarray->newindex((void**)&parytet); *parytet = tetloop; // tetloop's face number is 11 & 3 = 3. decode(tetloop.tet[3], neightet); if (!infected(neightet)) { infect(neightet); tetarray->newindex((void**)&parytet); *parytet = neightet; } } } tetloop.tet = alltetrahedrontraverse(); } if (in->numberofholes > 0) { // Mark as infected any tets inside volume holes. for (i = 0; i < 3 * in->numberofholes; i += 3) { // Search a tet containing the i-th hole point. neightet.tet = NULL; randomsample(&(in->holelist[i]), &neightet); if (locate(&(in->holelist[i]), &neightet) != OUTSIDE) { // The tet 'neightet' contain this point. if (!infected(neightet)) { infect(neightet); tetarray->newindex((void**)&parytet); *parytet = neightet; // Add its adjacent tet if it is not protected. if (!issubface(neightet)) { decode(neightet.tet[neightet.ver & 3], tetloop); if (!infected(tetloop)) { infect(tetloop); if (ishulltet(tetloop)) { hullarray->newindex((void**)&parytet); } else { tetarray->newindex((void**)&parytet); } *parytet = tetloop; } } else { // It is protected. Check if its adjacent tet is a hull tet. decode(neightet.tet[neightet.ver & 3], tetloop); if (ishulltet(tetloop)) { // It is hull tet, add it into the list. Moreover, the subface // is dead, i.e., both sides are in exterior. if (!infected(tetloop)) { infect(tetloop); hullarray->newindex((void**)&parytet); *parytet = tetloop; } } if (infected(tetloop)) { // Both sides of this subface are in exterior. tspivot(neightet, checksh); sinfect(checksh); // Only queue it once. subfacstack->newindex((void**)&parysh); *parysh = checksh; } } } // if (!infected(neightet)) } else { // A hole point locates outside of the convex hull. if (!b->quiet) { printf("Warning: The %d-th hole point ", i / 3 + 1); printf("lies outside the convex hull.\n"); } } } // i } // if (in->numberofholes > 0) if (b->hole_mesh && (b->hole_mesh_filename[0] != 0)) { // A hole mesh (***.ele) is given. // enum tetgenbehavior::objecttype object; char filebasename[256]; strcpy(filebasename, b->hole_mesh_filename); // object = tetgenbehavior::MESH; if (!strcmp(&filebasename[strlen(filebasename) - 4], ".ele")) { filebasename[strlen(filebasename) - 4] = '\0'; // object = tetgenbehavior::MESH; } bool hole_mesh_loaded = false; tetgenio io; if (io.load_node(filebasename)) { if (io.load_tet(filebasename)) { hole_mesh_loaded = true; } } if (hole_mesh_loaded) { if (b->verbose) { printf(" Adding hole tets from the mesh %s\n", b->hole_mesh_filename); } int count = 0, hcount = 0, scount = 0; int shift = io.firstnumber > 0 ? -1 : 0; double *p1, *p2, *p3, *p4; double searchpt[3]; for (i = 0; i < io.numberoftetrahedra; i++) { int* idx = &(io.tetrahedronlist[i * 4]); p1 = &(io.pointlist[(idx[0] + shift) * 3]); p2 = &(io.pointlist[(idx[1] + shift) * 3]); p3 = &(io.pointlist[(idx[2] + shift) * 3]); p4 = &(io.pointlist[(idx[3] + shift) * 3]); for (j = 0; j < 3; j++) { searchpt[j] = (p1[j] + p2[j] + p3[j] + p4[j]) / 4.; } // Search the point. neightet.tet = NULL; if (locate(searchpt, &neightet) != OUTSIDE) { // The tet 'neightet' contain this point. if (!infected(neightet)) { infect(neightet); tetarray->newindex((void**)&parytet); *parytet = neightet; count++; // Add its adjacent tet if it is not protected. if (!issubface(neightet)) { decode(neightet.tet[neightet.ver & 3], tetloop); if (!infected(tetloop)) { infect(tetloop); if (ishulltet(tetloop)) { hullarray->newindex((void**)&parytet); hcount++; } else { tetarray->newindex((void**)&parytet); count++; } *parytet = tetloop; } } else { // It is protected. Check if its adjacent tet is a hull tet. decode(neightet.tet[neightet.ver & 3], tetloop); if (ishulltet(tetloop)) { // It is hull tet, add it into the list. Moreover, the subface // is dead, i.e., both sides are in exterior. if (!infected(tetloop)) { infect(tetloop); hullarray->newindex((void**)&parytet); *parytet = tetloop; hcount++; } } if (infected(tetloop)) { // Both sides of this subface are in exterior. tspivot(neightet, checksh); sinfect(checksh); // Only queue it once. subfacstack->newindex((void**)&parysh); *parysh = checksh; scount++; } } } } } // i if (b->verbose) { printf(" Added %d hole tets, %d hull tet, %d hole subfaces\n", count, hcount, scount); } } // if (hole_mesh_loaded) } if (b->regionattrib && (in->numberofregions > 0)) { // -A option. // Record the tetrahedra that contains the region points for assigning // region attributes after the holes have been carved. regiontets = new triface[in->numberofregions]; // Mark as marktested any tetrahedra inside volume regions. for (i = 0; i < 5 * in->numberofregions; i += 5) { // Search a tet containing the i-th region point. neightet.tet = NULL; randomsample(&(in->regionlist[i]), &neightet); if (locate(&(in->regionlist[i]), &neightet) != OUTSIDE) { regiontets[i / 5] = neightet; } else { if (!b->quiet) { printf("Warning: The %d-th region point ", i / 5 + 1); printf("lies outside the convex hull.\n"); } regiontets[i / 5].tet = NULL; } } } // Collect all exterior tets (in concave place and in holes). for (i = 0; i < tetarray->objects; i++) { parytet = (triface*)fastlookup(tetarray, i); j = (parytet->ver & 3); // j is the current face number. // Check the other three adjacent tets. for (k = 1; k < 4; k++) { decode(parytet->tet[(j + k) % 4], neightet); // neightet may be a hull tet. if (!infected(neightet)) { // Is neightet protected by a subface. if (!issubface(neightet)) { // Not proected. Collect it. (It must not be a hull tet). infect(neightet); tetarray->newindex((void**)&parytet1); *parytet1 = neightet; } else { // Protected. Check if it is a hull tet. if (ishulltet(neightet)) { // A hull tet. Collect it. infect(neightet); hullarray->newindex((void**)&parytet1); *parytet1 = neightet; // Both sides of this subface are exterior. tspivot(neightet, checksh); // Queue this subface (to be deleted later). sinfect(checksh); // Only queue it once. subfacstack->newindex((void**)&parysh); *parysh = checksh; } } } else { // Both sides of this face are in exterior. // If there is a subface. It should be collected. if (issubface(neightet)) { tspivot(neightet, checksh); if (!sinfected(checksh)) { sinfect(checksh); subfacstack->newindex((void**)&parysh); *parysh = checksh; } } } } // j, k } // i if (b->regionattrib && (in->numberofregions > 0)) { // Re-check saved region tets to see if they lie outside. for (i = 0; i < in->numberofregions; i++) { if (infected(regiontets[i])) { if (b->verbose) { printf("Warning: The %d-th region point ", i + 1); printf("lies in the exterior of the domain.\n"); } regiontets[i].tet = NULL; } } } // Collect vertices which point to infected tets. These vertices // may get deleted after the removal of exterior tets. // If -Y1 option is used, collect all Steiner points for removal. // The lists 'cavetetvertlist' and 'subvertstack' are re-used. points->traversalinit(); ptloop = pointtraverse(); while (ptloop != NULL) { if ((pointtype(ptloop) != UNUSEDVERTEX) && (pointtype(ptloop) != DUPLICATEDVERTEX)) { decode(point2tet(ptloop), neightet); if (infected(neightet)) { cavetetvertlist->newindex((void**)&parypt); *parypt = ptloop; } if (b->nobisect && (b->supsteiner_level > 0)) { // -Y/1 // Queue it if it is a Steiner point. if (pointmark(ptloop) > (in->numberofpoints - (in->firstnumber ? 0 : 1))) { subvertstack->newindex((void**)&parypt); *parypt = ptloop; } } } ptloop = pointtraverse(); } if (!b->convex && (tetarray->objects > 0l)) { // No -c option. // Remove exterior tets. Hull tets are updated. arraypool* newhullfacearray; triface hulltet, casface; face segloop, *paryseg; point pa, pb, pc; long delsegcount = 0l; // Collect segments which point to infected tets. Some segments // may get deleted after the removal of exterior tets. subsegs->traversalinit(); segloop.sh = shellfacetraverse(subsegs); while (segloop.sh != NULL) { sstpivot1(segloop, neightet); if (infected(neightet)) { subsegstack->newindex((void**)&paryseg); *paryseg = segloop; } segloop.sh = shellfacetraverse(subsegs); } newhullfacearray = new arraypool(sizeof(triface), 10); // Create and save new hull tets. for (i = 0; i < tetarray->objects; i++) { parytet = (triface*)fastlookup(tetarray, i); for (j = 0; j < 4; j++) { decode(parytet->tet[j], tetloop); if (!infected(tetloop)) { // Found a new hull face (must be a subface). tspivot(tetloop, checksh); maketetrahedron(&hulltet); pa = org(tetloop); pb = dest(tetloop); pc = apex(tetloop); setvertices(hulltet, pb, pa, pc, dummypoint); bond(tetloop, hulltet); // Update the subface-to-tet map. sesymself(checksh); tsbond(hulltet, checksh); // Update the segment-to-tet map. for (k = 0; k < 3; k++) { if (issubseg(tetloop)) { tsspivot1(tetloop, checkseg); tssbond1(hulltet, checkseg); sstbond1(checkseg, hulltet); } enextself(tetloop); eprevself(hulltet); } // Update the point-to-tet map. setpoint2tet(pa, (tetrahedron)tetloop.tet); setpoint2tet(pb, (tetrahedron)tetloop.tet); setpoint2tet(pc, (tetrahedron)tetloop.tet); // Save the exterior tet at this hull face. It still holds pointer // to the adjacent interior tet. Use it to connect new hull tets. newhullfacearray->newindex((void**)&parytet1); parytet1->tet = parytet->tet; parytet1->ver = j; } // if (!infected(tetloop)) } // j } // i // Connect new hull tets. for (i = 0; i < newhullfacearray->objects; i++) { parytet = (triface*)fastlookup(newhullfacearray, i); fsym(*parytet, neightet); // Get the new hull tet. fsym(neightet, hulltet); for (j = 0; j < 3; j++) { esym(hulltet, casface); if (casface.tet[casface.ver & 3] == NULL) { // Since the boundary of the domain may not be a manifold, we // find the adjacent hull face by traversing the tets in the // exterior (which are all infected tets). neightet = *parytet; while (1) { fnextself(neightet); if (!infected(neightet)) break; } if (!ishulltet(neightet)) { // An interior tet. Get the new hull tet. fsymself(neightet); esymself(neightet); } // Bond them together. bond(casface, neightet); } enextself(hulltet); enextself(*parytet); } // j } // i if (subfacstack->objects > 0l) { // Remove all subfaces which do not attach to any tetrahedron. // Segments which are not attached to any subfaces and tets // are deleted too. face casingout, casingin; for (i = 0; i < subfacstack->objects; i++) { parysh = (face*)fastlookup(subfacstack, i); if (i == 0) { if (b->verbose) { printf("Warning: Removed an exterior face (%d, %d, %d) #%d\n", pointmark(sorg(*parysh)), pointmark(sdest(*parysh)), pointmark(sapex(*parysh)), shellmark(*parysh)); } } // Dissolve this subface from face links. for (j = 0; j < 3; j++) { spivot(*parysh, casingout); sspivot(*parysh, checkseg); if (casingout.sh != NULL) { casingin = casingout; while (1) { spivot(casingin, checksh); if (checksh.sh == parysh->sh) break; casingin = checksh; } if (casingin.sh != casingout.sh) { // Update the link: ... -> casingin -> casingout ->... sbond1(casingin, casingout); } else { // Only one subface at this edge is left. sdissolve(casingout); } if (checkseg.sh != NULL) { // Make sure the segment does not connect to a dead one. ssbond(casingout, checkseg); } } else { if (checkseg.sh != NULL) { // if (checkseg.sh[3] != NULL) { if (delsegcount == 0) { if (b->verbose) { printf("Warning: Removed an exterior segment (%d, %d) #%d\n", pointmark(sorg(checkseg)), pointmark(sdest(checkseg)), shellmark(checkseg)); } } shellfacedealloc(subsegs, checkseg.sh); delsegcount++; } } senextself(*parysh); } // j // Delete this subface. shellfacedealloc(subfaces, parysh->sh); } // i if (b->verbose) { printf(" Deleted %ld subfaces.\n", subfacstack->objects); } subfacstack->restart(); } // if (subfacstack->objects > 0l) if (subsegstack->objects > 0l) { for (i = 0; i < subsegstack->objects; i++) { paryseg = (face*)fastlookup(subsegstack, i); if (paryseg->sh && (paryseg->sh[3] != NULL)) { sstpivot1(*paryseg, neightet); if (infected(neightet)) { if (b->verbose) { printf("Warning: Removed an exterior segment (%d, %d) #%d\n", pointmark(sorg(*paryseg)), pointmark(sdest(*paryseg)), shellmark(*paryseg)); } shellfacedealloc(subsegs, paryseg->sh); delsegcount++; } } } subsegstack->restart(); } // if (subsegstack->objects > 0l) if (delsegcount > 0) { if (b->verbose) { printf(" Deleted %ld segments.\n", delsegcount); } } if (cavetetvertlist->objects > 0l) { // Some vertices may lie in exterior. Marke them as UNUSEDVERTEX. long delvertcount = unuverts; long delsteinercount = 0l; for (i = 0; i < cavetetvertlist->objects; i++) { parypt = (point*)fastlookup(cavetetvertlist, i); decode(point2tet(*parypt), neightet); if (infected(neightet)) { // Found an exterior vertex. if (pointmark(*parypt) > (in->numberofpoints - (in->firstnumber ? 0 : 1))) { // A Steiner point. if (pointtype(*parypt) == FREESEGVERTEX) { st_segref_count--; } else if (pointtype(*parypt) == FREEFACETVERTEX) { st_facref_count--; } else { st_volref_count--; } delsteinercount++; if (steinerleft > 0) steinerleft++; } setpointtype(*parypt, UNUSEDVERTEX); unuverts++; } } if (b->verbose) { if (unuverts > delvertcount) { if (delsteinercount > 0l) { if (unuverts > (delvertcount + delsteinercount)) { printf(" Removed %ld exterior input vertices.\n", unuverts - delvertcount - delsteinercount); } printf(" Removed %ld exterior Steiner vertices.\n", delsteinercount); } else { printf(" Removed %ld exterior input vertices.\n", unuverts - delvertcount); } } } cavetetvertlist->restart(); // Comment: 'subvertstack' will be cleaned in routine // suppresssteinerpoints(). } // if (cavetetvertlist->objects > 0l) // Update the hull size. hullsize += (newhullfacearray->objects - hullarray->objects); // Delete all exterior tets and old hull tets. for (i = 0; i < tetarray->objects; i++) { parytet = (triface*)fastlookup(tetarray, i); tetrahedrondealloc(parytet->tet); } tetarray->restart(); for (i = 0; i < hullarray->objects; i++) { parytet = (triface*)fastlookup(hullarray, i); tetrahedrondealloc(parytet->tet); } hullarray->restart(); delete newhullfacearray; } // if (!b->convex && (tetarray->objects > 0l)) if (b->convex && (tetarray->objects > 0l)) { // With -c option // In this case, all exterior tets get a region marker '-1'. int attrnum = numelemattrib - 1; for (i = 0; i < tetarray->objects; i++) { parytet = (triface*)fastlookup(tetarray, i); setelemattribute(parytet->tet, attrnum, -1); } tetarray->restart(); for (i = 0; i < hullarray->objects; i++) { parytet = (triface*)fastlookup(hullarray, i); uninfect(*parytet); } hullarray->restart(); if (subfacstack->objects > 0l) { for (i = 0; i < subfacstack->objects; i++) { parysh = (face*)fastlookup(subfacstack, i); suninfect(*parysh); } subfacstack->restart(); } if (cavetetvertlist->objects > 0l) { cavetetvertlist->restart(); } } // if (b->convex && (tetarray->objects > 0l)) if (b->regionattrib) { // With -A option. if (!b->quiet) { printf("Spreading region attributes.\n"); } REAL volume; int attr, maxattr = 0; // Choose a small number here. int attrnum = numelemattrib - 1; // Comment: The element region marker is at the end of the list of // the element attributes. int regioncount = 0; // If has user-defined region attributes. if (in->numberofregions > 0) { // Spread region attributes. for (i = 0; i < 5 * in->numberofregions; i += 5) { if (regiontets[i / 5].tet != NULL) { attr = (int)in->regionlist[i + 3]; if (attr > maxattr) { maxattr = attr; } volume = in->regionlist[i + 4]; tetarray->restart(); // Re-use this array. infect(regiontets[i / 5]); tetarray->newindex((void**)&parytet); *parytet = regiontets[i / 5]; // Collect and set attrs for all tets of this region. for (j = 0; j < tetarray->objects; j++) { parytet = (triface*)fastlookup(tetarray, j); tetloop = *parytet; setelemattribute(tetloop.tet, attrnum, attr); if (b->varvolume) { // If has -a option. setvolumebound(tetloop.tet, volume); } for (k = 0; k < 4; k++) { decode(tetloop.tet[k], neightet); // Is the adjacent already checked? if (!infected(neightet)) { // Is this side protected by a subface? if (!issubface(neightet)) { infect(neightet); tetarray->newindex((void**)&parytet); *parytet = neightet; } } } // k } // j regioncount++; } // if (regiontets[i/5].tet != NULL) } // i } // Set attributes for all tetrahedra. attr = maxattr + 1; tetrahedrons->traversalinit(); tetloop.tet = tetrahedrontraverse(); while (tetloop.tet != (tetrahedron*)NULL) { if (!infected(tetloop)) { // An unmarked region. tetarray->restart(); // Re-use this array. infect(tetloop); tetarray->newindex((void**)&parytet); *parytet = tetloop; // Find and mark all tets. for (j = 0; j < tetarray->objects; j++) { parytet = (triface*)fastlookup(tetarray, j); tetloop = *parytet; setelemattribute(tetloop.tet, attrnum, attr); for (k = 0; k < 4; k++) { decode(tetloop.tet[k], neightet); // Is the adjacent tet already checked? if (!infected(neightet)) { // Is this side protected by a subface? if (!issubface(neightet)) { infect(neightet); tetarray->newindex((void**)&parytet); *parytet = neightet; } } } // k } // j attr++; // Increase the attribute. regioncount++; } tetloop.tet = tetrahedrontraverse(); } // Until here, every tet has a region attribute. // Uninfect processed tets. tetrahedrons->traversalinit(); tetloop.tet = tetrahedrontraverse(); while (tetloop.tet != (tetrahedron*)NULL) { uninfect(tetloop); tetloop.tet = tetrahedrontraverse(); } if (b->verbose) { // assert(regioncount > 0); if (regioncount > 1) { printf(" Found %d subdomains.\n", regioncount); } else { printf(" Found %d domain.\n", regioncount); } } } // if (b->regionattrib) if (regiontets != NULL) { delete[] regiontets; } delete tetarray; delete hullarray; if (!b->convex) { // No -c option // The mesh is non-convex now. nonconvex = 1; // Push all hull tets into 'flipstack'. tetrahedrons->traversalinit(); tetloop.ver = 11; // The face opposite to dummypoint. tetloop.tet = alltetrahedrontraverse(); while (tetloop.tet != (tetrahedron*)NULL) { if ((point)tetloop.tet[7] == dummypoint) { fsym(tetloop, neightet); flippush(flipstack, &neightet); } tetloop.tet = alltetrahedrontraverse(); } flipconstraints fc; fc.enqflag = 2; long sliver_peel_count = lawsonflip3d(&fc); if (sliver_peel_count > 0l) { if (b->verbose) { printf(" Removed %ld hull slivers.\n", sliver_peel_count); } } unflipqueue->restart(); } // if (!b->convex) } // [2018-07-30] // Search a face with given indices (i,j,k). // This function is only called when the default fast search fails. // It is possible when there are non-manifold edges on the hull. // On finish, tetloop return this face if it exists, otherwise, return 0. int tetgenmesh::search_face(point pi, point pj, point pk, triface& tetloop) { pinfect(pi); pinfect(pj); pinfect(pk); int t1ver; triface t, t1; point *pts, toppo; int pcount = 0; t.ver = t1.ver = 0; tetrahedrons->traversalinit(); t.tet = tetrahedrontraverse(); while (t.tet != NULL) { pts = (point*)t.tet; pcount = 0; if (pinfected(pts[4])) pcount++; if (pinfected(pts[5])) pcount++; if (pinfected(pts[6])) pcount++; if (pinfected(pts[7])) pcount++; if (pcount == 3) { // Found a tet containing this face. for (t.ver = 0; t.ver < 4; t.ver++) { toppo = oppo(t); if (!pinfected(toppo)) break; } int ii; for (ii = 0; ii < 3; ii++) { if (org(t) == pi) break; enextself(t); } if (dest(t) == pj) { } else { eprevself(t); fsymself(t); } break; } t.tet = tetrahedrontraverse(); } puninfect(pi); puninfect(pj); puninfect(pk); if (t.tet != NULL) { tetloop = t; return 1; } else { return 0; } } int tetgenmesh::search_edge(point p0, point p1, triface& tetloop) { triface t; int ii; tetrahedrons->traversalinit(); t.tet = tetrahedrontraverse(); while (t.tet != NULL) { for (ii = 0; ii < 6; ii++) { t.ver = edge2ver[ii]; if (((org(t) == p0) && (dest(t) == p1)) || ((org(t) == p1) && (dest(t) == p0))) { // Found the tet. tetloop = t; return 1; } } t.tet = tetrahedrontraverse(); } tetloop.tet = NULL; return 0; } /////////////////////////////////////////////////////////////////////////////// // // // reconstructmesh() Reconstruct a tetrahedral mesh. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::reconstructmesh() { tetrahedron* ver2tetarray; point* idx2verlist; triface tetloop, checktet, prevchktet; triface hulltet, face1, face2; tetrahedron tptr; face subloop, neighsh, nextsh; face segloop; shellface sptr; point p[4], q[3]; REAL ori, attrib, volume; REAL cosang_tol, cosang; REAL n1[3], n2[3]; int eextras, marker = 0; int bondflag; int t1ver; int idx, i, j, k; if (!b->quiet) { printf("Reconstructing mesh ...\n"); } if (b->convex) { // -c option. // Assume the mesh is convex. Exterior tets have region attribute -1. if (!(in->numberoftetrahedronattributes > 0)) { terminatetetgen(this, 2); } } else { // Assume the mesh is non-convex. nonconvex = 1; } // Create a map from indices to vertices. makeindex2pointmap(idx2verlist); // 'idx2verlist' has length 'in->numberofpoints + 1'. if (in->firstnumber == 1) { idx2verlist[0] = dummypoint; // Let 0th-entry be dummypoint. } // Allocate an array that maps each vertex to its adjacent tets. ver2tetarray = new tetrahedron[in->numberofpoints + 1]; unuverts = in->numberofpoints; // All vertices are unused yet. // for (i = 0; i < in->numberofpoints + 1; i++) { for (i = in->firstnumber; i < in->numberofpoints + in->firstnumber; i++) { ver2tetarray[i] = NULL; } // Create the tetrahedra and connect those that share a common face. for (i = 0; i < in->numberoftetrahedra; i++) { // Get the four vertices. idx = i * in->numberofcorners; for (j = 0; j < 4; j++) { p[j] = idx2verlist[in->tetrahedronlist[idx++]]; if (pointtype(p[j]) == UNUSEDVERTEX) { setpointtype(p[j], VOLVERTEX); // initial type. unuverts--; } } // Check the orientation. ori = orient3d(p[0], p[1], p[2], p[3]); if (ori > 0.0) { // Swap the first two vertices. q[0] = p[0]; p[0] = p[1]; p[1] = q[0]; } else if (ori == 0.0) { if (!b->quiet) { printf("Warning: Tet #%d is degenerate.\n", i + in->firstnumber); } } // Create a new tetrahedron. maketetrahedron(&tetloop); // tetloop.ver = 11. setvertices(tetloop, p[0], p[1], p[2], p[3]); // Set element attributes if they exist. for (j = 0; j < in->numberoftetrahedronattributes; j++) { idx = i * in->numberoftetrahedronattributes; attrib = in->tetrahedronattributelist[idx + j]; setelemattribute(tetloop.tet, j, attrib); } // If -a switch is used (with no number follows) Set a volume // constraint if it exists. if (b->varvolume) { if (in->tetrahedronvolumelist != (REAL*)NULL) { volume = in->tetrahedronvolumelist[i]; } else { volume = -1.0; } setvolumebound(tetloop.tet, volume); } // Try connecting this tet to others that share the common faces. for (tetloop.ver = 0; tetloop.ver < 4; tetloop.ver++) { p[3] = oppo(tetloop); // Look for other tets having this vertex. idx = pointmark(p[3]); tptr = ver2tetarray[idx]; // Link the current tet to the next one in the stack. tetloop.tet[8 + tetloop.ver] = tptr; // Push the current tet onto the stack. ver2tetarray[idx] = encode(tetloop); decode(tptr, checktet); if (checktet.tet != NULL) { p[0] = org(tetloop); // a p[1] = dest(tetloop); // b p[2] = apex(tetloop); // c prevchktet = tetloop; do { q[0] = org(checktet); // a' q[1] = dest(checktet); // b' q[2] = apex(checktet); // c' // Check the three faces at 'd' in 'checktet'. bondflag = 0; for (j = 0; j < 3; j++) { // Go to the face [b',a',d], or [c',b',d], or [a',c',d]. esym(checktet, face2); if (face2.tet[face2.ver & 3] == NULL) { k = ((j + 1) % 3); if (q[k] == p[0]) { // b', c', a' = a if (q[j] == p[1]) { // a', b', c' = b // [#,#,d] is matched to [b,a,d]. esym(tetloop, face1); bond(face1, face2); bondflag++; } } if (q[k] == p[1]) { // b',c',a' = b if (q[j] == p[2]) { // a',b',c' = c // [#,#,d] is matched to [c,b,d]. enext(tetloop, face1); esymself(face1); bond(face1, face2); bondflag++; } } if (q[k] == p[2]) { // b',c',a' = c if (q[j] == p[0]) { // a',b',c' = a // [#,#,d] is matched to [a,c,d]. eprev(tetloop, face1); esymself(face1); bond(face1, face2); bondflag++; } } } else { bondflag++; } enextself(checktet); } // j // Go to the next tet in the link. tptr = checktet.tet[8 + checktet.ver]; if (bondflag == 3) { // All three faces at d in 'checktet' have been connected. // It can be removed from the link. prevchktet.tet[8 + prevchktet.ver] = tptr; } else { // Bakup the previous tet in the link. prevchktet = checktet; } decode(tptr, checktet); } while (checktet.tet != NULL); } // if (checktet.tet != NULL) } // for (tetloop.ver = 0; ... } // i // Remember a tet of the mesh. recenttet = tetloop; // Create hull tets, create the point-to-tet map, and clean up the // temporary spaces used in each tet. hullsize = tetrahedrons->items; tetrahedrons->traversalinit(); tetloop.tet = tetrahedrontraverse(); while (tetloop.tet != (tetrahedron*)NULL) { tptr = encode(tetloop); for (tetloop.ver = 0; tetloop.ver < 4; tetloop.ver++) { if (tetloop.tet[tetloop.ver] == NULL) { // Create a hull tet. maketetrahedron(&hulltet); p[0] = org(tetloop); p[1] = dest(tetloop); p[2] = apex(tetloop); setvertices(hulltet, p[1], p[0], p[2], dummypoint); bond(tetloop, hulltet); // Try connecting this to others that share common hull edges. for (j = 0; j < 3; j++) { fsym(hulltet, face2); while (1) { if (face2.tet == NULL) break; esymself(face2); if (apex(face2) == dummypoint) break; fsymself(face2); } if (face2.tet != NULL) { // Found an adjacent hull tet. esym(hulltet, face1); bond(face1, face2); } enextself(hulltet); } } // Create the point-to-tet map. setpoint2tet((point)(tetloop.tet[4 + tetloop.ver]), tptr); // Clean the temporary used space. tetloop.tet[8 + tetloop.ver] = NULL; } tetloop.tet = tetrahedrontraverse(); } hullsize = tetrahedrons->items - hullsize; // Subfaces will be inserted into the mesh. if (in->trifacelist != NULL) { // A .face file is given. It may contain boundary faces. Insert them. for (i = 0; i < in->numberoftrifaces; i++) { // Is it a subface? if (in->trifacemarkerlist != NULL) { marker = in->trifacemarkerlist[i]; } else { // Face markers are not available. Assume all of them are subfaces. marker = -1; // The default marker. } if (marker != 0) { idx = i * 3; for (j = 0; j < 3; j++) { p[j] = idx2verlist[in->trifacelist[idx++]]; } // Search the subface. bondflag = 0; neighsh.sh = NULL; // Make sure all vertices are in the mesh. Avoid crash. for (j = 0; j < 3; j++) { decode(point2tet(p[j]), checktet); if (checktet.tet == NULL) break; } if ((j == 3) && getedge(p[0], p[1], &checktet)) { tetloop = checktet; q[2] = apex(checktet); while (1) { if (apex(tetloop) == p[2]) { // Found the face. // Check if there exist a subface already? tspivot(tetloop, neighsh); if (neighsh.sh != NULL) { // Found a duplicated subface. // This happens when the mesh was generated by other mesher. bondflag = 0; } else { bondflag = 1; } break; } fnextself(tetloop); if (apex(tetloop) == q[2]) break; } } if (!bondflag) { if (neighsh.sh == NULL) { if (b->verbose > 1) { printf("Warning: Searching subface #%d [%d,%d,%d] mark=%d.\n", i + in->firstnumber, pointmark(p[0]), pointmark(p[1]), pointmark(p[2]), marker); } // Search it globally. if (search_face(p[0], p[1], p[2], tetloop)) { bondflag = 1; } } } if (bondflag) { // Create a new subface. makeshellface(subfaces, &subloop); setshvertices(subloop, p[0], p[1], p[2]); // Create the point-to-subface map. sptr = sencode(subloop); for (j = 0; j < 3; j++) { setpointtype(p[j], FACETVERTEX); // initial type. setpoint2sh(p[j], sptr); } setshellmark(subloop, marker); // Insert the subface into the mesh. tsbond(tetloop, subloop); fsymself(tetloop); sesymself(subloop); tsbond(tetloop, subloop); } else { if (neighsh.sh != NULL) { // The subface already exists. Only set its mark. setshellmark(neighsh, marker); } else { if (!b->quiet) { printf("Warning: Subface #%d [%d,%d,%d] mark=%d is not found.\n", i + in->firstnumber, pointmark(p[0]), pointmark(p[1]), pointmark(p[2]), marker); } } } // if (bondflag) } // if (marker != 0) } // i } // if (in->trifacelist) // Indentify subfaces from the mesh. // Create subfaces for hull faces (if they're not subface yet) and // interior faces which separate two different materials. eextras = in->numberoftetrahedronattributes; tetrahedrons->traversalinit(); tetloop.tet = tetrahedrontraverse(); while (tetloop.tet != (tetrahedron*)NULL) { for (tetloop.ver = 0; tetloop.ver < 4; tetloop.ver++) { tspivot(tetloop, neighsh); if (neighsh.sh == NULL) { bondflag = 0; fsym(tetloop, checktet); if (ishulltet(checktet)) { // A hull face. if (!b->convex) { bondflag = 1; // Insert a hull subface. } } else { if (eextras > 0) { if (elemattribute(tetloop.tet, eextras - 1) != elemattribute(checktet.tet, eextras - 1)) { bondflag = 1; // Insert an interior interface. } } } if (bondflag) { // Create a new subface. makeshellface(subfaces, &subloop); p[0] = org(tetloop); p[1] = dest(tetloop); p[2] = apex(tetloop); setshvertices(subloop, p[0], p[1], p[2]); // Create the point-to-subface map. sptr = sencode(subloop); for (j = 0; j < 3; j++) { setpointtype(p[j], FACETVERTEX); // initial type. setpoint2sh(p[j], sptr); } setshellmark(subloop, -1); // Default marker. // Insert the subface into the mesh. tsbond(tetloop, subloop); sesymself(subloop); tsbond(checktet, subloop); } // if (bondflag) } // if (neighsh.sh == NULL) } tetloop.tet = tetrahedrontraverse(); } // Connect subfaces together. subfaces->traversalinit(); subloop.shver = 0; subloop.sh = shellfacetraverse(subfaces); while (subloop.sh != (shellface*)NULL) { for (i = 0; i < 3; i++) { spivot(subloop, neighsh); if (neighsh.sh == NULL) { // Form a subface ring by linking all subfaces at this edge. // Traversing all faces of the tets at this edge. stpivot(subloop, tetloop); q[2] = apex(tetloop); neighsh = subloop; while (1) { fnextself(tetloop); tspivot(tetloop, nextsh); if (nextsh.sh != NULL) { // Do not connect itself. if (nextsh.sh != neighsh.sh) { // Link neighsh <= nextsh. sbond1(neighsh, nextsh); neighsh = nextsh; } } if (apex(tetloop) == q[2]) { break; } } // while (1) } // if (neighsh.sh == NULL) senextself(subloop); } subloop.sh = shellfacetraverse(subfaces); } // Segments will be introduced. if (in->edgelist != NULL) { // A .edge file is given. It may contain boundary edges. Insert them. for (i = 0; i < in->numberofedges; i++) { // Is it a segment? if (in->edgemarkerlist != NULL) { marker = in->edgemarkerlist[i]; } else { // Edge markers are not available. Assume all of them are segments. marker = -1; // Default marker. } if (marker != 0) { // Insert a segment. idx = i * 2; for (j = 0; j < 2; j++) { p[j] = idx2verlist[in->edgelist[idx++]]; } // Make sure all vertices are in the mesh. Avoid crash. for (j = 0; j < 2; j++) { decode(point2tet(p[j]), checktet); if (checktet.tet == NULL) break; } // Search the segment. bondflag = 0; if (j == 2) { if (getedge(p[0], p[1], &checktet)) { bondflag = 1; } else { if (b->verbose > 1) { printf("Warning: Searching segment #%d [%d,%d] mark=%d.\n", i + in->firstnumber, pointmark(p[0]), pointmark(p[1]), marker); } // Search it globally. if (search_edge(p[0], p[1], checktet)) { bondflag = 1; } } } if (bondflag > 0) { // Create a new segment. makeshellface(subsegs, &segloop); setshvertices(segloop, p[0], p[1], NULL); // Create the point-to-segment map. sptr = sencode(segloop); for (j = 0; j < 2; j++) { setpointtype(p[j], RIDGEVERTEX); // initial type. setpoint2sh(p[j], sptr); } setshellmark(segloop, marker); // Insert the segment into the mesh. tetloop = checktet; q[2] = apex(checktet); subloop.sh = NULL; while (1) { tssbond1(tetloop, segloop); tspivot(tetloop, subloop); if (subloop.sh != NULL) { ssbond1(subloop, segloop); sbond1(segloop, subloop); } fnextself(tetloop); if (apex(tetloop) == q[2]) break; } // while (1) // Remember an adjacent tet for this segment. sstbond1(segloop, tetloop); } else { if (!b->quiet) { printf("Warning: Segment #%d [%d,%d] is missing.\n", i + in->firstnumber, pointmark(p[0]), pointmark(p[1])); } } } // if (marker != 0) } // i } // if (in->edgelist) // Identify segments from the mesh. // Create segments for non-manifold edges (which are shared by more // than two subfaces), and for non-coplanar edges, i.e., two subfaces // form an dihedral angle > 'b->facet_separate_ang_tol' (degree). cosang_tol = cos(b->facet_separate_ang_tol / 180.0 * PI); subfaces->traversalinit(); subloop.shver = 0; subloop.sh = shellfacetraverse(subfaces); while (subloop.sh != (shellface*)NULL) { for (i = 0; i < 3; i++) { sspivot(subloop, segloop); if (segloop.sh == NULL) { // Check if this edge is a segment. bondflag = 0; // Counter the number of subfaces at this edge. idx = 0; nextsh = subloop; while (1) { idx++; spivotself(nextsh); if (nextsh.sh == subloop.sh) break; } if (idx != 2) { // It's a non-manifold edge. Insert a segment. p[0] = sorg(subloop); p[1] = sdest(subloop); bondflag = 1; } else { spivot(subloop, neighsh); if (shellmark(subloop) != shellmark(neighsh)) { // It's an interior interface. Insert a segment. p[0] = sorg(subloop); p[1] = sdest(subloop); bondflag = 1; } else { if (!b->convex) { // Check the dihedral angle formed by the two subfaces. p[0] = sorg(subloop); p[1] = sdest(subloop); p[2] = sapex(subloop); p[3] = sapex(neighsh); facenormal(p[0], p[1], p[2], n1, 1, NULL); facenormal(p[0], p[1], p[3], n2, 1, NULL); cosang = dot(n1, n2) / (sqrt(dot(n1, n1)) * sqrt(dot(n2, n2))); // Rounding. if (cosang > 1.0) cosang = 1.0; else if (cosang < -1.0) cosang = -1.0; if (cosang > cosang_tol) { bondflag = 1; } } } } if (bondflag) { // Create a new segment. makeshellface(subsegs, &segloop); setshvertices(segloop, p[0], p[1], NULL); // Create the point-to-segment map. sptr = sencode(segloop); for (j = 0; j < 2; j++) { setpointtype(p[j], RIDGEVERTEX); // initial type. setpoint2sh(p[j], sptr); } setshellmark(segloop, -1); // Default marker. // Insert the subface into the mesh. stpivot(subloop, tetloop); q[2] = apex(tetloop); while (1) { tssbond1(tetloop, segloop); tspivot(tetloop, neighsh); if (neighsh.sh != NULL) { ssbond1(neighsh, segloop); } fnextself(tetloop); if (apex(tetloop) == q[2]) break; } // while (1) // Remember an adjacent tet for this segment. sstbond1(segloop, tetloop); sbond1(segloop, subloop); } // if (bondflag) } // if (neighsh.sh == NULL) senextself(subloop); } // i subloop.sh = shellfacetraverse(subfaces); } // Remember the number of input segments. insegments = subsegs->items; if (!b->nobisect || checkconstraints) { // Mark Steiner points on segments and facets. // - all vertices which remaining type FEACTVERTEX become // Steiner points in facets (= FREEFACERVERTEX). // - vertices on segment need to be checked. face* segperverlist; int* idx2seglist; face parentseg, nextseg; verttype vt; REAL area, len, l1, l2; int fmarker; makepoint2submap(subsegs, idx2seglist, segperverlist); points->traversalinit(); point ptloop = pointtraverse(); while (ptloop != NULL) { vt = pointtype(ptloop); if (vt == VOLVERTEX) { setpointtype(ptloop, FREEVOLVERTEX); st_volref_count++; } else if (vt == FACETVERTEX) { setpointtype(ptloop, FREEFACETVERTEX); st_facref_count++; } else if (vt == RIDGEVERTEX) { idx = pointmark(ptloop) - in->firstnumber; if ((idx2seglist[idx + 1] - idx2seglist[idx]) == 2) { i = idx2seglist[idx]; parentseg = segperverlist[i]; nextseg = segperverlist[i + 1]; sesymself(nextseg); p[0] = sorg(nextseg); p[1] = sdest(parentseg); // Check if three points p[0], ptloop, p[2] are (nearly) collinear. len = distance(p[0], p[1]); l1 = distance(p[0], ptloop); l2 = distance(ptloop, p[1]); if (((l1 + l2 - len) / len) < b->epsilon) { // They are (nearly) collinear. setpointtype(ptloop, FREESEGVERTEX); // Connect nextseg and parentseg together at ptloop. senextself(nextseg); senext2self(parentseg); sbond(nextseg, parentseg); st_segref_count++; } } } ptloop = pointtraverse(); } // Are there area constraints? if (b->quality && (in->facetconstraintlist != (REAL*)NULL)) { // Set maximum area constraints on facets. for (i = 0; i < in->numberoffacetconstraints; i++) { fmarker = (int)in->facetconstraintlist[i * 2]; area = in->facetconstraintlist[i * 2 + 1]; subfaces->traversalinit(); subloop.sh = shellfacetraverse(subfaces); while (subloop.sh != NULL) { if (shellmark(subloop) == fmarker) { setareabound(subloop, area); } subloop.sh = shellfacetraverse(subfaces); } } } // Are there length constraints? if (b->quality && (in->segmentconstraintlist != (REAL*)NULL)) { // Set maximum length constraints on segments. int e1, e2; for (i = 0; i < in->numberofsegmentconstraints; i++) { e1 = (int)in->segmentconstraintlist[i * 3]; e2 = (int)in->segmentconstraintlist[i * 3 + 1]; len = in->segmentconstraintlist[i * 3 + 2]; // Search for edge [e1, e2]. idx = e1 - in->firstnumber; for (j = idx2seglist[idx]; j < idx2seglist[idx + 1]; j++) { parentseg = segperverlist[j]; if (pointmark(sdest(parentseg)) == e2) { setareabound(parentseg, len); break; } } } } delete[] idx2seglist; delete[] segperverlist; } // Set global flags. checksubsegflag = 1; checksubfaceflag = 1; delete[] idx2verlist; delete[] ver2tetarray; } /////////////////////////////////////////////////////////////////////////////// // // // scoutpoint() Search a point in mesh. // // // // This function searches the point in a mesh whose domain may be not convex.// // In case of a convex domain, the locate() function is sufficient. // // // // If 'randflag' is used, randomly select a start searching tet. Otherwise, // // start searching directly from 'searchtet'. // // // /////////////////////////////////////////////////////////////////////////////// int tetgenmesh::scoutpoint(point searchpt, triface* searchtet, int randflag) { point pa, pb, pc, pd; enum locateresult loc = OUTSIDE; REAL vol, ori1, ori2 = 0, ori3 = 0, ori4 = 0; int t1ver; // Randomly select a good starting tet. if (randflag) { randomsample(searchpt, searchtet); } else { if (searchtet->tet == NULL) { *searchtet = recenttet; } } loc = locate(searchpt, searchtet); if (loc == OUTSIDE) { if (b->convex) { // -c option // The point lies outside of the convex hull. return (int)loc; } // Test if it lies nearly on the hull face. // Reuse vol, ori1. pa = org(*searchtet); pb = dest(*searchtet); pc = apex(*searchtet); vol = triarea(pa, pb, pc); ori1 = orient3dfast(pa, pb, pc, searchpt); if (fabs(ori1 / vol) < b->epsilon) { loc = ONFACE; // On face (or on edge, or on vertex). fsymself(*searchtet); } } if (loc != OUTSIDE) { // Round the result of location. pa = org(*searchtet); pb = dest(*searchtet); pc = apex(*searchtet); pd = oppo(*searchtet); vol = orient3dfast(pa, pb, pc, pd); ori1 = orient3dfast(pa, pb, pc, searchpt); ori2 = orient3dfast(pb, pa, pd, searchpt); ori3 = orient3dfast(pc, pb, pd, searchpt); ori4 = orient3dfast(pa, pc, pd, searchpt); if (fabs(ori1 / vol) < b->epsilon) ori1 = 0; if (fabs(ori2 / vol) < b->epsilon) ori2 = 0; if (fabs(ori3 / vol) < b->epsilon) ori3 = 0; if (fabs(ori4 / vol) < b->epsilon) ori4 = 0; } else { // if (loc == OUTSIDE) { // Do a brute force search for the point (with rounding). tetrahedrons->traversalinit(); searchtet->tet = tetrahedrontraverse(); while (searchtet->tet != NULL) { pa = org(*searchtet); pb = dest(*searchtet); pc = apex(*searchtet); pd = oppo(*searchtet); vol = orient3dfast(pa, pb, pc, pd); if (vol < 0) { ori1 = orient3dfast(pa, pb, pc, searchpt); if (fabs(ori1 / vol) < b->epsilon) ori1 = 0; // Rounding. if (ori1 <= 0) { ori2 = orient3dfast(pb, pa, pd, searchpt); if (fabs(ori2 / vol) < b->epsilon) ori2 = 0; if (ori2 <= 0) { ori3 = orient3dfast(pc, pb, pd, searchpt); if (fabs(ori3 / vol) < b->epsilon) ori3 = 0; if (ori3 <= 0) { ori4 = orient3dfast(pa, pc, pd, searchpt); if (fabs(ori4 / vol) < b->epsilon) ori4 = 0; if (ori4 <= 0) { // Found the tet. Return its location. break; } // ori4 } // ori3 } // ori2 } // ori1 } searchtet->tet = tetrahedrontraverse(); } // while (searchtet->tet != NULL) nonregularcount++; // Re-use this counter. } if (searchtet->tet != NULL) { // Return the point location. if (ori1 == 0) { // on face [a,b,c] if (ori2 == 0) { // on edge [a,b]. if (ori3 == 0) { // on vertex [b]. enextself(*searchtet); // [b,c,a,d] loc = ONVERTEX; } else { if (ori4 == 0) { // on vertex [a] loc = ONVERTEX; // [a,b,c,d] } else { loc = ONEDGE; // [a,b,c,d] } } } else { // ori2 != 0 if (ori3 == 0) { // on edge [b,c] if (ori4 == 0) { // on vertex [c] eprevself(*searchtet); // [c,a,b,d] loc = ONVERTEX; } else { enextself(*searchtet); // [b,c,a,d] loc = ONEDGE; } } else { // ori3 != 0 if (ori4 == 0) { // on edge [c,a] eprevself(*searchtet); // [c,a,b,d] loc = ONEDGE; } else { loc = ONFACE; } } } } else { // ori1 != 0 if (ori2 == 0) { // on face [b,a,d] esymself(*searchtet); // [b,a,d,c] if (ori3 == 0) { // on edge [b,d] eprevself(*searchtet); // [d,b,a,c] if (ori4 == 0) { // on vertex [d] loc = ONVERTEX; } else { loc = ONEDGE; } } else { // ori3 != 0 if (ori4 == 0) { // on edge [a,d] enextself(*searchtet); // [a,d,b,c] loc = ONEDGE; } else { loc = ONFACE; } } } else { // ori2 != 0 if (ori3 == 0) { // on face [c,b,d] enextself(*searchtet); esymself(*searchtet); if (ori4 == 0) { // on edge [c,d] eprevself(*searchtet); loc = ONEDGE; } else { loc = ONFACE; } } else { if (ori4 == 0) { // on face [a,c,d] eprevself(*searchtet); esymself(*searchtet); loc = ONFACE; } else { // inside tet [a,b,c,d] loc = INTETRAHEDRON; } // ori4 } // ori3 } // ori2 } // ori1 } else { loc = OUTSIDE; } return (int)loc; } /////////////////////////////////////////////////////////////////////////////// // // // getpointmeshsize() Interpolate the mesh size at given point. // // // // 'iloc' indicates the location of the point w.r.t. 'searchtet'. The size // // is obtained by linear interpolation on the vertices of the tet. // // // /////////////////////////////////////////////////////////////////////////////// REAL tetgenmesh::getpointmeshsize(point searchpt, triface* searchtet, int iloc) { point *pts, pa, pb, pc; REAL volume, vol[4], wei[4]; REAL size; int i; size = 0; if (iloc == (int)INTETRAHEDRON) { pts = (point*)&(searchtet->tet[4]); // Only do interpolation if all vertices have non-zero sizes. if ((pts[0][pointmtrindex] > 0) && (pts[1][pointmtrindex] > 0) && (pts[2][pointmtrindex] > 0) && (pts[3][pointmtrindex] > 0)) { // P1 interpolation. volume = orient3dfast(pts[0], pts[1], pts[2], pts[3]); vol[0] = orient3dfast(searchpt, pts[1], pts[2], pts[3]); vol[1] = orient3dfast(pts[0], searchpt, pts[2], pts[3]); vol[2] = orient3dfast(pts[0], pts[1], searchpt, pts[3]); vol[3] = orient3dfast(pts[0], pts[1], pts[2], searchpt); for (i = 0; i < 4; i++) { wei[i] = fabs(vol[i] / volume); size += (wei[i] * pts[i][pointmtrindex]); } } } else if (iloc == (int)ONFACE) { pa = org(*searchtet); pb = dest(*searchtet); pc = apex(*searchtet); if ((pa[pointmtrindex] > 0) && (pb[pointmtrindex] > 0) && (pc[pointmtrindex] > 0)) { volume = triarea(pa, pb, pc); vol[0] = triarea(searchpt, pb, pc); vol[1] = triarea(pa, searchpt, pc); vol[2] = triarea(pa, pb, searchpt); size = (vol[0] / volume) * pa[pointmtrindex] + (vol[1] / volume) * pb[pointmtrindex] + (vol[2] / volume) * pc[pointmtrindex]; } } else if (iloc == (int)ONEDGE) { pa = org(*searchtet); pb = dest(*searchtet); if ((pa[pointmtrindex] > 0) && (pb[pointmtrindex] > 0)) { volume = distance(pa, pb); vol[0] = distance(searchpt, pb); vol[1] = distance(pa, searchpt); size = (vol[0] / volume) * pa[pointmtrindex] + (vol[1] / volume) * pb[pointmtrindex]; } } else if (iloc == (int)ONVERTEX) { pa = org(*searchtet); if (pa[pointmtrindex] > 0) { size = pa[pointmtrindex]; } } return size; } /////////////////////////////////////////////////////////////////////////////// // // // interpolatemeshsize() Interpolate the mesh size from a background mesh // // (source) to the current mesh (destination). // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::interpolatemeshsize() { triface searchtet; point ploop; REAL minval = 0.0, maxval = 0.0; int iloc; int count; if (!b->quiet) { printf("Interpolating mesh size ...\n"); } long bak_nonregularcount = nonregularcount; nonregularcount = 0l; // Count the number of (slow) global searches. long baksmaples = bgm->samples; bgm->samples = 3l; count = 0; // Count the number of interpolated points. // Interpolate sizes for all points in the current mesh. points->traversalinit(); ploop = pointtraverse(); while (ploop != NULL) { // Search a tet in bgm which containing this point. searchtet.tet = NULL; iloc = bgm->scoutpoint(ploop, &searchtet, 1); // randflag = 1 if (iloc != (int)OUTSIDE) { // Interpolate the mesh size. ploop[pointmtrindex] = bgm->getpointmeshsize(ploop, &searchtet, iloc); setpoint2bgmtet(ploop, bgm->encode(searchtet)); if (count == 0) { // This is the first interpolated point. minval = maxval = ploop[pointmtrindex]; } else { if (ploop[pointmtrindex] < minval) { minval = ploop[pointmtrindex]; } if (ploop[pointmtrindex] > maxval) { maxval = ploop[pointmtrindex]; } } count++; } else { if (!b->quiet) { printf("Warnning: Failed to locate point %d in source mesh.\n", pointmark(ploop)); } } ploop = pointtraverse(); } if (b->verbose) { printf(" Interoplated %d points.\n", count); if (nonregularcount > 0l) { printf(" Performed %ld brute-force searches.\n", nonregularcount); } printf(" Size rangle [%.17g, %.17g].\n", minval, maxval); } bgm->samples = baksmaples; nonregularcount = bak_nonregularcount; } /////////////////////////////////////////////////////////////////////////////// // // // insertconstrainedpoints() Insert a list of points into the mesh. // // // // Assumption: The bounding box of the insert point set should be no larger // // than the bounding box of the mesh. (Required by point sorting). // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::insertconstrainedpoints(point* insertarray, int arylen, int rejflag) { triface searchtet, spintet; face splitsh; face splitseg; insertvertexflags ivf; flipconstraints fc; int randflag = 0; int t1ver; int i; if (b->verbose) { printf(" Inserting %d constrained points\n", arylen); } if (b->no_sort) { // -b/1 option. if (b->verbose) { printf(" Using the input order.\n"); } } else { if (b->verbose) { printf(" Permuting vertices.\n"); } point swappoint; int randindex; srand(arylen); for (i = 0; i < arylen; i++) { randindex = rand() % (i + 1); swappoint = insertarray[i]; insertarray[i] = insertarray[randindex]; insertarray[randindex] = swappoint; } if (b->brio_hilbert) { // -b1 option if (b->verbose) { printf(" Sorting vertices.\n"); } hilbert_init(in->mesh_dim); int ngroup = 0; brio_multiscale_sort(insertarray, arylen, b->brio_threshold, b->brio_ratio, &ngroup); } else { // -b0 option. randflag = 1; } // if (!b->brio_hilbert) } // if (!b->no_sort) long bak_nonregularcount = nonregularcount; nonregularcount = 0l; long baksmaples = samples; samples = 3l; // Use at least 3 samples. Updated in randomsample(). long bak_seg_count = st_segref_count; long bak_fac_count = st_facref_count; long bak_vol_count = st_volref_count; // Initialize the insertion parameters. if (b->incrflip) { // -l option // Use incremental flip algorithm. ivf.bowywat = 0; ivf.lawson = 1; ivf.validflag = 0; // No need to validate the cavity. fc.enqflag = 2; } else { // Use Bowyer-Watson algorithm. ivf.bowywat = 1; ivf.lawson = 0; ivf.validflag = 1; // Validate the B-W cavity. } ivf.rejflag = rejflag; ivf.chkencflag = 0; ivf.sloc = (int)INSTAR; ivf.sbowywat = 3; ivf.splitbdflag = 1; ivf.respectbdflag = 1; ivf.assignmeshsize = b->metric; encseglist = new arraypool(sizeof(face), 8); encshlist = new arraypool(sizeof(badface), 8); // Insert the points. for (i = 0; i < arylen; i++) { // Find the location of the inserted point. // Do not use 'recenttet', since the mesh may be non-convex. searchtet.tet = NULL; ivf.iloc = scoutpoint(insertarray[i], &searchtet, randflag); // Decide the right type for this point. setpointtype(insertarray[i], FREEVOLVERTEX); // Default. splitsh.sh = NULL; splitseg.sh = NULL; if (ivf.iloc == (int)ONEDGE) { if (issubseg(searchtet)) { tsspivot1(searchtet, splitseg); setpointtype(insertarray[i], FREESEGVERTEX); // ivf.rejflag = 0; } else { // Check if it is a subface edge. spintet = searchtet; while (1) { if (issubface(spintet)) { tspivot(spintet, splitsh); setpointtype(insertarray[i], FREEFACETVERTEX); // ivf.rejflag |= 1; break; } fnextself(spintet); if (spintet.tet == searchtet.tet) break; } } } else if (ivf.iloc == (int)ONFACE) { if (issubface(searchtet)) { tspivot(searchtet, splitsh); setpointtype(insertarray[i], FREEFACETVERTEX); // ivf.rejflag |= 1; } } // Now insert the point. if (insertpoint(insertarray[i], &searchtet, &splitsh, &splitseg, &ivf)) { if (flipstack != NULL) { // There are queued faces. Use flips to recover Delaunayness. lawsonflip3d(&fc); // There may be unflippable edges. Ignore them. unflipqueue->restart(); } // Update the Steiner counters. if (pointtype(insertarray[i]) == FREESEGVERTEX) { st_segref_count++; } else if (pointtype(insertarray[i]) == FREEFACETVERTEX) { st_facref_count++; } else { st_volref_count++; } } else { // Point is not inserted. // pointdealloc(insertarray[i]); setpointtype(insertarray[i], UNUSEDVERTEX); unuverts++; encseglist->restart(); encshlist->restart(); } } // i delete encseglist; delete encshlist; if (b->verbose) { printf(" Inserted %ld (%ld, %ld, %ld) vertices.\n", st_segref_count + st_facref_count + st_volref_count - (bak_seg_count + bak_fac_count + bak_vol_count), st_segref_count - bak_seg_count, st_facref_count - bak_fac_count, st_volref_count - bak_vol_count); if (nonregularcount > 0l) { printf(" Performed %ld brute-force searches.\n", nonregularcount); } } nonregularcount = bak_nonregularcount; samples = baksmaples; } void tetgenmesh::insertconstrainedpoints(tetgenio* addio) { point *insertarray, newpt; REAL x, y, z, w; int index, attribindex, mtrindex; int arylen, i, j; if (!b->quiet) { printf("Inserting constrained points ...\n"); } insertarray = new point[addio->numberofpoints]; arylen = 0; index = 0; attribindex = 0; mtrindex = 0; for (i = 0; i < addio->numberofpoints; i++) { x = addio->pointlist[index++]; y = addio->pointlist[index++]; z = addio->pointlist[index++]; // Test if this point lies inside the bounding box. if ((x < xmin) || (x > xmax) || (y < ymin) || (y > ymax) || (z < zmin) || (z > zmax)) { if (b->verbose) { printf("Warning: Point #%d lies outside the bounding box. Ignored\n", i + in->firstnumber); } continue; } makepoint(&newpt, UNUSEDVERTEX); newpt[0] = x; newpt[1] = y; newpt[2] = z; // Read the point attributes. (Including point weights.) for (j = 0; j < addio->numberofpointattributes; j++) { newpt[3 + j] = addio->pointattributelist[attribindex++]; } // Read the point metric tensor. for (j = 0; j < addio->numberofpointmtrs; j++) { newpt[pointmtrindex + j] = addio->pointmtrlist[mtrindex++]; } if (b->weighted) { // -w option if (addio->numberofpointattributes > 0) { // The first point attribute is its weight. w = newpt[3]; } else { // No given weight available. Default choose the maximum // absolute value among its coordinates. w = fabs(x); if (w < fabs(y)) w = fabs(y); if (w < fabs(z)) w = fabs(z); } if (b->weighted_param == 0) { newpt[3] = x * x + y * y + z * z - w; // Weighted DT. } else { // -w1 option newpt[3] = w; // Regular tetrahedralization. } } insertarray[arylen] = newpt; arylen++; } // i // Insert the points. int rejflag = 0; // Do not check encroachment. if (b->metric) { // -m option. rejflag |= 4; // Reject it if it lies in some protecting balls. } insertconstrainedpoints(insertarray, arylen, rejflag); delete[] insertarray; } /////////////////////////////////////////////////////////////////////////////// // // // meshcoarsening() Deleting (selected) vertices. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::collectremovepoints(arraypool* remptlist) { point ptloop, *parypt; verttype vt; // If a mesh sizing function is given. Collect vertices whose mesh size // is greater than its smallest edge length. if (b->metric) { // -m option REAL len, smlen; int i; points->traversalinit(); ptloop = pointtraverse(); while (ptloop != NULL) { // Do not remove a boundary vertex vt = pointtype(ptloop); if ((vt == RIDGEVERTEX) || (vt == ACUTEVERTEX) || (vt == FACETVERTEX) || (vt == FREEFACETVERTEX) || (vt == FREESEGVERTEX) || (vt == UNUSEDVERTEX)) { ptloop = pointtraverse(); continue; } if (ptloop[pointmtrindex] > 0) { // Get the smallest edge length at this vertex. getvertexstar(1, ptloop, cavetetlist, cavetetvertlist, NULL); parypt = (point*)fastlookup(cavetetvertlist, 0); smlen = distance(ptloop, *parypt); for (i = 1; i < cavetetvertlist->objects; i++) { parypt = (point*)fastlookup(cavetetvertlist, i); len = distance(ptloop, *parypt); if (len < smlen) { smlen = len; } } cavetetvertlist->restart(); cavetetlist->restart(); if (smlen < ptloop[pointmtrindex]) { pinfect(ptloop); remptlist->newindex((void**)&parypt); *parypt = ptloop; } } ptloop = pointtraverse(); } if (b->verbose > 1) { printf(" Coarsen %ld oversized points.\n", remptlist->objects); } } // If 'in->pointmarkerlist' exists, Collect vertices with markers '-1'. if (in->pointmarkerlist != NULL) { long bak_count = remptlist->objects; points->traversalinit(); ptloop = pointtraverse(); int index = 0; while (ptloop != NULL) { if (index < in->numberofpoints) { if (in->pointmarkerlist[index] == -1) { pinfect(ptloop); remptlist->newindex((void**)&parypt); *parypt = ptloop; } } else { // Remaining are not input points. Stop here. break; } index++; ptloop = pointtraverse(); } if (b->verbose > 1) { printf(" Coarsen %ld marked points.\n", remptlist->objects - bak_count); } } // if (in->pointmarkerlist != NULL) if (b->coarsen_param > 0) { // -R1/# // Remove a coarsen_percent number of interior points. if (b->verbose > 1) { printf(" Coarsen %g percent of interior points.\n", b->coarsen_percent * 100.0); } arraypool* intptlist = new arraypool(sizeof(point*), 10); // Count the total number of interior points. points->traversalinit(); ptloop = pointtraverse(); while (ptloop != NULL) { vt = pointtype(ptloop); if ((vt == VOLVERTEX) || (vt == FREEVOLVERTEX) || (vt == FREEFACETVERTEX) || (vt == FREESEGVERTEX)) { intptlist->newindex((void**)&parypt); *parypt = ptloop; } ptloop = pointtraverse(); } if (intptlist->objects > 0l) { // Sort the list of points randomly. point *parypt_i, swappt; int randindex, i; srand(intptlist->objects); for (i = 0; i < intptlist->objects; i++) { randindex = rand() % (i + 1); // randomnation(i + 1); parypt_i = (point*)fastlookup(intptlist, i); parypt = (point*)fastlookup(intptlist, randindex); // Swap this two points. swappt = *parypt_i; *parypt_i = *parypt; *parypt = swappt; } int remcount = (int)((REAL)intptlist->objects * b->coarsen_percent); // Return the first remcount points. for (i = 0; i < remcount; i++) { parypt_i = (point*)fastlookup(intptlist, i); if (!pinfected(*parypt_i)) { pinfected(*parypt_i); remptlist->newindex((void**)&parypt); *parypt = *parypt_i; } } } delete intptlist; } // Unmark all collected vertices. for (int i = 0; i < remptlist->objects; i++) { parypt = (point*)fastlookup(remptlist, i); puninfect(*parypt); } } void tetgenmesh::meshcoarsening() { arraypool* remptlist; if (!b->quiet) { printf("Mesh coarsening ...\n"); } // Collect the set of points to be removed remptlist = new arraypool(sizeof(point*), 10); collectremovepoints(remptlist); if (remptlist->objects == 0l) { delete remptlist; return; } if (b->verbose) { if (remptlist->objects > 0l) { printf(" Removing %ld points...\n", remptlist->objects); } } point *parypt, *plastpt; long ms = remptlist->objects; int nit = 0; int bak_fliplinklevel = b->fliplinklevel; b->fliplinklevel = -1; autofliplinklevel = 1; // Init value. int i; while (1) { if (b->verbose > 1) { printf(" Removing points [%s level = %2d] #: %ld.\n", (b->fliplinklevel > 0) ? "fixed" : "auto", (b->fliplinklevel > 0) ? b->fliplinklevel : autofliplinklevel, remptlist->objects); } // Remove the list of points. for (i = 0; i < remptlist->objects; i++) { parypt = (point*)fastlookup(remptlist, i); if (removevertexbyflips(*parypt)) { // Move the last entry to the current place. plastpt = (point*)fastlookup(remptlist, remptlist->objects - 1); *parypt = *plastpt; remptlist->objects--; i--; } } if (remptlist->objects > 0l) { if (b->fliplinklevel >= 0) { break; // We have tried all levels. } if (remptlist->objects == ms) { nit++; if (nit >= 3) { // Do the last round with unbounded flip link level. b->fliplinklevel = 100000; } } else { ms = remptlist->objects; if (nit > 0) { nit--; } } autofliplinklevel += b->fliplinklevelinc; } else { // All points are removed. break; } } // while (1) if (remptlist->objects > 0l) { if (b->verbose) { printf(" %ld points are not removed !\n", remptlist->objects); } } b->fliplinklevel = bak_fliplinklevel; delete remptlist; } //// //// //// //// //// reconstruct_cxx ////////////////////////////////////////////////////////// //// refine_cxx /////////////////////////////////////////////////////////////// //// //// //// //// /////////////////////////////////////////////////////////////////////////////// // // // makefacetverticesmap() Create a map from facet to its vertices. // // // // All facets will be indexed (starting from 0). The map is saved in two // // global arrays: 'idx2facetlist' and 'facetverticeslist'. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::makefacetverticesmap() { arraypool *facetvertexlist, *vertlist, **paryvertlist; face subloop, neighsh, *parysh, *parysh1; point pa, *ppt, *parypt; verttype vt; int facetindex, totalvertices; int i, j, k; if (b->verbose) { printf(" Creating the facet vertices map.\n"); } facetvertexlist = new arraypool(sizeof(arraypool*), 10); facetindex = totalvertices = 0; subfaces->traversalinit(); subloop.sh = shellfacetraverse(subfaces); while (subloop.sh != NULL) { if (!sinfected(subloop)) { // A new facet. Create its vertices list. vertlist = new arraypool(sizeof(point*), 8); ppt = (point*)&(subloop.sh[3]); for (k = 0; k < 3; k++) { vt = pointtype(ppt[k]); if ((vt != FREESEGVERTEX) && (vt != FREEFACETVERTEX)) { pinfect(ppt[k]); vertlist->newindex((void**)&parypt); *parypt = ppt[k]; } } sinfect(subloop); caveshlist->newindex((void**)&parysh); *parysh = subloop; for (i = 0; i < caveshlist->objects; i++) { parysh = (face*)fastlookup(caveshlist, i); setfacetindex(*parysh, facetindex); for (j = 0; j < 3; j++) { if (!isshsubseg(*parysh)) { spivot(*parysh, neighsh); if (!sinfected(neighsh)) { pa = sapex(neighsh); if (!pinfected(pa)) { vt = pointtype(pa); if ((vt != FREESEGVERTEX) && (vt != FREEFACETVERTEX)) { pinfect(pa); vertlist->newindex((void**)&parypt); *parypt = pa; } } sinfect(neighsh); caveshlist->newindex((void**)&parysh1); *parysh1 = neighsh; } } senextself(*parysh); } } // i totalvertices += (int)vertlist->objects; // Uninfect facet vertices. for (k = 0; k < vertlist->objects; k++) { parypt = (point*)fastlookup(vertlist, k); puninfect(*parypt); } caveshlist->restart(); // Save this vertex list. facetvertexlist->newindex((void**)&paryvertlist); *paryvertlist = vertlist; facetindex++; } subloop.sh = shellfacetraverse(subfaces); } // All subfaces are infected. Uninfect them. subfaces->traversalinit(); subloop.sh = shellfacetraverse(subfaces); while (subloop.sh != NULL) { suninfect(subloop); subloop.sh = shellfacetraverse(subfaces); } if (b->verbose) { printf(" Found %ld facets.\n", facetvertexlist->objects); } idx2facetlist = new int[facetindex + 1]; facetverticeslist = new point[totalvertices]; totalworkmemory += ((facetindex + 1) * sizeof(int) + totalvertices * sizeof(point*)); idx2facetlist[0] = 0; for (i = 0, k = 0; i < facetindex; i++) { paryvertlist = (arraypool**)fastlookup(facetvertexlist, i); vertlist = *paryvertlist; idx2facetlist[i + 1] = (idx2facetlist[i] + (int)vertlist->objects); for (j = 0; j < vertlist->objects; j++) { parypt = (point*)fastlookup(vertlist, j); facetverticeslist[k] = *parypt; k++; } } // Free the lists. for (i = 0; i < facetvertexlist->objects; i++) { paryvertlist = (arraypool**)fastlookup(facetvertexlist, i); vertlist = *paryvertlist; delete vertlist; } delete facetvertexlist; } /////////////////////////////////////////////////////////////////////////////// // // // Check whether two segments, or a segment and a facet, or two facets are // // adjacent to each other. // // // /////////////////////////////////////////////////////////////////////////////// int tetgenmesh::segsegadjacent(face* seg1, face* seg2) { int segidx1 = getfacetindex(*seg1); int segidx2 = getfacetindex(*seg2); if (segidx1 == segidx2) return 0; point pa1 = segmentendpointslist[segidx1 * 2]; point pb1 = segmentendpointslist[segidx1 * 2 + 1]; point pa2 = segmentendpointslist[segidx2 * 2]; point pb2 = segmentendpointslist[segidx2 * 2 + 1]; if ((pa1 == pa2) || (pa1 == pb2) || (pb1 == pa2) || (pb1 == pb2)) { return 1; } return 0; } int tetgenmesh::segfacetadjacent(face* subseg, face* subsh) { int segidx = getfacetindex(*subseg); point pa = segmentendpointslist[segidx * 2]; point pb = segmentendpointslist[segidx * 2 + 1]; pinfect(pa); pinfect(pb); int fidx = getfacetindex(*subsh); int count = 0, i; for (i = idx2facetlist[fidx]; i < idx2facetlist[fidx + 1]; i++) { if (pinfected(facetverticeslist[i])) count++; } puninfect(pa); puninfect(pb); return count == 1; } int tetgenmesh::facetfacetadjacent(face* subsh1, face* subsh2) { int count = 0, i; int fidx1 = getfacetindex(*subsh1); int fidx2 = getfacetindex(*subsh2); if (fidx1 == fidx2) return 0; for (i = idx2facetlist[fidx1]; i < idx2facetlist[fidx1 + 1]; i++) { pinfect(facetverticeslist[i]); } for (i = idx2facetlist[fidx2]; i < idx2facetlist[fidx2 + 1]; i++) { if (pinfected(facetverticeslist[i])) count++; } // Uninfect the vertices. for (i = idx2facetlist[fidx1]; i < idx2facetlist[fidx1 + 1]; i++) { puninfect(facetverticeslist[i]); } return count > 0; } /////////////////////////////////////////////////////////////////////////////// // // // save_segmentpoint_insradius(), save_facetpoint_insradius() // // // // Determine and save the relaxed insertion radius of a Steiner point on a // // segment or a facet. By default, it is the closet distance to the parent // // point of this Steiner point. But may be larger than it. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::save_segmentpoint_insradius(point segpt, point parentpt, REAL r) { REAL rv = r, rp; if (pointtype(parentpt) == FREESEGVERTEX) { face parentseg1, parentseg2; sdecode(point2sh(segpt), parentseg1); sdecode(point2sh(parentpt), parentseg2); if (segsegadjacent(&parentseg1, &parentseg2)) { rp = getpointinsradius(parentpt); if (rv < rp) { // The relaxed insertion radius of 'newpt'. rv = rp; } } } else if (pointtype(parentpt) == FREEFACETVERTEX) { face parentseg, parentsh; sdecode(point2sh(segpt), parentseg); sdecode(point2sh(parentpt), parentsh); if (segfacetadjacent(&parentseg, &parentsh)) { rp = getpointinsradius(parentpt); if ((sqrt(2.0) * rv) < rp) { // if (rv < rp) { // The relaxed insertion radius of 'newpt'. rv = rp / sqrt(2.0); // rv = rp; } } } setpointinsradius(segpt, rv); } void tetgenmesh::save_facetpoint_insradius(point facpt, point parentpt, REAL r) { REAL rv = r, rp; if (pointtype(parentpt) == FREESEGVERTEX) { face parentseg, parentsh; sdecode(point2sh(parentpt), parentseg); sdecode(point2sh(facpt), parentsh); if (segfacetadjacent(&parentseg, &parentsh)) { rp = getpointinsradius(parentpt); if (rv < (sqrt(2.0) * rp)) { rv = sqrt(2.0) * rp; // The relaxed insertion radius of 'newpt'. } } } else if (pointtype(parentpt) == FREEFACETVERTEX) { face parentsh1, parentsh2; sdecode(point2sh(parentpt), parentsh1); sdecode(point2sh(facpt), parentsh2); if (facetfacetadjacent(&parentsh1, &parentsh2)) { rp = getpointinsradius(parentpt); if (rv < rp) { rv = rp; // The relaxed insertion radius of 'newpt'. } } } setpointinsradius(facpt, rv); } /////////////////////////////////////////////////////////////////////////////// // // // enqueuesubface() Queue a subface or a subsegment for encroachment chk. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::enqueuesubface(memorypool* pool, face* chkface) { if (!smarktest2ed(*chkface)) { smarktest2(*chkface); // Only queue it once. face* queface = (face*)pool->alloc(); *queface = *chkface; } } /////////////////////////////////////////////////////////////////////////////// // // // enqueuetetrahedron() Queue a tetrahedron for quality check. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::enqueuetetrahedron(triface* chktet) { if (!marktest2ed(*chktet)) { marktest2(*chktet); // Only queue it once. triface* quetet = (triface*)badtetrahedrons->alloc(); *quetet = *chktet; } } /////////////////////////////////////////////////////////////////////////////// // // // checkseg4encroach() Check if an edge is encroached upon by a point. // // // /////////////////////////////////////////////////////////////////////////////// int tetgenmesh::checkseg4encroach(point pa, point pb, point checkpt) { // Check if the point lies inside the diametrical sphere of this seg. REAL v1[3], v2[3]; v1[0] = pa[0] - checkpt[0]; v1[1] = pa[1] - checkpt[1]; v1[2] = pa[2] - checkpt[2]; v2[0] = pb[0] - checkpt[0]; v2[1] = pb[1] - checkpt[1]; v2[2] = pb[2] - checkpt[2]; if (dot(v1, v2) < 0) { // Inside. if (b->metric) { // -m option. if ((pa[pointmtrindex] > 0) && (pb[pointmtrindex] > 0)) { // The projection of 'checkpt' lies inside the segment [a,b]. REAL prjpt[3], u, v, t; projpt2edge(checkpt, pa, pb, prjpt); // Interoplate the mesh size at the location 'prjpt'. u = distance(pa, pb); v = distance(pa, prjpt); t = v / u; // 'u' is the mesh size at 'prjpt' u = pa[pointmtrindex] + t * (pb[pointmtrindex] - pa[pointmtrindex]); v = distance(checkpt, prjpt); if (v < u) { return 1; // Encroached prot-ball! } } else { return 1; // NO protecting ball. Encroached. } } else { return 1; // Inside! Encroached. } } return 0; } /////////////////////////////////////////////////////////////////////////////// // // // checkseg4split() Check if we need to split a segment. // // // // A segment needs to be split if it is in the following case: // // (1) It is encroached by an existing vertex. // // (2) It has bad quality (too long). // // (3) Its length is larger than the mesh sizes at its endpoints. // // // // Return 1 if it needs to be split, otherwise, return 0. 'pencpt' returns // // an encroaching point if there exists. 'qflag' returns '1' if the segment // // has a length larger than the desired edge length. // // // /////////////////////////////////////////////////////////////////////////////// int tetgenmesh::checkseg4split(face* chkseg, point& encpt, int& qflag) { REAL ccent[3], len, r; int i; point forg = sorg(*chkseg); point fdest = sdest(*chkseg); // Initialize the return values. encpt = NULL; qflag = 0; len = distance(forg, fdest); r = 0.5 * len; for (i = 0; i < 3; i++) { ccent[i] = 0.5 * (forg[i] + fdest[i]); } // First check its quality. if (checkconstraints && (areabound(*chkseg) > 0.0)) { if (len > areabound(*chkseg)) { qflag = 1; return 1; } } if (b->fixedvolume) { if ((len * len * len) > b->maxvolume) { qflag = 1; return 1; } } if (b->metric) { // -m option. Check mesh size. // Check if the ccent lies outside one of the prot.balls at vertices. if (((forg[pointmtrindex] > 0) && (r > forg[pointmtrindex])) || ((fdest[pointmtrindex]) > 0 && (r > fdest[pointmtrindex]))) { qflag = 1; // Enforce mesh size. return 1; } } // Second check if it is encroached. // Comment: There may exist more than one encroaching points of this segment. // The 'encpt' returns the one which is closet to it. triface searchtet, spintet; point eapex; REAL d, diff, smdist = 0; int t1ver; sstpivot1(*chkseg, searchtet); spintet = searchtet; while (1) { eapex = apex(spintet); if (eapex != dummypoint) { d = distance(ccent, eapex); diff = d - r; if (fabs(diff) / r < b->epsilon) diff = 0.0; // Rounding. if (diff < 0) { // This segment is encroached by eapex. if (useinsertradius) { if (encpt == NULL) { encpt = eapex; smdist = d; } else { // Choose the closet encroaching point. if (d < smdist) { encpt = eapex; smdist = d; } } } else { encpt = eapex; break; } } } fnextself(spintet); if (spintet.tet == searchtet.tet) break; } // while (1) if (encpt != NULL) { return 1; } return 0; // No need to split it. } /////////////////////////////////////////////////////////////////////////////// // // // splitsegment() Split a segment. // // // // The segment 'splitseg' is intended to be split. It will be split if it // // is in one of the following cases: // // (1) It is encroached by an existing vertex 'encpt != NULL'; or // // (2) It is in bad quality 'qflag == 1'; or // // (3) Its length is larger than the mesh sizes at its endpoints. // // // /////////////////////////////////////////////////////////////////////////////// int tetgenmesh::splitsegment(face* splitseg, point encpt, REAL rrp, point encpt1, point encpt2, int qflag, int chkencflag) { if (!qflag && smarktest3ed(*splitseg)) { // Do not try to re-split a marked segment. return 0; } if (b->nobisect) { // With -Y option. // Only split this segment if it is allowed to be split. if (checkconstraints) { // Check if it has a non-zero length bound. if (areabound(*splitseg) == 0) { // It is not allowed. However, if all of facets containing this seg // is allowed to be split, we still split it. face parentsh, spinsh; // splitseg.shver = 0; spivot(*splitseg, parentsh); if (parentsh.sh == NULL) { return 0; // A dangling segment. Do not split it. } spinsh = parentsh; while (1) { if (areabound(spinsh) == 0) break; spivotself(spinsh); if (spinsh.sh == parentsh.sh) break; if (spinsh.sh == NULL) break; // It belongs to only one facet. } if ((!spinsh.sh) || (areabound(spinsh) == 0)) { // All facets at this seg are not allowed to be split. return 0; // Do not split it. } } } else { return 0; // Do not split this segment. } } // if (b->nobisect) triface searchtet; face searchsh; point newpt; insertvertexflags ivf; makepoint(&newpt, FREESEGVERTEX); getsteinerptonsegment(splitseg, encpt, newpt); if (!qflag && !b->cdtrefine) { // Do not insert the point if it encroaches upon an adjacent segment. face parentsh; spivot(*splitseg, parentsh); if (parentsh.sh != NULL) { face spinsh, neighsh; face neighseg; spinsh = parentsh; while (1) { for (int i = 0; i < 2; i++) { if (i == 0) { senext(spinsh, neighsh); } else { senext2(spinsh, neighsh); } if (isshsubseg(neighsh)) { sspivot(neighsh, neighseg); if (checkseg4encroach(sorg(neighseg), sdest(neighseg), newpt)) { pointdealloc(newpt); return 0; // Do not split this segment. } } } // i spivotself(spinsh); if (spinsh.sh == NULL) break; if (spinsh.sh == parentsh.sh) break; } // while (1) } } // Split the segment by the Bowyer-Watson algorithm. sstpivot1(*splitseg, searchtet); ivf.iloc = (int)ONEDGE; ivf.bowywat = 3; // Use Bowyer-Watson, preserve subsegments and subfaces; ivf.validflag = 1; // Validate the B-W cavity. ivf.lawson = 2; // Do flips to recover Delaunayness. ivf.rejflag = 0; // Do not check encroachment of new segments/facets. if (b->metric) { ivf.rejflag |= 4; // Do check encroachment of protecting balls. } ivf.chkencflag = chkencflag; ivf.sloc = (int)INSTAR; // ivf.iloc; ivf.sbowywat = 3; // ivf.bowywat; // Surface mesh options. ivf.splitbdflag = 1; ivf.respectbdflag = 1; ivf.assignmeshsize = b->metric; ivf.smlenflag = useinsertradius; // Return the closet mesh vertex. if (insertpoint(newpt, &searchtet, &searchsh, splitseg, &ivf)) { st_segref_count++; if (steinerleft > 0) steinerleft--; if (useinsertradius) { save_segmentpoint_insradius(newpt, ivf.parentpt, ivf.smlen); } if (flipstack != NULL) { flipconstraints fc; fc.chkencflag = chkencflag; fc.enqflag = 2; lawsonflip3d(&fc); unflipqueue->restart(); } return 1; } else { // Point is not inserted. if (ivf.iloc == (int)NEARVERTEX) { terminatetetgen(this, 2); } pointdealloc(newpt); // Mark this segment to avoid splitting in the future. smarktest3(*splitseg); return 0; } } /////////////////////////////////////////////////////////////////////////////// // // // repairencsegs() Repair encroached (sub) segments. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::repairencsegs(int chkencflag) { face* bface; point encpt = NULL; int qflag = 0; // Loop until the pool 'badsubsegs' is empty. Note that steinerleft == -1 // if an unlimited number of Steiner points is allowed. while ((badsubsegs->items > 0) && (steinerleft != 0)) { badsubsegs->traversalinit(); bface = (face*)badsubsegs->traverse(); while ((bface != NULL) && (steinerleft != 0)) { // Skip a deleleted element. if (bface->shver >= 0) { // A queued segment may have been deleted (split). if ((bface->sh != NULL) && (bface->sh[3] != NULL)) { // A queued segment may have been processed. if (smarktest2ed(*bface)) { sunmarktest2(*bface); if (checkseg4split(bface, encpt, qflag)) { splitsegment(bface, encpt, 0, NULL, NULL, qflag, chkencflag); } } } // Remove this entry from list. bface->shver = -1; // Signal it as a deleted element. badsubsegs->dealloc((void*)bface); } bface = (face*)badsubsegs->traverse(); } } if (badsubsegs->items > 0) { if (b->verbose) { printf("The desired number of Steiner points is reached.\n"); } badsubsegs->traversalinit(); bface = (face*)badsubsegs->traverse(); while (bface != NULL) { // Skip a deleleted element. if (bface->shver >= 0) { if ((bface->sh != NULL) && (bface->sh[3] != NULL)) { if (smarktest2ed(*bface)) { sunmarktest2(*bface); } } } bface = (face*)badsubsegs->traverse(); } badsubsegs->restart(); } } /////////////////////////////////////////////////////////////////////////////// // // // checkfac4encroach() Check if a subface is encroached by a point. // // // /////////////////////////////////////////////////////////////////////////////// int tetgenmesh::checkfac4encroach(point pa, point pb, point pc, point checkpt, REAL* cent, REAL* r) { REAL rd, len; int encroached = 0; circumsphere(pa, pb, pc, NULL, cent, &rd); if (rd == 0) { terminatetetgen(this, 2); } if (b->use_equatorial_lens) { REAL normal[3], fcenter[3]; REAL xta, yta, zta; REAL multiplier; fcenter[0] = cent[0] - pc[0]; fcenter[1] = cent[1] - pc[1]; fcenter[2] = cent[2] - pc[2]; // Get the normal of the oriented face [a->b->c], without normalized. facenormal(pa, pb, pc, normal, 1, NULL); multiplier = 0.985 * sqrt((fcenter[0] * fcenter[0] + fcenter[1] * fcenter[1] + fcenter[2] * fcenter[2]) / (3.0 * (normal[0] * normal[0] + normal[1] * normal[1] + normal[2] * normal[2]))); xta = checkpt[0] - pc[0]; yta = checkpt[1] - pc[1]; zta = checkpt[2] - pc[2]; // Make sure that the normal is pointing to "checkpt". if ((xta * normal[0] + yta * normal[1] + zta * normal[2]) < 0) { // Reverse the normal direction. normal[0] = -normal[0]; normal[1] = -normal[1]; normal[2] = -normal[2]; } if (xta * xta + yta * yta + zta * zta <= 2.0 * (xta * (fcenter[0] - multiplier * normal[0]) + yta * (fcenter[1] - multiplier * normal[1]) + zta * (fcenter[2] - multiplier * normal[2]))) { encroached = 1; } } else { len = distance(cent, checkpt); if ((fabs(len - rd) / rd) < b->epsilon) len = rd; // Rounding. if (len < rd) { encroached = 1; } } if (encroached) { // The point lies inside the circumsphere of this face. if (b->metric) { // -m option. if ((pa[pointmtrindex] > 0) && (pb[pointmtrindex] > 0) && (pc[pointmtrindex] > 0)) { // Get the projection of 'checkpt' in the plane of pa, pb, and pc. REAL prjpt[3], n[3]; REAL a, a1, a2, a3; projpt2face(checkpt, pa, pb, pc, prjpt); // Get the face area of [a,b,c]. facenormal(pa, pb, pc, n, 1, NULL); a = sqrt(dot(n, n)); // Get the face areas of [a,b,p], [b,c,p], and [c,a,p]. facenormal(pa, pb, prjpt, n, 1, NULL); a1 = sqrt(dot(n, n)); facenormal(pb, pc, prjpt, n, 1, NULL); a2 = sqrt(dot(n, n)); facenormal(pc, pa, prjpt, n, 1, NULL); a3 = sqrt(dot(n, n)); if ((fabs(a1 + a2 + a3 - a) / a) < b->epsilon) { // This face contains the projection. // Get the mesh size at the location of the projection point. rd = a1 / a * pc[pointmtrindex] + a2 / a * pa[pointmtrindex] + a3 / a * pb[pointmtrindex]; len = distance(prjpt, checkpt); if (len < rd) { return 1; // Encroached. } } } else { return 1; // No protecting ball. Encroached. } } else { *r = rd; return 1; // Encroached. } } return 0; } /////////////////////////////////////////////////////////////////////////////// // // // checkfac4split() Check if a subface needs to be split. // // // // A subface needs to be split if it is in the following case: // // (1) It is encroached by an existing vertex. // // (2) It has bad quality (has a small angle, -q). // // (3) It's area is larger than a prescribed value (.var). // // // // Return 1 if it needs to be split, otherwise, return 0. // // 'chkfac' represents its longest edge. // // // /////////////////////////////////////////////////////////////////////////////// int tetgenmesh::checkfac4split(face* chkfac, point& encpt, int& qflag, REAL* cent) { point pa, pb, pc; REAL area, rd, len; REAL A[4][4], rhs[4], D; int indx[4]; int i; encpt = NULL; qflag = 0; pa = sorg(*chkfac); pb = sdest(*chkfac); pc = sapex(*chkfac); // Compute the coefficient matrix A (3x3). A[0][0] = pb[0] - pa[0]; A[0][1] = pb[1] - pa[1]; A[0][2] = pb[2] - pa[2]; // vector V1 (pa->pb) A[1][0] = pc[0] - pa[0]; A[1][1] = pc[1] - pa[1]; A[1][2] = pc[2] - pa[2]; // vector V2 (pa->pc) cross(A[0], A[1], A[2]); // vector V3 (V1 X V2) area = 0.5 * sqrt(dot(A[2], A[2])); // The area of [a,b,c]. // Compute the right hand side vector b (3x1). rhs[0] = 0.5 * dot(A[0], A[0]); // edge [a,b] rhs[1] = 0.5 * dot(A[1], A[1]); // edge [a,c] rhs[2] = 0.0; // Solve the 3 by 3 equations use LU decomposition with partial // pivoting and backward and forward substitute. if (!lu_decmp(A, 3, indx, &D, 0)) { // A degenerate triangle. terminatetetgen(this, 2); } lu_solve(A, 3, indx, rhs, 0); cent[0] = pa[0] + rhs[0]; cent[1] = pa[1] + rhs[1]; cent[2] = pa[2] + rhs[2]; rd = sqrt(rhs[0] * rhs[0] + rhs[1] * rhs[1] + rhs[2] * rhs[2]); if (checkconstraints && (areabound(*chkfac) > 0.0)) { // Check if the subface has too big area. if (area > areabound(*chkfac)) { qflag = 1; return 1; } } if (b->fixedvolume) { if ((area * sqrt(area)) > b->maxvolume) { qflag = 1; return 1; } } if (b->varvolume) { triface adjtet; REAL volbnd; int t1ver; stpivot(*chkfac, adjtet); if (!ishulltet(adjtet)) { volbnd = volumebound(adjtet.tet); if ((volbnd > 0) && (area * sqrt(area)) > volbnd) { qflag = 1; return 1; } } fsymself(adjtet); if (!ishulltet(adjtet)) { volbnd = volumebound(adjtet.tet); if ((volbnd > 0) && (area * sqrt(area)) > volbnd) { qflag = 1; return 1; } } } if (b->metric) { // -m option. Check mesh size. // Check if the ccent lies outside one of the prot.balls at vertices. if (((pa[pointmtrindex] > 0) && (rd > pa[pointmtrindex])) || ((pb[pointmtrindex] > 0) && (rd > pb[pointmtrindex])) || ((pc[pointmtrindex] > 0) && (rd > pc[pointmtrindex]))) { qflag = 1; // Enforce mesh size. return 1; } } triface searchtet; REAL smlen = 0; // Check if this subface is locally encroached. for (i = 0; i < 2; i++) { stpivot(*chkfac, searchtet); if (!ishulltet(searchtet)) { int encroached = 0; len = distance(oppo(searchtet), cent); if ((fabs(len - rd) / rd) < b->epsilon) len = rd; // Rounding. if (b->use_equatorial_lens) { point tettapex = oppo(searchtet); REAL normal[3], fcenter[3]; REAL xta, yta, zta; REAL multiplier; // Get the normal of the oriented face [a->b->c], without normalized. point fa = org(searchtet); point fb = dest(searchtet); point fc = apex(searchtet); fcenter[0] = cent[0] - fc[0]; fcenter[1] = cent[1] - fc[1]; fcenter[2] = cent[2] - fc[2]; facenormal(fa, fb, fc, normal, 1, NULL); multiplier = 0.985 * sqrt((fcenter[0] * fcenter[0] + fcenter[1] * fcenter[1] + fcenter[2] * fcenter[2]) / (3.0 * (normal[0] * normal[0] + normal[1] * normal[1] + normal[2] * normal[2]))); xta = tettapex[0] - fc[0]; yta = tettapex[1] - fc[1]; zta = tettapex[2] - fc[2]; if (xta * xta + yta * yta + zta * zta <= 2.0 * (xta * (fcenter[0] - multiplier * normal[0]) + yta * (fcenter[1] - multiplier * normal[1]) + zta * (fcenter[2] - multiplier * normal[2]))) { encroached = 1; } } else { if (len < rd) { encroached = 1; } } if (encroached) { if (smlen == 0) { smlen = len; encpt = oppo(searchtet); } else { if (len < smlen) { smlen = len; encpt = oppo(searchtet); } } // return 1; } } sesymself(*chkfac); } return encpt != NULL; // return 0; } /////////////////////////////////////////////////////////////////////////////// // // // splitsubface() Split a subface. // // // // The subface may be encroached, or in bad-quality. It is split at its cir- // // cumcenter ('ccent'). Do not split it if 'ccent' encroaches upon any seg- // // ment. Instead, one of the encroached segments is split. It is possible // // that none of the encroached segments can be split. // // // // The return value indicates whether a new point is inserted (> 0) or not // // (= 0). Furthermore, it is inserted on an encroached segment (= 1) or // // in-side the facet (= 2). // // // // 'encpt' is a vertex encroaching upon this subface, i.e., it causes the // // split of this subface. If 'encpt' is NULL, then the cause of the split // // this subface is a rejected tet circumcenter 'p', and 'encpt1' is the // // parent of 'p'. // // // /////////////////////////////////////////////////////////////////////////////// int tetgenmesh::splitsubface(face* splitfac, point encpt, point encpt1, int qflag, REAL* ccent, int chkencflag) { if (!qflag && smarktest3ed(*splitfac)) { // Do not try to re-split a marked subface. return 0; } if (b->nobisect) { // With -Y option. if (checkconstraints) { // Only split if it is allowed to be split. // Check if this facet has a non-zero constraint. if (areabound(*splitfac) == 0) { return 0; // Do not split it. } } else { return 0; } } // if (b->nobisect) if (useinsertradius) { if (encpt != NULL) { REAL rp; // Insertion radius of newpt. REAL rv = distance(encpt, ccent); if (pointtype(encpt) == FREESEGVERTEX) { face parentseg; sdecode(point2sh(encpt), parentseg); if (segfacetadjacent(&parentseg, splitfac)) { rp = getpointinsradius(encpt); if (rv < (sqrt(2.0) * rp)) { // This insertion may cause no termination. return 0; // Reject the insertion of newpt. } } } else if (pointtype(encpt) == FREEFACETVERTEX) { face parentsh; sdecode(point2sh(encpt), parentsh); if (facetfacetadjacent(&parentsh, splitfac)) { rp = getpointinsradius(encpt); if (rv < rp) { return 0; // Reject the insertion of newpt. } } } } } // if (useinsertradius) face searchsh; insertvertexflags ivf; point newpt; int i; // Initialize the inserting point. makepoint(&newpt, FREEFACETVERTEX); // Split the subface at its circumcenter. for (i = 0; i < 3; i++) newpt[i] = ccent[i]; // Search a subface which contains 'newpt'. searchsh = *splitfac; // Calculate an above point. It lies above the plane containing // the subface [a,b,c], and save it in dummypoint. Moreover, // the vector cent->dummypoint is the normal of the plane. calculateabovepoint4(newpt, sorg(*splitfac), sdest(*splitfac), sapex(*splitfac)); // Parameters: 'aflag' = 1, - above point exists. // 'cflag' = 0, - non-convex, check co-planarity of the result. // 'rflag' = 0, - no need to round the locating result. ivf.iloc = (int)slocate(newpt, &searchsh, 1, 0, 0); if (!((ivf.iloc == (int)ONFACE) || (ivf.iloc == (int)ONEDGE))) { // Point location failed. pointdealloc(newpt); // Mark this subface to avoid splitting in the future. smarktest3(*splitfac); return 0; } triface searchtet; // Insert the point. stpivot(searchsh, searchtet); ivf.bowywat = 3; // Use Bowyer-Watson. Preserve subsegments and subfaces; ivf.lawson = 2; ivf.rejflag = 1; // Do check the encroachment of segments. if (b->metric) { ivf.rejflag |= 4; // Do check encroachment of protecting balls. } ivf.chkencflag = chkencflag; ivf.sloc = (int)INSTAR; // ivf.iloc; ivf.sbowywat = 3; // ivf.bowywat; ivf.splitbdflag = 1; ivf.validflag = 1; ivf.respectbdflag = 1; ivf.assignmeshsize = b->metric; ivf.refineflag = 2; ivf.refinesh = *splitfac; ivf.smlenflag = useinsertradius; // Update the insertion radius. if (insertpoint(newpt, &searchtet, &searchsh, NULL, &ivf)) { st_facref_count++; if (steinerleft > 0) steinerleft--; if (useinsertradius) { save_facetpoint_insradius(newpt, ivf.parentpt, ivf.smlen); } // if (useinsertradius) if (flipstack != NULL) { flipconstraints fc; fc.chkencflag = chkencflag; fc.enqflag = 2; lawsonflip3d(&fc); unflipqueue->restart(); } return 1; } else { // Point was not inserted. pointdealloc(newpt); if (ivf.iloc == (int)ENCSEGMENT) { // Select an encroached segment and split it. face* paryseg; int splitflag = 0; for (i = 0; i < encseglist->objects; i++) { paryseg = (face*)fastlookup(encseglist, i); if (splitsegment(paryseg, NULL, 0.0, encpt, encpt1, qflag, chkencflag | 1)) { splitflag = 1; // A point is inserted on a segment. break; } } // i encseglist->restart(); if (splitflag) { // Some segments may need to be repaired. if (badsubsegs->items > 0) { repairencsegs(chkencflag | 1); } return 1; } } else { if (ivf.iloc == (int)NEARVERTEX) { terminatetetgen(this, 2); } } // Mark this subface to avoid splitting in the future. smarktest3(*splitfac); return 0; } } /////////////////////////////////////////////////////////////////////////////// // // // repairencfacs() Repair encroached subfaces. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::repairencfacs(int chkencflag) { face* bface; point encpt = NULL; int qflag = 0; REAL ccent[3]; // Loop until the pool 'badsubfacs' is empty. Note that steinerleft == -1 // if an unlimited number of Steiner points is allowed. while ((badsubfacs->items > 0) && (steinerleft != 0)) { badsubfacs->traversalinit(); bface = (face*)badsubfacs->traverse(); while ((bface != NULL) && (steinerleft != 0)) { // Skip a deleted element. if (bface->shver >= 0) { // A queued subface may have been deleted (split). if ((bface->sh != NULL) && (bface->sh[3] != NULL)) { // A queued subface may have been processed. if (smarktest2ed(*bface)) { sunmarktest2(*bface); if (checkfac4split(bface, encpt, qflag, ccent)) { splitsubface(bface, encpt, NULL, qflag, ccent, chkencflag); } } } bface->shver = -1; // Signal it as a deleted element. badsubfacs->dealloc((void*)bface); // Remove this entry from list. } bface = (face*)badsubfacs->traverse(); } } if (badsubfacs->items > 0) { if (steinerleft == 0) { if (b->verbose) { printf("The desired number of Steiner points is reached.\n"); } } else { terminatetetgen(this, 2); } badsubfacs->traversalinit(); bface = (face*)badsubfacs->traverse(); while (bface != NULL) { // Skip a deleted element. if (bface->shver >= 0) { if ((bface->sh != NULL) && (bface->sh[3] != NULL)) { if (smarktest2ed(*bface)) { sunmarktest2(*bface); } } } bface = (face*)badsubfacs->traverse(); } badsubfacs->restart(); } } /////////////////////////////////////////////////////////////////////////////// // // // checktet4split() Check if the tet needs to be split. // // // /////////////////////////////////////////////////////////////////////////////// int tetgenmesh::checktet4split(triface* chktet, int& qflag, REAL* ccent) { point pa, pb, pc, pd, *ppt; REAL vda[3], vdb[3], vdc[3]; REAL vab[3], vbc[3], vca[3]; REAL N[4][3], L[4], cosd[6], elen[6]; REAL maxcosd, vol, volbnd, smlen = 0, rd; REAL A[4][4], rhs[4], D; int indx[4]; int i, j; if (b->convex) { // -c // Skip this tet if it lies in the exterior. if (elemattribute(chktet->tet, numelemattrib - 1) == -1.0) { return 0; } } qflag = 0; pd = (point)chktet->tet[7]; if (pd == dummypoint) { return 0; // Do not split a hull tet. } pa = (point)chktet->tet[4]; pb = (point)chktet->tet[5]; pc = (point)chktet->tet[6]; // Get the edge vectors vda: d->a, vdb: d->b, vdc: d->c. // Set the matrix A = [vda, vdb, vdc]^T. for (i = 0; i < 3; i++) A[0][i] = vda[i] = pa[i] - pd[i]; for (i = 0; i < 3; i++) A[1][i] = vdb[i] = pb[i] - pd[i]; for (i = 0; i < 3; i++) A[2][i] = vdc[i] = pc[i] - pd[i]; // Get the other edge vectors. for (i = 0; i < 3; i++) vab[i] = pb[i] - pa[i]; for (i = 0; i < 3; i++) vbc[i] = pc[i] - pb[i]; for (i = 0; i < 3; i++) vca[i] = pa[i] - pc[i]; if (!lu_decmp(A, 3, indx, &D, 0)) { // A degenerated tet (vol = 0). // This is possible due to the use of exact arithmetic. We temporarily // leave this tet. It should be fixed by mesh optimization. return 0; } // Check volume if '-a#' and '-a' options are used. if (b->varvolume || b->fixedvolume) { vol = fabs(A[indx[0]][0] * A[indx[1]][1] * A[indx[2]][2]) / 6.0; if (b->fixedvolume) { if (vol > b->maxvolume) { qflag = 1; } } if (!qflag && b->varvolume) { volbnd = volumebound(chktet->tet); if ((volbnd > 0.0) && (vol > volbnd)) { qflag = 1; } } if (qflag == 1) { // Calculate the circumcenter of this tet. rhs[0] = 0.5 * dot(vda, vda); rhs[1] = 0.5 * dot(vdb, vdb); rhs[2] = 0.5 * dot(vdc, vdc); lu_solve(A, 3, indx, rhs, 0); for (i = 0; i < 3; i++) ccent[i] = pd[i] + rhs[i]; return 1; } } if (b->metric) { // -m option. Check mesh size. // Calculate the circumradius of this tet. rhs[0] = 0.5 * dot(vda, vda); rhs[1] = 0.5 * dot(vdb, vdb); rhs[2] = 0.5 * dot(vdc, vdc); lu_solve(A, 3, indx, rhs, 0); for (i = 0; i < 3; i++) ccent[i] = pd[i] + rhs[i]; rd = sqrt(dot(rhs, rhs)); // Check if the ccent lies outside one of the prot.balls at vertices. ppt = (point*)&(chktet->tet[4]); for (i = 0; i < 4; i++) { if (ppt[i][pointmtrindex] > 0) { if (rd > ppt[i][pointmtrindex]) { qflag = 1; // Enforce mesh size. return 1; } } } } if (in->tetunsuitable != NULL) { // Execute the user-defined meshing sizing evaluation. if ((*(in->tetunsuitable))(pa, pb, pc, pd, NULL, 0)) { // Calculate the circumcenter of this tet. rhs[0] = 0.5 * dot(vda, vda); rhs[1] = 0.5 * dot(vdb, vdb); rhs[2] = 0.5 * dot(vdc, vdc); lu_solve(A, 3, indx, rhs, 0); for (i = 0; i < 3; i++) ccent[i] = pd[i] + rhs[i]; return 1; } } if (useinsertradius) { // Do not split this tet if the shortest edge is shorter than the // insertion radius of one of its endpoints. triface checkedge; point e1, e2; REAL rrv, smrrv; // Get the shortest edge of this tet. checkedge.tet = chktet->tet; for (i = 0; i < 6; i++) { checkedge.ver = edge2ver[i]; e1 = org(checkedge); e2 = dest(checkedge); elen[i] = distance(e1, e2); if (i == 0) { smlen = elen[i]; j = 0; } else { if (elen[i] < smlen) { smlen = elen[i]; j = i; } } } // Check if the edge is too short. checkedge.ver = edge2ver[j]; // Get the smallest rrv of e1 and e2. // Note: if rrv of e1 and e2 is zero. Do not use it. e1 = org(checkedge); smrrv = getpointinsradius(e1); e2 = dest(checkedge); rrv = getpointinsradius(e2); if (rrv > 0) { if (smrrv > 0) { if (rrv < smrrv) { smrrv = rrv; } } else { smrrv = rrv; } } if (smrrv > 0) { // To avoid rounding error, round smrrv before doing comparison. if ((fabs(smrrv - smlen) / smlen) < b->epsilon) { smrrv = smlen; } if (smrrv > smlen) { return 0; } } } // if (useinsertradius) // Check the radius-edge ratio. Set by -q#. if (b->minratio > 0) { // Calculate the circumcenter and radius of this tet. rhs[0] = 0.5 * dot(vda, vda); rhs[1] = 0.5 * dot(vdb, vdb); rhs[2] = 0.5 * dot(vdc, vdc); lu_solve(A, 3, indx, rhs, 0); for (i = 0; i < 3; i++) ccent[i] = pd[i] + rhs[i]; rd = sqrt(dot(rhs, rhs)); if (!useinsertradius) { // Calculate the shortest edge length. elen[0] = dot(vda, vda); elen[1] = dot(vdb, vdb); elen[2] = dot(vdc, vdc); elen[3] = dot(vab, vab); elen[4] = dot(vbc, vbc); elen[5] = dot(vca, vca); smlen = elen[0]; // sidx = 0; for (i = 1; i < 6; i++) { if (smlen > elen[i]) { smlen = elen[i]; // sidx = i; } } smlen = sqrt(smlen); } D = rd / smlen; if (D > b->minratio) { // A bad radius-edge ratio. return 1; } } // Check the minimum dihedral angle. Set by -qq#. if (b->mindihedral > 0) { // Compute the 4 face normals (N[0], ..., N[3]). for (j = 0; j < 3; j++) { for (i = 0; i < 3; i++) N[j][i] = 0.0; N[j][j] = 1.0; // Positive means the inside direction lu_solve(A, 3, indx, N[j], 0); } for (i = 0; i < 3; i++) N[3][i] = -N[0][i] - N[1][i] - N[2][i]; // Normalize the normals. for (i = 0; i < 4; i++) { L[i] = sqrt(dot(N[i], N[i])); if (L[i] == 0) { terminatetetgen(this, 2); } for (j = 0; j < 3; j++) N[i][j] /= L[i]; } // Calculate the six dihedral angles. cosd[0] = -dot(N[0], N[1]); // Edge cd, bd, bc. cosd[1] = -dot(N[0], N[2]); cosd[2] = -dot(N[0], N[3]); cosd[3] = -dot(N[1], N[2]); // Edge ad, ac cosd[4] = -dot(N[1], N[3]); cosd[5] = -dot(N[2], N[3]); // Edge ab // Get the smallest dihedral angle. // maxcosd = mincosd = cosd[0]; maxcosd = cosd[0]; for (i = 1; i < 6; i++) { // if (cosd[i] > maxcosd) maxcosd = cosd[i]; maxcosd = (cosd[i] > maxcosd ? cosd[i] : maxcosd); // mincosd = (cosd[i] < mincosd ? cosd[i] : maxcosd); } if (maxcosd > cosmindihed) { // Calculate the circumcenter of this tet. // A bad dihedral angle. // if ((b->quality & 1) == 0) { rhs[0] = 0.5 * dot(vda, vda); rhs[1] = 0.5 * dot(vdb, vdb); rhs[2] = 0.5 * dot(vdc, vdc); lu_solve(A, 3, indx, rhs, 0); for (i = 0; i < 3; i++) ccent[i] = pd[i] + rhs[i]; //*rd = sqrt(dot(rhs, rhs)); //} return 1; } } return 0; } /////////////////////////////////////////////////////////////////////////////// // // // splittetrahedron() Split a tetrahedron. // // // /////////////////////////////////////////////////////////////////////////////// int tetgenmesh::splittetrahedron(triface* splittet, int qflag, REAL* ccent, int chkencflag) { triface searchtet; face* paryseg; point newpt, *ppt; badface* bface; insertvertexflags ivf; int splitflag = 0; int i; REAL rv = 0.; // Insertion radius of 'newpt'. makepoint(&newpt, FREEVOLVERTEX); for (i = 0; i < 3; i++) newpt[i] = ccent[i]; // Locate the new point. Starting from an interior point 'q' of the // splittet. We perform a walk from q to the 'newpt', stop walking // either we hit a subface or enter OUTSIDE. searchtet = *splittet; ivf.iloc = (int)OUTSIDE; ivf.iloc = locate(newpt, &searchtet, 1); // 'chkencflag' = 1. if ((ivf.iloc == (int)OUTSIDE) || (ivf.iloc == (int)ENCSUBFACE)) { // The circumcenter 'c' is not visible from 'q' (the interior of the tet). // iffalse if (b->verbose > 2) { printf(" New point %d is blocked by a polygon.\n", pointmark(newpt)); } // \fi pointdealloc(newpt); // Do not insert this vertex. if (b->nobisect) return 0; // -Y option. // There must be a polygon that blocks the visibility. // Search a subpolygon that contains the proj(c). face searchsh; REAL prjpt[3]; locateresult sloc = OUTSIDE; tspivot(searchtet, searchsh); ppt = (point*)&(searchsh.sh[3]); projpt2face(ccent, ppt[0], ppt[1], ppt[2], prjpt); // Locate proj(c) on polygon. sloc = slocate(prjpt, &searchsh, 0, 0, 1); if ((sloc == ONEDGE) || (sloc == ONFACE)) { // Found a subface/edge containing proj(c). // Check if 'c' encoraches upon this subface. REAL fcent[3], r = 0; ppt = (point*)&(searchsh.sh[3]); if (checkfac4encroach(ppt[0], ppt[1], ppt[2], ccent, fcent, &r)) { // Encroached. Split this subface. splitflag = splitsubface(&searchsh, NULL, org(*splittet), qflag, fcent, chkencflag | 2); if (splitflag) { // Some subfaces may need to be repaired. repairencfacs(chkencflag | 2); } } } else if ((sloc == OUTSIDE) || (sloc == ENCSEGMENT)) { // Hit a segment. We should split it. // To be done... // printf("hit segment, split it.\n"); // For debug only } if (splitflag) { // Queue the tet if it is still alive. if ((splittet->tet != NULL) && (splittet->tet[4] != NULL)) { enqueuetetrahedron(splittet); } } return splitflag; } // Use Bowyer-Watson algorithm. Preserve subsegments and subfaces; ivf.bowywat = 3; ivf.lawson = 2; ivf.rejflag = 3; // Do check for encroached segments and subfaces. if (b->metric) { ivf.rejflag |= 4; // Reject it if it lies in some protecting balls. } ivf.chkencflag = chkencflag; ivf.sloc = ivf.sbowywat = 0; // No use. ivf.splitbdflag = 0; // No use. ivf.validflag = 1; ivf.respectbdflag = 1; ivf.assignmeshsize = b->metric; ivf.refineflag = 1; ivf.refinetet = *splittet; if (useinsertradius) { // Need to save insertion radius for this new point. ivf.smlenflag = 1; // Return the shortest edge length after inserting // the new vertex. [2016-09-19] } if (insertpoint(newpt, &searchtet, NULL, NULL, &ivf)) { // Vertex is inserted. st_volref_count++; if (steinerleft > 0) steinerleft--; if (useinsertradius) { setpointinsradius(newpt, ivf.smlen); setpoint2ppt(newpt, ivf.parentpt); } if (flipstack != NULL) { flipconstraints fc; fc.chkencflag = chkencflag; fc.enqflag = 2; lawsonflip3d(&fc); unflipqueue->restart(); } return 1; } else { // Point is not inserted. pointdealloc(newpt); // Check if there are encroached segments/subfaces. if (ivf.iloc == (int)ENCSEGMENT) { if (!b->nobisect || checkconstraints) { // Select an encroached segment and split it. for (i = 0; i < encseglist->objects; i++) { paryseg = (face*)fastlookup(encseglist, i); if (splitsegment(paryseg, NULL, rv, org(*splittet), NULL, qflag, chkencflag | 3)) { splitflag = 1; // A point is inserted on a segment. break; } } } // if (!b->nobisect) encseglist->restart(); if (splitflag) { // Some segments may need to be repaired. if (badsubsegs->items > 0) { repairencsegs(chkencflag | 3); } // Some subfaces may need to be repaired. if (badsubfacs->items > 0) { repairencfacs(chkencflag | 2); } } } else if (ivf.iloc == (int)ENCSUBFACE) { if (!b->nobisect || checkconstraints) { // Select an encroached subface and split it. for (i = 0; i < encshlist->objects; i++) { bface = (badface*)fastlookup(encshlist, i); if (splitsubface(&(bface->ss), NULL, org(*splittet), qflag, bface->cent, chkencflag | 2)) { splitflag = 1; // A point is inserted on a subface or a segment. break; } } } // if (!b->nobisect) encshlist->restart(); if (splitflag) { // Some subfaces may need to be repaired. if (badsubfacs->items > 0) { repairencfacs(chkencflag | 2); } } } else { if (ivf.iloc == (int)NEARVERTEX) { terminatetetgen(this, 2); } } if (splitflag) { // Queue the tet if it is still alive. if ((splittet->tet != NULL) && (splittet->tet[4] != NULL)) { enqueuetetrahedron(splittet); } } else { // assert(0); // If no small angle, why can this happen? } return splitflag; } } /////////////////////////////////////////////////////////////////////////////// // // // repairbadtets() Repair bad quality tetrahedra. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::repairbadtets(int chkencflag) { triface* bface; REAL ccent[3]; int qflag = 0; // Loop until the pool 'badsubfacs' is empty. Note that steinerleft == -1 // if an unlimited number of Steiner points is allowed. while ((badtetrahedrons->items > 0) && (steinerleft != 0)) { badtetrahedrons->traversalinit(); bface = (triface*)badtetrahedrons->traverse(); while ((bface != NULL) && (steinerleft != 0)) { // Skip a deleted element. if (bface->ver >= 0) { // A queued tet may have been deleted. if (!isdeadtet(*bface)) { // A queued tet may have been processed. if (marktest2ed(*bface)) { unmarktest2(*bface); if (checktet4split(bface, qflag, ccent)) { splittetrahedron(bface, qflag, ccent, chkencflag); } } } bface->ver = -1; // Signal it as a deleted element. badtetrahedrons->dealloc((void*)bface); } bface = (triface*)badtetrahedrons->traverse(); } } if (badtetrahedrons->items > 0) { if (steinerleft == 0) { if (b->verbose) { printf("The desired number of Steiner points is reached.\n"); } } else { terminatetetgen(this, 2); // Unknown case. } // Unmark all queued tet. badtetrahedrons->traversalinit(); bface = (triface*)badtetrahedrons->traverse(); while (bface != NULL) { // Skip a deleted element. if (bface->ver >= 0) { if (!isdeadtet(*bface)) { if (marktest2ed(*bface)) { unmarktest2(*bface); } } } bface = (triface*)badtetrahedrons->traverse(); } // Clear the pool. badtetrahedrons->restart(); } } /////////////////////////////////////////////////////////////////////////////// // // // delaunayrefinement() Refine the mesh by Delaunay refinement. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::delaunayrefinement() { triface checktet; face checksh; face checkseg; long steinercount; int chkencflag; long bak_segref_count, bak_facref_count, bak_volref_count; long bak_flipcount = flip23count + flip32count + flip44count; if (!b->quiet) { printf("Refining mesh...\n"); } if (b->verbose) { printf(" Min radius-edge ratio = %g.\n", b->minratio); printf(" Min dihedral angle = %g.\n", b->mindihedral); // printf(" Min Edge length = %g.\n", b->minedgelength); } steinerleft = b->steinerleft; // Upperbound of # Steiner points (by -S#). if (steinerleft > 0) { // Check if we've already used up the given number of Steiner points. steinercount = st_segref_count + st_facref_count + st_volref_count; if (steinercount < steinerleft) { steinerleft -= steinercount; } else { if (!b->quiet) { printf("\nWarning: "); printf("The desired number of Steiner points (%d) has reached.\n\n", b->steinerleft); } return; // No more Steiner points. } } if (useinsertradius) { if ((b->plc && b->nobisect) || b->refine) { // '-pY' or '-r' option. makesegmentendpointsmap(); makefacetverticesmap(); } } encseglist = new arraypool(sizeof(face), 8); encshlist = new arraypool(sizeof(badface), 8); // if (!b->nobisect) { // if no '-Y' option if (!b->nobisect || checkconstraints) { if (b->verbose) { printf(" Splitting encroached subsegments.\n"); } chkencflag = 1; // Only check encroaching subsegments. steinercount = points->items; // Initialize the pool of encroached subsegments. badsubsegs = new memorypool(sizeof(face), b->shellfaceperblock, sizeof(void*), 0); // Add all segments into the pool. subsegs->traversalinit(); checkseg.sh = shellfacetraverse(subsegs); while (checkseg.sh != (shellface*)NULL) { enqueuesubface(badsubsegs, &checkseg); checkseg.sh = shellfacetraverse(subsegs); } // Split all encroached segments. repairencsegs(chkencflag); if (b->verbose) { printf(" Added %ld Steiner points.\n", points->items - steinercount); } if (b->reflevel > 1) { // '-D2' option if (b->verbose) { printf(" Splitting encroached subfaces.\n"); } chkencflag = 2; // Only check encroaching subfaces. steinercount = points->items; bak_segref_count = st_segref_count; bak_facref_count = st_facref_count; // Initialize the pool of encroached subfaces. badsubfacs = new memorypool(sizeof(face), b->shellfaceperblock, sizeof(void*), 0); // Add all subfaces into the pool. subfaces->traversalinit(); checksh.sh = shellfacetraverse(subfaces); while (checksh.sh != (shellface*)NULL) { enqueuesubface(badsubfacs, &checksh); checksh.sh = shellfacetraverse(subfaces); } // Split all encroached subfaces. repairencfacs(chkencflag); if (b->verbose) { printf(" Added %ld (%ld,%ld) Steiner points.\n", points->items - steinercount, st_segref_count - bak_segref_count, st_facref_count - bak_facref_count); } } // if (b->reflevel > 1) } // if (!b->nobisect) if (b->reflevel > 2) { // '-D3' option (The default option) if (b->verbose) { printf(" Splitting bad quality tets.\n"); } chkencflag = 4; // Only check tetrahedra. steinercount = points->items; bak_segref_count = st_segref_count; bak_facref_count = st_facref_count; bak_volref_count = st_volref_count; // The cosine value of the min dihedral angle (-qq) for tetrahedra. cosmindihed = cos(b->mindihedral / 180.0 * PI); // Initialize the pool of bad quality tetrahedra. badtetrahedrons = new memorypool(sizeof(triface), b->tetrahedraperblock, sizeof(void*), 0); // Add all tetrahedra (no hull tets) into the pool. tetrahedrons->traversalinit(); checktet.tet = tetrahedrontraverse(); while (checktet.tet != NULL) { enqueuetetrahedron(&checktet); checktet.tet = tetrahedrontraverse(); } // Split all bad quality tetrahedra. repairbadtets(chkencflag); if (b->verbose) { printf(" Added %ld (%ld,%ld,%ld) Steiner points.\n", points->items - steinercount, st_segref_count - bak_segref_count, st_facref_count - bak_facref_count, st_volref_count - bak_volref_count); } } // if (b->reflevel > 2) if (b->verbose) { if (flip23count + flip32count + flip44count > bak_flipcount) { printf(" Performed %ld flips.\n", flip23count + flip32count + flip44count - bak_flipcount); } } if (steinerleft == 0) { if (!b->quiet) { printf("\nWarnning: "); printf("The desired number of Steiner points (%d) is reached.\n\n", b->steinerleft); } } delete encseglist; delete encshlist; encseglist = NULL; encshlist = NULL; if (!b->nobisect || checkconstraints) { totalworkmemory += (badsubsegs->maxitems * badsubsegs->itembytes); delete badsubsegs; badsubsegs = NULL; if (b->reflevel > 1) { totalworkmemory += (badsubfacs->maxitems * badsubfacs->itembytes); delete badsubfacs; badsubfacs = NULL; } } if (b->reflevel > 2) { totalworkmemory += (badtetrahedrons->maxitems * badtetrahedrons->itembytes); delete badtetrahedrons; badtetrahedrons = NULL; } } //// //// //// //// //// refine_cxx /////////////////////////////////////////////////////////////// //// optimize_cxx ///////////////////////////////////////////////////////////// //// //// //// //// /////////////////////////////////////////////////////////////////////////////// // // // lawsonflip3d() A three-dimensional Lawson's algorithm. // // // /////////////////////////////////////////////////////////////////////////////// long tetgenmesh::lawsonflip3d(flipconstraints* fc) { triface fliptets[5], neightet, hulltet; face checksh, casingout; badface *popface, *bface; point pd, pe, *pts; REAL sign, ori; REAL vol, len3; long flipcount, totalcount = 0l; long sliver_peels = 0l; int t1ver; int i; while (1) { if (b->verbose > 2) { printf(" Lawson flip %ld faces.\n", flippool->items); } flipcount = 0l; while (flipstack != (badface*)NULL) { // Pop a face from the stack. popface = flipstack; fliptets[0] = popface->tt; flipstack = flipstack->nextitem; // The next top item in stack. flippool->dealloc((void*)popface); // Skip it if it is a dead tet (destroyed by previous flips). if (isdeadtet(fliptets[0])) continue; // Skip it if it is not the same tet as we saved. if (!facemarked(fliptets[0])) continue; unmarkface(fliptets[0]); if (ishulltet(fliptets[0])) continue; fsym(fliptets[0], fliptets[1]); if (ishulltet(fliptets[1])) { if (nonconvex) { // Check if 'fliptets[0]' it is a hull sliver. tspivot(fliptets[0], checksh); for (i = 0; i < 3; i++) { if (!isshsubseg(checksh)) { spivot(checksh, casingout); // assert(casingout.sh != NULL); if (sorg(checksh) != sdest(casingout)) sesymself(casingout); stpivot(casingout, neightet); if (neightet.tet == fliptets[0].tet) { // Found a hull sliver 'neightet'. Let it be [e,d,a,b], where // [e,d,a] and [d,e,b] are hull faces. edestoppo(neightet, hulltet); // [a,b,e,d] fsymself(hulltet); // [b,a,e,#] if (oppo(hulltet) == dummypoint) { pe = org(neightet); if ((pointtype(pe) == FREEFACETVERTEX) || (pointtype(pe) == FREESEGVERTEX)) { removevertexbyflips(pe); } } else { eorgoppo(neightet, hulltet); // [b,a,d,e] fsymself(hulltet); // [a,b,d,#] if (oppo(hulltet) == dummypoint) { pd = dest(neightet); if ((pointtype(pd) == FREEFACETVERTEX) || (pointtype(pd) == FREESEGVERTEX)) { removevertexbyflips(pd); } } else { // Perform a 3-to-2 flip to remove the sliver. fliptets[0] = neightet; // [e,d,a,b] fnext(fliptets[0], fliptets[1]); // [e,d,b,c] fnext(fliptets[1], fliptets[2]); // [e,d,c,a] flip32(fliptets, 1, fc); // Update counters. flip32count--; flip22count--; sliver_peels++; if (fc->remove_ndelaunay_edge) { // Update the volume (must be decreased). // assert(fc->tetprism_vol_sum <= 0); tetprism_vol_sum += fc->tetprism_vol_sum; fc->tetprism_vol_sum = 0.0; // Clear it. } } } break; } // if (neightet.tet == fliptets[0].tet) } // if (!isshsubseg(checksh)) senextself(checksh); } // i } // if (nonconvex) continue; } if (checksubfaceflag) { // Do not flip if it is a subface. if (issubface(fliptets[0])) continue; } // Test whether the face is locally Delaunay or not. pts = (point*)fliptets[1].tet; sign = insphere_s(pts[4], pts[5], pts[6], pts[7], oppo(fliptets[0])); if (sign < 0) { // A non-Delaunay face. Try to flip it. pd = oppo(fliptets[0]); pe = oppo(fliptets[1]); // Use the length of the edge [d,e] as a reference to determine // a nearly degenerated new tet. len3 = distance(pd, pe); len3 = (len3 * len3 * len3); int round_flag = 0; // [2017-10-20] // Check the convexity of its three edges. Stop checking either a // locally non-convex edge (ori < 0) or a flat edge (ori = 0) is // encountered, and 'fliptet' represents that edge. for (i = 0; i < 3; i++) { ori = orient3d(org(fliptets[0]), dest(fliptets[0]), pd, pe); if (ori > 0) { // Avoid creating a nearly degenerated new tet at boundary. // Re-use fliptets[2], fliptets[3]; esym(fliptets[0], fliptets[2]); esym(fliptets[1], fliptets[3]); if (issubface(fliptets[2]) || issubface(fliptets[3])) { vol = orient3dfast(org(fliptets[0]), dest(fliptets[0]), pd, pe); if ((fabs(vol) / len3) < b->epsilon) { ori = 0.0; // Do rounding. round_flag = 1; // [2017-10-20] } } } // Rounding check if (ori <= 0) break; enextself(fliptets[0]); eprevself(fliptets[1]); } if (ori > 0) { // A 2-to-3 flip is found. // [0] [a,b,c,d], // [1] [b,a,c,e]. no dummypoint. flip23(fliptets, 0, fc); flipcount++; if (fc->remove_ndelaunay_edge) { // Update the volume (must be decreased). // assert(fc->tetprism_vol_sum <= 0); tetprism_vol_sum += fc->tetprism_vol_sum; fc->tetprism_vol_sum = 0.0; // Clear it. } continue; } else { // ori <= 0 // The edge ('fliptets[0]' = [a',b',c',d]) is non-convex or flat, // where the edge [a',b'] is one of [a,b], [b,c], and [c,a]. if (checksubsegflag) { // Do not flip if it is a segment. if (issubseg(fliptets[0])) continue; } // Check if there are three or four tets sharing at this edge. esymself(fliptets[0]); // [b,a,d,c] for (i = 0; i < 3; i++) { fnext(fliptets[i], fliptets[i + 1]); } if (fliptets[3].tet == fliptets[0].tet) { // A 3-to-2 flip is found. (No hull tet.) flip32(fliptets, 0, fc); flipcount++; if (fc->remove_ndelaunay_edge) { // Update the volume (must be decreased). // assert(fc->tetprism_vol_sum <= 0); tetprism_vol_sum += fc->tetprism_vol_sum; fc->tetprism_vol_sum = 0.0; // Clear it. } continue; } else { // There are more than 3 tets at this edge. fnext(fliptets[3], fliptets[4]); if (fliptets[4].tet == fliptets[0].tet) { // There are exactly 4 tets at this edge. if (round_flag == 1) { continue; // [2017-10-20] } if (nonconvex) { if (apex(fliptets[3]) == dummypoint) { // This edge is locally non-convex on the hull. // It can be removed by a 4-to-4 flip. ori = 0; } } // if (nonconvex) if (ori == 0) { // A 4-to-4 flip is found. (Two hull tets may be involved.) // Current tets in 'fliptets': // [0] [b,a,d,c] (d may be newpt) // [1] [b,a,c,e] // [2] [b,a,e,f] (f may be dummypoint) // [3] [b,a,f,d] esymself(fliptets[0]); // [a,b,c,d] // A 2-to-3 flip replaces face [a,b,c] by edge [e,d]. // This creates a degenerate tet [e,d,a,b] (tmpfliptets[0]). // It will be removed by the followed 3-to-2 flip. flip23(fliptets, 0, fc); // No hull tet. fnext(fliptets[3], fliptets[1]); fnext(fliptets[1], fliptets[2]); // Current tets in 'fliptets': // [0] [...] // [1] [b,a,d,e] (degenerated, d may be new point). // [2] [b,a,e,f] (f may be dummypoint) // [3] [b,a,f,d] // A 3-to-2 flip replaces edge [b,a] by face [d,e,f]. // Hull tets may be involved (f may be dummypoint). flip32(&(fliptets[1]), (apex(fliptets[3]) == dummypoint), fc); flipcount++; flip23count--; flip32count--; flip44count++; if (fc->remove_ndelaunay_edge) { // Update the volume (must be decreased). // assert(fc->tetprism_vol_sum <= 0); tetprism_vol_sum += fc->tetprism_vol_sum; fc->tetprism_vol_sum = 0.0; // Clear it. } /////// Debug // if (checkmesh(0) > 0) { // assert(0); //} continue; } // if (ori == 0) } } } // if (ori <= 0) // This non-Delaunay face is unflippable. Save it. unflipqueue->newindex((void**)&bface); bface->tt = fliptets[0]; bface->forg = org(fliptets[0]); bface->fdest = dest(fliptets[0]); bface->fapex = apex(fliptets[0]); } // if (sign < 0) } // while (flipstack) if (b->verbose > 2) { if (flipcount > 0) { printf(" Performed %ld flips.\n", flipcount); } } // Accumulate the counter of flips. totalcount += flipcount; // Return if no unflippable faces left. if (unflipqueue->objects == 0l) break; // Return if no flip has been performed. if (flipcount == 0l) break; // Try to flip the unflippable faces. for (i = 0; i < unflipqueue->objects; i++) { bface = (badface*)fastlookup(unflipqueue, i); if (!isdeadtet(bface->tt) && (org(bface->tt) == bface->forg) && (dest(bface->tt) == bface->fdest) && (apex(bface->tt) == bface->fapex)) { flippush(flipstack, &(bface->tt)); } } unflipqueue->restart(); } // while (1) if (b->verbose > 2) { if (totalcount > 0) { printf(" Performed %ld flips.\n", totalcount); } if (sliver_peels > 0) { printf(" Removed %ld hull slivers.\n", sliver_peels); } if (unflipqueue->objects > 0l) { printf(" %ld unflippable edges remained.\n", unflipqueue->objects); } } return totalcount + sliver_peels; } /////////////////////////////////////////////////////////////////////////////// // // // recoverdelaunay() Recovery the locally Delaunay property. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::recoverdelaunay() { arraypool *flipqueue, *nextflipqueue, *swapqueue; triface tetloop, neightet, *parytet; badface *bface, *parybface; point* ppt; flipconstraints fc; int i, j; if (!b->quiet) { printf("Recovering Delaunayness...\n"); } tetprism_vol_sum = 0.0; // Initialize it. // Put all interior faces of the mesh into 'flipstack'. tetrahedrons->traversalinit(); tetloop.tet = tetrahedrontraverse(); while (tetloop.tet != NULL) { for (tetloop.ver = 0; tetloop.ver < 4; tetloop.ver++) { decode(tetloop.tet[tetloop.ver], neightet); if (!facemarked(neightet)) { flippush(flipstack, &tetloop); } } ppt = (point*)&(tetloop.tet[4]); tetprism_vol_sum += tetprismvol(ppt[0], ppt[1], ppt[2], ppt[3]); tetloop.tet = tetrahedrontraverse(); } // Calulate a relatively lower bound for small improvement. // Used to avoid rounding error in volume calculation. fc.bak_tetprism_vol = tetprism_vol_sum * b->epsilon * 1e-3; if (b->verbose) { printf(" Initial obj = %.17g\n", tetprism_vol_sum); } if (b->verbose > 1) { printf(" Recover Delaunay [Lawson] : %ld\n", flippool->items); } // First only use the basic Lawson's flip. fc.remove_ndelaunay_edge = 1; fc.enqflag = 2; lawsonflip3d(&fc); if (b->verbose > 1) { printf(" obj (after Lawson) = %.17g\n", tetprism_vol_sum); } if (unflipqueue->objects == 0l) { return; // The mesh is Delaunay. } fc.unflip = 1; // Unflip if the edge is not flipped. fc.collectnewtets = 1; // new tets are returned in 'cavetetlist'. fc.enqflag = 0; autofliplinklevel = 1; // Init level. b->fliplinklevel = -1; // No fixed level. // For efficiency reason, we limit the maximium size of the edge star. int bakmaxflipstarsize = b->flipstarsize; b->flipstarsize = 10; // default flipqueue = new arraypool(sizeof(badface), 10); nextflipqueue = new arraypool(sizeof(badface), 10); // Swap the two flip queues. swapqueue = flipqueue; flipqueue = unflipqueue; unflipqueue = swapqueue; while (flipqueue->objects > 0l) { if (b->verbose > 1) { printf(" Recover Delaunay [level = %2d] #: %ld.\n", autofliplinklevel, flipqueue->objects); } for (i = 0; i < flipqueue->objects; i++) { bface = (badface*)fastlookup(flipqueue, i); if (getedge(bface->forg, bface->fdest, &bface->tt)) { if (removeedgebyflips(&(bface->tt), &fc) == 2) { tetprism_vol_sum += fc.tetprism_vol_sum; fc.tetprism_vol_sum = 0.0; // Clear it. // Queue new faces for flips. for (j = 0; j < cavetetlist->objects; j++) { parytet = (triface*)fastlookup(cavetetlist, j); // A queued new tet may be dead. if (!isdeadtet(*parytet)) { for (parytet->ver = 0; parytet->ver < 4; parytet->ver++) { // Avoid queue a face twice. decode(parytet->tet[parytet->ver], neightet); if (!facemarked(neightet)) { flippush(flipstack, parytet); } } // parytet->ver } } // j cavetetlist->restart(); // Remove locally non-Delaunay faces. New non-Delaunay edges // may be found. They are saved in 'unflipqueue'. fc.enqflag = 2; lawsonflip3d(&fc); fc.enqflag = 0; // There may be unflipable faces. Add them in flipqueue. for (j = 0; j < unflipqueue->objects; j++) { bface = (badface*)fastlookup(unflipqueue, j); flipqueue->newindex((void**)&parybface); *parybface = *bface; } unflipqueue->restart(); } else { // Unable to remove this edge. Save it. nextflipqueue->newindex((void**)&parybface); *parybface = *bface; // Normally, it should be zero. // assert(fc.tetprism_vol_sum == 0.0); // However, due to rounding errors, a tiny value may appear. fc.tetprism_vol_sum = 0.0; } } } // i if (b->verbose > 1) { printf(" obj (after level %d) = %.17g.\n", autofliplinklevel, tetprism_vol_sum); } flipqueue->restart(); // Swap the two flip queues. swapqueue = flipqueue; flipqueue = nextflipqueue; nextflipqueue = swapqueue; if (flipqueue->objects > 0l) { // default 'b->delmaxfliplevel' is 1. if (autofliplinklevel >= b->delmaxfliplevel) { // For efficiency reason, we do not search too far. break; } autofliplinklevel += b->fliplinklevelinc; } } // while (flipqueue->objects > 0l) if (flipqueue->objects > 0l) { if (b->verbose > 1) { printf(" %ld non-Delaunay edges remained.\n", flipqueue->objects); } } if (b->verbose) { printf(" Final obj = %.17g\n", tetprism_vol_sum); } b->flipstarsize = bakmaxflipstarsize; delete flipqueue; delete nextflipqueue; } /////////////////////////////////////////////////////////////////////////////// // // // gettetrahedron() Get a tetrahedron which have the given vertices. // // // /////////////////////////////////////////////////////////////////////////////// int tetgenmesh::gettetrahedron(point pa, point pb, point pc, point pd, triface* searchtet) { triface spintet; int t1ver; if (getedge(pa, pb, searchtet)) { spintet = *searchtet; while (1) { if (apex(spintet) == pc) { *searchtet = spintet; break; } fnextself(spintet); if (spintet.tet == searchtet->tet) break; } if (apex(*searchtet) == pc) { if (oppo(*searchtet) == pd) { return 1; } else { fsymself(*searchtet); if (oppo(*searchtet) == pd) { return 1; } } } } return 0; } /////////////////////////////////////////////////////////////////////////////// // // // improvequalitybyflips() Improve the mesh quality by flips. // // // /////////////////////////////////////////////////////////////////////////////// long tetgenmesh::improvequalitybyflips() { arraypool *flipqueue, *nextflipqueue, *swapqueue; badface *bface, *parybface; triface* parytet; point* ppt; flipconstraints fc; REAL *cosdd, ncosdd[6], maxdd; long totalremcount, remcount; int remflag; int n, i, j, k; // assert(unflipqueue->objects > 0l); flipqueue = new arraypool(sizeof(badface), 10); nextflipqueue = new arraypool(sizeof(badface), 10); // Backup flip edge options. int bakautofliplinklevel = autofliplinklevel; int bakfliplinklevel = b->fliplinklevel; int bakmaxflipstarsize = b->flipstarsize; // Set flip edge options. autofliplinklevel = 1; b->fliplinklevel = -1; b->flipstarsize = 10; // b->optmaxflipstarsize; fc.remove_large_angle = 1; fc.unflip = 1; fc.collectnewtets = 1; fc.checkflipeligibility = 1; totalremcount = 0l; // Swap the two flip queues. swapqueue = flipqueue; flipqueue = unflipqueue; unflipqueue = swapqueue; while (flipqueue->objects > 0l) { remcount = 0l; while (flipqueue->objects > 0l) { if (b->verbose > 1) { printf(" Improving mesh qualiy by flips [%d]#: %ld.\n", autofliplinklevel, flipqueue->objects); } for (k = 0; k < flipqueue->objects; k++) { bface = (badface*)fastlookup(flipqueue, k); if (gettetrahedron(bface->forg, bface->fdest, bface->fapex, bface->foppo, &bface->tt)) { // assert(!ishulltet(bface->tt)); // There are bad dihedral angles in this tet. if (bface->tt.ver != 11) { // The dihedral angles are permuted. // Here we simply re-compute them. Slow!!. ppt = (point*)&(bface->tt.tet[4]); tetalldihedral(ppt[0], ppt[1], ppt[2], ppt[3], bface->cent, &bface->key, NULL); bface->forg = ppt[0]; bface->fdest = ppt[1]; bface->fapex = ppt[2]; bface->foppo = ppt[3]; bface->tt.ver = 11; } if (bface->key == 0) { // Re-comput the quality values. Due to smoothing operations. ppt = (point*)&(bface->tt.tet[4]); tetalldihedral(ppt[0], ppt[1], ppt[2], ppt[3], bface->cent, &bface->key, NULL); } cosdd = bface->cent; remflag = 0; for (i = 0; (i < 6) && !remflag; i++) { if (cosdd[i] < cosmaxdihed) { // Found a large dihedral angle. bface->tt.ver = edge2ver[i]; // Go to the edge. fc.cosdihed_in = cosdd[i]; fc.cosdihed_out = 0.0; // 90 degree. n = removeedgebyflips(&(bface->tt), &fc); if (n == 2) { // Edge is flipped. remflag = 1; if (fc.cosdihed_out < cosmaxdihed) { // Queue new bad tets for further improvements. for (j = 0; j < cavetetlist->objects; j++) { parytet = (triface*)fastlookup(cavetetlist, j); if (!isdeadtet(*parytet)) { ppt = (point*)&(parytet->tet[4]); // Do not test a hull tet. if (ppt[3] != dummypoint) { tetalldihedral(ppt[0], ppt[1], ppt[2], ppt[3], ncosdd, &maxdd, NULL); if (maxdd < cosmaxdihed) { // There are bad dihedral angles in this tet. nextflipqueue->newindex((void**)&parybface); parybface->tt.tet = parytet->tet; parybface->tt.ver = 11; parybface->forg = ppt[0]; parybface->fdest = ppt[1]; parybface->fapex = ppt[2]; parybface->foppo = ppt[3]; parybface->key = maxdd; for (n = 0; n < 6; n++) { parybface->cent[n] = ncosdd[n]; } } } // if (ppt[3] != dummypoint) } } // j } // if (fc.cosdihed_out < cosmaxdihed) cavetetlist->restart(); remcount++; } } } // i if (!remflag) { // An unremoved bad tet. Queue it again. unflipqueue->newindex((void**)&parybface); *parybface = *bface; } } // if (gettetrahedron(...)) } // k flipqueue->restart(); // Swap the two flip queues. swapqueue = flipqueue; flipqueue = nextflipqueue; nextflipqueue = swapqueue; } // while (flipqueues->objects > 0) if (b->verbose > 1) { printf(" Removed %ld bad tets.\n", remcount); } totalremcount += remcount; if (unflipqueue->objects > 0l) { // if (autofliplinklevel >= b->optmaxfliplevel) { if (autofliplinklevel >= b->optlevel) { break; } autofliplinklevel += b->fliplinklevelinc; // b->flipstarsize = 10 + (1 << (b->optlevel - 1)); } // Swap the two flip queues. swapqueue = flipqueue; flipqueue = unflipqueue; unflipqueue = swapqueue; } // while (flipqueues->objects > 0) // Restore original flip edge options. autofliplinklevel = bakautofliplinklevel; b->fliplinklevel = bakfliplinklevel; b->flipstarsize = bakmaxflipstarsize; delete flipqueue; delete nextflipqueue; return totalremcount; } /////////////////////////////////////////////////////////////////////////////// // // // smoothpoint() Moving a vertex to improve the mesh quality. // // // // 'smtpt' (p) is a point to be smoothed. Generally, it is a Steiner point. // // It may be not a vertex of the mesh. // // // // This routine tries to move 'p' inside its star until a selected objective // // function over all tetrahedra in the star is improved. The function may be // // the some quality measures, i.e., aspect ratio, maximum dihedral angel, or // // simply the volume of the tetrahedra. // // // // 'linkfacelist' contains the list of link faces of 'p'. Since a link face // // has two orientations, ccw or cw, with respect to 'p'. 'ccw' indicates // // the orientation is ccw (1) or not (0). // // // // 'opm' is a structure contains the parameters of the objective function. // // It is needed by the evaluation of the function value. // // // // The return value indicates weather the point is smoothed or not. // // // // ASSUMPTION: This routine assumes that all link faces are true faces, i.e, // // no face has 'dummypoint' as its vertex. // // // /////////////////////////////////////////////////////////////////////////////// int tetgenmesh::smoothpoint(point smtpt, arraypool* linkfacelist, int ccw, optparameters* opm) { triface *parytet, *parytet1, swaptet; point pa, pb, pc; REAL fcent[3], startpt[3], nextpt[3], bestpt[3]; REAL oldval, minval = 0.0, val; REAL maxcosd; // oldang, newang; REAL ori, diff; int numdirs, iter; int i, j, k; // Decide the number of moving directions. numdirs = (int)linkfacelist->objects; if (numdirs > opm->numofsearchdirs) { numdirs = opm->numofsearchdirs; // Maximum search directions. } // Set the initial value. opm->imprval = opm->initval; iter = 0; for (i = 0; i < 3; i++) { bestpt[i] = startpt[i] = smtpt[i]; } // Iterate until the obj function is not improved. while (1) { // Find the best next location. oldval = opm->imprval; for (i = 0; i < numdirs; i++) { // Randomly pick a link face (0 <= k <= objects - i - 1). k = (int)randomnation(linkfacelist->objects - i); parytet = (triface*)fastlookup(linkfacelist, k); // Calculate a new position from 'p' to the center of this face. pa = org(*parytet); pb = dest(*parytet); pc = apex(*parytet); for (j = 0; j < 3; j++) { fcent[j] = (pa[j] + pb[j] + pc[j]) / 3.0; } for (j = 0; j < 3; j++) { nextpt[j] = startpt[j] + opm->searchstep * (fcent[j] - startpt[j]); } // Calculate the largest minimum function value for the new location. for (j = 0; j < linkfacelist->objects; j++) { parytet = (triface*)fastlookup(linkfacelist, j); if (ccw) { pa = org(*parytet); pb = dest(*parytet); } else { pb = org(*parytet); pa = dest(*parytet); } pc = apex(*parytet); ori = orient3d(pa, pb, pc, nextpt); if (ori < 0.0) { // Calcuate the objective function value. if (opm->max_min_volume) { // val = -ori; val = -orient3dfast(pa, pb, pc, nextpt); } else if (opm->min_max_aspectratio) { val = 1.0 / tetaspectratio(pa, pb, pc, nextpt); } else if (opm->min_max_dihedangle) { tetalldihedral(pa, pb, pc, nextpt, NULL, &maxcosd, NULL); if (maxcosd < -1) maxcosd = -1.0; // Rounding. val = maxcosd + 1.0; // Make it be positive. } else { // Unknown objective function. val = 0.0; } } else { // ori >= 0.0; // An invalid new tet. // This may happen if the mesh contains inverted elements. if (opm->max_min_volume) { // val = -ori; val = -orient3dfast(pa, pb, pc, nextpt); } else { // Discard this point. break; // j } } // if (ori >= 0.0) // Stop looping when the object value is not improved. if (val <= opm->imprval) { break; // j } else { // Remember the smallest improved value. if (j == 0) { minval = val; } else { minval = (val < minval) ? val : minval; } } } // j if (j == linkfacelist->objects) { // The function value has been improved. opm->imprval = minval; // Save the new location of the point. for (j = 0; j < 3; j++) bestpt[j] = nextpt[j]; } // Swap k-th and (object-i-1)-th entries. j = linkfacelist->objects - i - 1; parytet = (triface*)fastlookup(linkfacelist, k); parytet1 = (triface*)fastlookup(linkfacelist, j); swaptet = *parytet1; *parytet1 = *parytet; *parytet = swaptet; } // i diff = opm->imprval - oldval; if (diff > 0.0) { // Is the function value improved effectively? if (opm->max_min_volume) { // if ((diff / oldval) < b->epsilon) diff = 0.0; } else if (opm->min_max_aspectratio) { if ((diff / oldval) < 1e-3) diff = 0.0; } else if (opm->min_max_dihedangle) { // oldang = acos(oldval - 1.0); // newang = acos(opm->imprval - 1.0); // if ((oldang - newang) < 0.00174) diff = 0.0; // about 0.1 degree. } else { // Unknown objective function. terminatetetgen(this, 2); } } if (diff > 0.0) { // Yes, move p to the new location and continue. for (j = 0; j < 3; j++) startpt[j] = bestpt[j]; iter++; if ((opm->maxiter > 0) && (iter >= opm->maxiter)) { // Maximum smoothing iterations reached. break; } } else { break; } } // while (1) if (iter > 0) { // The point has been smoothed. opm->smthiter = iter; // Remember the number of iterations. // The point has been smoothed. Update it to its new position. for (i = 0; i < 3; i++) smtpt[i] = startpt[i]; } return iter; } /////////////////////////////////////////////////////////////////////////////// // // // improvequalitysmoothing() Improve mesh quality by smoothing. // // // /////////////////////////////////////////////////////////////////////////////// long tetgenmesh::improvequalitybysmoothing(optparameters* opm) { arraypool *flipqueue, *swapqueue; triface* parytet; badface *bface, *parybface; point* ppt; long totalsmtcount, smtcount; int smtflag; int iter, i, j, k; // assert(unflipqueue->objects > 0l); flipqueue = new arraypool(sizeof(badface), 10); // Swap the two flip queues. swapqueue = flipqueue; flipqueue = unflipqueue; unflipqueue = swapqueue; totalsmtcount = 0l; iter = 0; while (flipqueue->objects > 0l) { smtcount = 0l; if (b->verbose > 1) { printf(" Improving mesh quality by smoothing [%d]#: %ld.\n", iter, flipqueue->objects); } for (k = 0; k < flipqueue->objects; k++) { bface = (badface*)fastlookup(flipqueue, k); if (gettetrahedron(bface->forg, bface->fdest, bface->fapex, bface->foppo, &bface->tt)) { // Operate on it if it is not in 'unflipqueue'. if (!marktested(bface->tt)) { // Here we simply re-compute the quality. Since other smoothing // operation may have moved the vertices of this tet. ppt = (point*)&(bface->tt.tet[4]); tetalldihedral(ppt[0], ppt[1], ppt[2], ppt[3], bface->cent, &bface->key, NULL); if (bface->key < cossmtdihed) { // if (maxdd < cosslidihed) { // It is a sliver. Try to smooth its vertices. smtflag = 0; opm->initval = bface->key + 1.0; for (i = 0; (i < 4) && !smtflag; i++) { if (pointtype(ppt[i]) == FREEVOLVERTEX) { getvertexstar(1, ppt[i], cavetetlist, NULL, NULL); opm->searchstep = 0.001; // Search step size smtflag = smoothpoint(ppt[i], cavetetlist, 1, opm); if (smtflag) { while (opm->smthiter == opm->maxiter) { opm->searchstep *= 10.0; // Increase the step size. opm->initval = opm->imprval; opm->smthiter = 0; // reset smoothpoint(ppt[i], cavetetlist, 1, opm); } // This tet is modifed. smtcount++; if ((opm->imprval - 1.0) < cossmtdihed) { // There are slivers in new tets. Queue them. for (j = 0; j < cavetetlist->objects; j++) { parytet = (triface*)fastlookup(cavetetlist, j); // Operate it if it is not in 'unflipqueue'. if (!marktested(*parytet)) { // Evaluate its quality. // Re-use ppt, bface->key, bface->cent. ppt = (point*)&(parytet->tet[4]); tetalldihedral(ppt[0], ppt[1], ppt[2], ppt[3], bface->cent, &bface->key, NULL); if (bface->key < cossmtdihed) { // A new sliver. Queue it. marktest(*parytet); // It is in unflipqueue. unflipqueue->newindex((void**)&parybface); parybface->tt = *parytet; parybface->forg = ppt[0]; parybface->fdest = ppt[1]; parybface->fapex = ppt[2]; parybface->foppo = ppt[3]; parybface->tt.ver = 11; parybface->key = 0.0; } } } // j } // if ((opm->imprval - 1.0) < cossmtdihed) } // if (smtflag) cavetetlist->restart(); } // if (pointtype(ppt[i]) == FREEVOLVERTEX) } // i if (!smtflag) { // Didn't smooth. Queue it again. marktest(bface->tt); // It is in unflipqueue. unflipqueue->newindex((void**)&parybface); parybface->tt = bface->tt; parybface->forg = ppt[0]; parybface->fdest = ppt[1]; parybface->fapex = ppt[2]; parybface->foppo = ppt[3]; parybface->tt.ver = 11; parybface->key = 0.0; } } // if (maxdd < cosslidihed) } // if (!marktested(...)) } // if (gettetrahedron(...)) } // k flipqueue->restart(); // Unmark the tets in unflipqueue. for (i = 0; i < unflipqueue->objects; i++) { bface = (badface*)fastlookup(unflipqueue, i); unmarktest(bface->tt); } if (b->verbose > 1) { printf(" Smooth %ld points.\n", smtcount); } totalsmtcount += smtcount; if (smtcount == 0l) { // No point has been smoothed. break; } else { iter++; if (iter == 2) { // if (iter >= b->optpasses) { break; } } // Swap the two flip queues. swapqueue = flipqueue; flipqueue = unflipqueue; unflipqueue = swapqueue; } // while delete flipqueue; return totalsmtcount; } /////////////////////////////////////////////////////////////////////////////// // // // splitsliver() Split a sliver. // // // /////////////////////////////////////////////////////////////////////////////// int tetgenmesh::splitsliver(triface* slitet, REAL cosd, int chkencflag) { triface* abtets; triface searchtet, spintet, *parytet; point pa, pb, steinerpt; optparameters opm; insertvertexflags ivf; REAL smtpt[3], midpt[3]; int success; int t1ver; int n, i; // 'slitet' is [c,d,a,b], where [c,d] has a big dihedral angle. // Go to the opposite edge [a,b]. edestoppo(*slitet, searchtet); // [a,b,c,d]. // Do not split a segment. if (issubseg(searchtet)) { return 0; } // Count the number of tets shared at [a,b]. // Do not split it if it is a hull edge. spintet = searchtet; n = 0; while (1) { if (ishulltet(spintet)) break; n++; fnextself(spintet); if (spintet.tet == searchtet.tet) break; } if (ishulltet(spintet)) { return 0; // It is a hull edge. } // Get all tets at edge [a,b]. abtets = new triface[n]; spintet = searchtet; for (i = 0; i < n; i++) { abtets[i] = spintet; fnextself(spintet); } // Initialize the list of 2n boundary faces. for (i = 0; i < n; i++) { eprev(abtets[i], searchtet); esymself(searchtet); // [a,p_i,p_i+1]. cavetetlist->newindex((void**)&parytet); *parytet = searchtet; enext(abtets[i], searchtet); esymself(searchtet); // [p_i,b,p_i+1]. cavetetlist->newindex((void**)&parytet); *parytet = searchtet; } // Init the Steiner point at the midpoint of edge [a,b]. pa = org(abtets[0]); pb = dest(abtets[0]); for (i = 0; i < 3; i++) { smtpt[i] = midpt[i] = 0.5 * (pa[i] + pb[i]); } // Point smooth options. opm.min_max_dihedangle = 1; opm.initval = cosd + 1.0; // Initial volume is zero. opm.numofsearchdirs = 20; opm.searchstep = 0.001; opm.maxiter = 100; // Limit the maximum iterations. success = smoothpoint(smtpt, cavetetlist, 1, &opm); if (success) { while (opm.smthiter == opm.maxiter) { // It was relocated and the prescribed maximum iteration reached. // Try to increase the search stepsize. opm.searchstep *= 10.0; // opm.maxiter = 100; // Limit the maximum iterations. opm.initval = opm.imprval; opm.smthiter = 0; // Init. smoothpoint(smtpt, cavetetlist, 1, &opm); } } // if (success) cavetetlist->restart(); if (!success) { delete[] abtets; return 0; } // Insert the Steiner point. makepoint(&steinerpt, FREEVOLVERTEX); for (i = 0; i < 3; i++) steinerpt[i] = smtpt[i]; // Insert the created Steiner point. for (i = 0; i < n; i++) { infect(abtets[i]); caveoldtetlist->newindex((void**)&parytet); *parytet = abtets[i]; } searchtet = abtets[0]; // No need point location. if (b->metric) { locate(steinerpt, &searchtet); // For size interpolation. } delete[] abtets; ivf.iloc = (int)INSTAR; ivf.chkencflag = chkencflag; ivf.assignmeshsize = b->metric; if (insertpoint(steinerpt, &searchtet, NULL, NULL, &ivf)) { // The vertex has been inserted. st_volref_count++; if (steinerleft > 0) steinerleft--; return 1; } else { // The Steiner point is too close to an existing vertex. Reject it. pointdealloc(steinerpt); return 0; } } /////////////////////////////////////////////////////////////////////////////// // // // removeslivers() Remove slivers by adding Steiner points. // // // /////////////////////////////////////////////////////////////////////////////// long tetgenmesh::removeslivers(int chkencflag) { arraypool *flipqueue, *swapqueue; badface *bface, *parybface; triface slitet, *parytet; point* ppt; REAL cosdd[6], maxcosd; long totalsptcount, sptcount; int iter, i, j, k; // assert(unflipqueue->objects > 0l); flipqueue = new arraypool(sizeof(badface), 10); // Swap the two flip queues. swapqueue = flipqueue; flipqueue = unflipqueue; unflipqueue = swapqueue; totalsptcount = 0l; iter = 0; while ((flipqueue->objects > 0l) && (steinerleft != 0)) { sptcount = 0l; if (b->verbose > 1) { printf(" Splitting bad quality tets [%d]#: %ld.\n", iter, flipqueue->objects); } for (k = 0; (k < flipqueue->objects) && (steinerleft != 0); k++) { bface = (badface*)fastlookup(flipqueue, k); if (gettetrahedron(bface->forg, bface->fdest, bface->fapex, bface->foppo, &bface->tt)) { if ((bface->key == 0) || (bface->tt.ver != 11)) { // Here we need to re-compute the quality. Since other smoothing // operation may have moved the vertices of this tet. ppt = (point*)&(bface->tt.tet[4]); tetalldihedral(ppt[0], ppt[1], ppt[2], ppt[3], bface->cent, &bface->key, NULL); } if (bface->key < cosslidihed) { // It is a sliver. Try to split it. slitet.tet = bface->tt.tet; // cosdd = bface->cent; for (j = 0; j < 6; j++) { if (bface->cent[j] < cosslidihed) { // Found a large dihedral angle. slitet.ver = edge2ver[j]; // Go to the edge. if (splitsliver(&slitet, bface->cent[j], chkencflag)) { sptcount++; break; } } } // j if (j < 6) { // A sliver is split. Queue new slivers. badtetrahedrons->traversalinit(); parytet = (triface*)badtetrahedrons->traverse(); while (parytet != NULL) { unmarktest2(*parytet); ppt = (point*)&(parytet->tet[4]); tetalldihedral(ppt[0], ppt[1], ppt[2], ppt[3], cosdd, &maxcosd, NULL); if (maxcosd < cosslidihed) { // A new sliver. Queue it. unflipqueue->newindex((void**)&parybface); parybface->forg = ppt[0]; parybface->fdest = ppt[1]; parybface->fapex = ppt[2]; parybface->foppo = ppt[3]; parybface->tt.tet = parytet->tet; parybface->tt.ver = 11; parybface->key = maxcosd; for (i = 0; i < 6; i++) { parybface->cent[i] = cosdd[i]; } } parytet = (triface*)badtetrahedrons->traverse(); } badtetrahedrons->restart(); } else { // Didn't split. Queue it again. unflipqueue->newindex((void**)&parybface); *parybface = *bface; } // if (j == 6) } // if (bface->key < cosslidihed) } // if (gettetrahedron(...)) } // k flipqueue->restart(); if (b->verbose > 1) { printf(" Split %ld tets.\n", sptcount); } totalsptcount += sptcount; if (sptcount == 0l) { // No point has been smoothed. break; } else { iter++; if (iter == 2) { // if (iter >= b->optpasses) { break; } } // Swap the two flip queues. swapqueue = flipqueue; flipqueue = unflipqueue; unflipqueue = swapqueue; } // while delete flipqueue; return totalsptcount; } /////////////////////////////////////////////////////////////////////////////// // // // optimizemesh() Optimize mesh for specified objective functions. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::optimizemesh() { badface* parybface; triface checktet; point* ppt; int optpasses; optparameters opm; REAL ncosdd[6], maxdd; long totalremcount, remcount; long totalsmtcount, smtcount; long totalsptcount, sptcount; int chkencflag; int iter; int n; if (!b->quiet) { printf("Optimizing mesh...\n"); } optpasses = ((1 << b->optlevel) - 1); if (b->verbose) { printf(" Optimization level = %d.\n", b->optlevel); printf(" Optimization scheme = %d.\n", b->optscheme); printf(" Number of iteration = %d.\n", optpasses); printf(" Min_Max dihed angle = %g.\n", b->optmaxdihedral); } totalsmtcount = totalsptcount = totalremcount = 0l; cosmaxdihed = cos(b->optmaxdihedral / 180.0 * PI); cossmtdihed = cos(b->optminsmtdihed / 180.0 * PI); cosslidihed = cos(b->optminslidihed / 180.0 * PI); int attrnum = numelemattrib - 1; // Put all bad tetrahedra into array. tetrahedrons->traversalinit(); checktet.tet = tetrahedrontraverse(); while (checktet.tet != NULL) { if (b->convex) { // -c // Skip this tet if it lies in the exterior. if (elemattribute(checktet.tet, attrnum) == -1.0) { checktet.tet = tetrahedrontraverse(); continue; } } ppt = (point*)&(checktet.tet[4]); tetalldihedral(ppt[0], ppt[1], ppt[2], ppt[3], ncosdd, &maxdd, NULL); if (maxdd < cosmaxdihed) { // There are bad dihedral angles in this tet. unflipqueue->newindex((void**)&parybface); parybface->tt.tet = checktet.tet; parybface->tt.ver = 11; parybface->forg = ppt[0]; parybface->fdest = ppt[1]; parybface->fapex = ppt[2]; parybface->foppo = ppt[3]; parybface->key = maxdd; for (n = 0; n < 6; n++) { parybface->cent[n] = ncosdd[n]; } } checktet.tet = tetrahedrontraverse(); } totalremcount = improvequalitybyflips(); if ((unflipqueue->objects > 0l) && ((b->optscheme & 2) || (b->optscheme & 4))) { // The pool is only used by removeslivers(). badtetrahedrons = new memorypool(sizeof(triface), b->tetrahedraperblock, sizeof(void*), 0); // Smoothing options. opm.min_max_dihedangle = 1; opm.numofsearchdirs = 10; // opm.searchstep = 0.001; opm.maxiter = 30; // Limit the maximum iterations. // opm.checkencflag = 4; // Queue affected tets after smoothing. chkencflag = 4; // Queue affected tets after splitting a sliver. iter = 0; while (iter < optpasses) { smtcount = sptcount = remcount = 0l; if (b->optscheme & 2) { smtcount += improvequalitybysmoothing(&opm); totalsmtcount += smtcount; if (smtcount > 0l) { remcount = improvequalitybyflips(); totalremcount += remcount; } } if (unflipqueue->objects > 0l) { if (b->optscheme & 4) { sptcount += removeslivers(chkencflag); totalsptcount += sptcount; if (sptcount > 0l) { remcount = improvequalitybyflips(); totalremcount += remcount; } } } if (unflipqueue->objects > 0l) { if (remcount > 0l) { iter++; } else { break; } } else { break; } } // while (iter) delete badtetrahedrons; badtetrahedrons = NULL; } if (unflipqueue->objects > 0l) { if (b->verbose > 1) { printf(" %ld bad tets remained.\n", unflipqueue->objects); } unflipqueue->restart(); } if (b->verbose) { if (totalremcount > 0l) { printf(" Removed %ld edges.\n", totalremcount); } if (totalsmtcount > 0l) { printf(" Smoothed %ld points.\n", totalsmtcount); } if (totalsptcount > 0l) { printf(" Split %ld slivers.\n", totalsptcount); } } } //// //// //// //// //// optimize_cxx ///////////////////////////////////////////////////////////// //// meshstat_cxx ///////////////////////////////////////////////////////////// //// //// //// //// /////////////////////////////////////////////////////////////////////////////// // // // printfcomma() Print a (large) number with the 'thousands separator'. // // // // The following code was simply copied from "stackoverflow". // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::printfcomma(unsigned long n) { unsigned long n2 = 0; int scale = 1; while (n >= 1000) { n2 = n2 + scale * (n % 1000); n /= 1000; scale *= 1000; } printf("%ld", n); while (scale != 1) { scale /= 1000; n = n2 / scale; n2 = n2 % scale; printf(",%03ld", n); } } /////////////////////////////////////////////////////////////////////////////// // // // checkmesh() Test the mesh for topological consistency. // // // // If 'topoflag' is set, only check the topological connection of the mesh, // // i.e., do not report degenerated or inverted elements. // // // /////////////////////////////////////////////////////////////////////////////// int tetgenmesh::checkmesh(int topoflag) { triface tetloop, neightet, symtet; point pa, pb, pc, pd; REAL ori; int horrors, i; if (!b->quiet) { printf(" Checking consistency of mesh...\n"); } horrors = 0; tetloop.ver = 0; // Run through the list of tetrahedra, checking each one. tetrahedrons->traversalinit(); tetloop.tet = alltetrahedrontraverse(); while (tetloop.tet != (tetrahedron*)NULL) { // Check all four faces of the tetrahedron. for (tetloop.ver = 0; tetloop.ver < 4; tetloop.ver++) { pa = org(tetloop); pb = dest(tetloop); pc = apex(tetloop); pd = oppo(tetloop); if (tetloop.ver == 0) { // Only test for inversion once. if (!ishulltet(tetloop)) { // Only do test if it is not a hull tet. if (!topoflag) { ori = orient3d(pa, pb, pc, pd); if (ori >= 0.0) { printf(" !! !! %s ", ori > 0.0 ? "Inverted" : "Degenerated"); printf(" (%d, %d, %d, %d) (ori = %.17g)\n", pointmark(pa), pointmark(pb), pointmark(pc), pointmark(pd), ori); horrors++; } } } if (infected(tetloop)) { // This may be a bug. Report it. printf(" !! (%d, %d, %d, %d) is infected.\n", pointmark(pa), pointmark(pb), pointmark(pc), pointmark(pd)); horrors++; } if (marktested(tetloop)) { // This may be a bug. Report it. printf(" !! (%d, %d, %d, %d) is marked.\n", pointmark(pa), pointmark(pb), pointmark(pc), pointmark(pd)); horrors++; } } if (tetloop.tet[tetloop.ver] == NULL) { printf(" !! !! No neighbor at face (%d, %d, %d).\n", pointmark(pa), pointmark(pb), pointmark(pc)); horrors++; } else { // Find the neighboring tetrahedron on this face. fsym(tetloop, neightet); if (neightet.tet != NULL) { // Check that the tetrahedron's neighbor knows it's a neighbor. fsym(neightet, symtet); if ((tetloop.tet != symtet.tet) || (tetloop.ver != symtet.ver)) { printf(" !! !! Asymmetric tetra-tetra bond:\n"); if (tetloop.tet == symtet.tet) { printf(" (Right tetrahedron, wrong orientation)\n"); } printf(" First: (%d, %d, %d, %d)\n", pointmark(pa), pointmark(pb), pointmark(pc), pointmark(pd)); printf(" Second: (%d, %d, %d, %d)\n", pointmark(org(neightet)), pointmark(dest(neightet)), pointmark(apex(neightet)), pointmark(oppo(neightet))); horrors++; } // Check if they have the same edge (the bond() operation). if ((org(neightet) != pb) || (dest(neightet) != pa)) { printf(" !! !! Wrong edge-edge bond:\n"); printf(" First: (%d, %d, %d, %d)\n", pointmark(pa), pointmark(pb), pointmark(pc), pointmark(pd)); printf(" Second: (%d, %d, %d, %d)\n", pointmark(org(neightet)), pointmark(dest(neightet)), pointmark(apex(neightet)), pointmark(oppo(neightet))); horrors++; } // Check if they have the same apex. if (apex(neightet) != pc) { printf(" !! !! Wrong face-face bond:\n"); printf(" First: (%d, %d, %d, %d)\n", pointmark(pa), pointmark(pb), pointmark(pc), pointmark(pd)); printf(" Second: (%d, %d, %d, %d)\n", pointmark(org(neightet)), pointmark(dest(neightet)), pointmark(apex(neightet)), pointmark(oppo(neightet))); horrors++; } // Check if they have the same opposite. if (oppo(neightet) == pd) { printf(" !! !! Two identical tetra:\n"); printf(" First: (%d, %d, %d, %d)\n", pointmark(pa), pointmark(pb), pointmark(pc), pointmark(pd)); printf(" Second: (%d, %d, %d, %d)\n", pointmark(org(neightet)), pointmark(dest(neightet)), pointmark(apex(neightet)), pointmark(oppo(neightet))); horrors++; } } else { printf(" !! !! Tet-face has no neighbor (%d, %d, %d) - %d:\n", pointmark(pa), pointmark(pb), pointmark(pc), pointmark(pd)); horrors++; } } if (facemarked(tetloop)) { // This may be a bug. Report it. printf(" !! tetface (%d, %d, %d) %d is marked.\n", pointmark(pa), pointmark(pb), pointmark(pc), pointmark(pd)); } } // Check the six edges of this tet. for (i = 0; i < 6; i++) { tetloop.ver = edge2ver[i]; if (edgemarked(tetloop)) { // This may be a bug. Report it. printf(" !! tetedge (%d, %d) %d, %d is marked.\n", pointmark(org(tetloop)), pointmark(dest(tetloop)), pointmark(apex(tetloop)), pointmark(oppo(tetloop))); } } tetloop.tet = alltetrahedrontraverse(); } if (horrors == 0) { if (!b->quiet) { printf(" In my studied opinion, the mesh appears to be consistent.\n"); } } else { printf(" !! !! !! !! %d %s witnessed.\n", horrors, horrors > 1 ? "abnormity" : "abnormities"); } return horrors; } /////////////////////////////////////////////////////////////////////////////// // // // checkshells() Test the boundary mesh for topological consistency. // // // /////////////////////////////////////////////////////////////////////////////// int tetgenmesh::checkshells() { triface neightet, symtet; face shloop, spinsh, nextsh; face checkseg; point pa, pb; int bakcount; int horrors, i; if (!b->quiet) { printf(" Checking consistency of the mesh boundary...\n"); } horrors = 0; void** bakpathblock = subfaces->pathblock; void* bakpathitem = subfaces->pathitem; int bakpathitemsleft = subfaces->pathitemsleft; int bakalignbytes = subfaces->alignbytes; subfaces->traversalinit(); shloop.sh = shellfacetraverse(subfaces); while (shloop.sh != NULL) { shloop.shver = 0; for (i = 0; i < 3; i++) { // Check the face ring at this edge. pa = sorg(shloop); pb = sdest(shloop); spinsh = shloop; spivot(spinsh, nextsh); bakcount = horrors; while ((nextsh.sh != NULL) && (nextsh.sh != shloop.sh)) { if (nextsh.sh[3] == NULL) { printf(" !! !! Wrong subface-subface connection (Dead subface).\n"); printf(" First: x%lx (%d, %d, %d).\n", (uintptr_t)spinsh.sh, pointmark(sorg(spinsh)), pointmark(sdest(spinsh)), pointmark(sapex(spinsh))); printf(" Second: x%lx (DEAD)\n", (uintptr_t)nextsh.sh); horrors++; break; } // check if they have the same edge. if (!(((sorg(nextsh) == pa) && (sdest(nextsh) == pb)) || ((sorg(nextsh) == pb) && (sdest(nextsh) == pa)))) { printf(" !! !! Wrong subface-subface connection.\n"); printf(" First: x%lx (%d, %d, %d).\n", (uintptr_t)spinsh.sh, pointmark(sorg(spinsh)), pointmark(sdest(spinsh)), pointmark(sapex(spinsh))); printf(" Scond: x%lx (%d, %d, %d).\n", (uintptr_t)nextsh.sh, pointmark(sorg(nextsh)), pointmark(sdest(nextsh)), pointmark(sapex(nextsh))); horrors++; break; } // Check they should not have the same apex. if (sapex(nextsh) == sapex(spinsh)) { printf(" !! !! Existing two duplicated subfaces.\n"); printf(" First: x%lx (%d, %d, %d).\n", (uintptr_t)spinsh.sh, pointmark(sorg(spinsh)), pointmark(sdest(spinsh)), pointmark(sapex(spinsh))); printf(" Scond: x%lx (%d, %d, %d).\n", (uintptr_t)nextsh.sh, pointmark(sorg(nextsh)), pointmark(sdest(nextsh)), pointmark(sapex(nextsh))); horrors++; break; } spinsh = nextsh; spivot(spinsh, nextsh); } // Check subface-subseg bond. sspivot(shloop, checkseg); if (checkseg.sh != NULL) { if (checkseg.sh[3] == NULL) { printf(" !! !! Wrong subface-subseg connection (Dead subseg).\n"); printf(" Sub: x%lx (%d, %d, %d).\n", (uintptr_t)shloop.sh, pointmark(sorg(shloop)), pointmark(sdest(shloop)), pointmark(sapex(shloop))); printf(" Sub: x%lx (Dead)\n", (uintptr_t)checkseg.sh); horrors++; } else { if (!(((sorg(checkseg) == pa) && (sdest(checkseg) == pb)) || ((sorg(checkseg) == pb) && (sdest(checkseg) == pa)))) { printf(" !! !! Wrong subface-subseg connection.\n"); printf(" Sub: x%lx (%d, %d, %d).\n", (uintptr_t)shloop.sh, pointmark(sorg(shloop)), pointmark(sdest(shloop)), pointmark(sapex(shloop))); printf(" Seg: x%lx (%d, %d).\n", (uintptr_t)checkseg.sh, pointmark(sorg(checkseg)), pointmark(sdest(checkseg))); horrors++; } } } if (horrors > bakcount) break; // An error detected. senextself(shloop); } // Check tet-subface connection. stpivot(shloop, neightet); if (neightet.tet != NULL) { if (neightet.tet[4] == NULL) { printf(" !! !! Wrong sub-to-tet connection (Dead tet)\n"); printf(" Sub: x%lx (%d, %d, %d).\n", (uintptr_t)shloop.sh, pointmark(sorg(shloop)), pointmark(sdest(shloop)), pointmark(sapex(shloop))); printf(" Tet: x%lx (DEAD)\n", (uintptr_t)neightet.tet); horrors++; } else { if (!((sorg(shloop) == org(neightet)) && (sdest(shloop) == dest(neightet)))) { printf(" !! !! Wrong sub-to-tet connection\n"); printf(" Sub: x%lx (%d, %d, %d).\n", (uintptr_t)shloop.sh, pointmark(sorg(shloop)), pointmark(sdest(shloop)), pointmark(sapex(shloop))); printf(" Tet: x%lx (%d, %d, %d, %d).\n", (uintptr_t)neightet.tet, pointmark(org(neightet)), pointmark(dest(neightet)), pointmark(apex(neightet)), pointmark(oppo(neightet))); horrors++; } tspivot(neightet, spinsh); if (!((sorg(spinsh) == org(neightet)) && (sdest(spinsh) == dest(neightet)))) { printf(" !! !! Wrong tet-sub connection.\n"); printf(" Sub: x%lx (%d, %d, %d).\n", (uintptr_t)spinsh.sh, pointmark(sorg(spinsh)), pointmark(sdest(spinsh)), pointmark(sapex(spinsh))); printf(" Tet: x%lx (%d, %d, %d, %d).\n", (uintptr_t)neightet.tet, pointmark(org(neightet)), pointmark(dest(neightet)), pointmark(apex(neightet)), pointmark(oppo(neightet))); horrors++; } fsym(neightet, symtet); tspivot(symtet, spinsh); if (spinsh.sh != NULL) { if (!((sorg(spinsh) == org(symtet)) && (sdest(spinsh) == dest(symtet)))) { printf(" !! !! Wrong tet-sub connection.\n"); printf(" Sub: x%lx (%d, %d, %d).\n", (uintptr_t)spinsh.sh, pointmark(sorg(spinsh)), pointmark(sdest(spinsh)), pointmark(sapex(spinsh))); printf(" Tet: x%lx (%d, %d, %d, %d).\n", (uintptr_t)symtet.tet, pointmark(org(symtet)), pointmark(dest(symtet)), pointmark(apex(symtet)), pointmark(oppo(symtet))); horrors++; } } else { printf(" Warning: Broken tet-sub-tet connection.\n"); } } } if (sinfected(shloop)) { // This may be a bug. report it. printf(" !! A infected subface: (%d, %d, %d).\n", pointmark(sorg(shloop)), pointmark(sdest(shloop)), pointmark(sapex(shloop))); } if (smarktested(shloop)) { // This may be a bug. report it. printf(" !! A marked subface: (%d, %d, %d).\n", pointmark(sorg(shloop)), pointmark(sdest(shloop)), pointmark(sapex(shloop))); } shloop.sh = shellfacetraverse(subfaces); } if (horrors == 0) { if (!b->quiet) { printf(" Mesh boundaries connected correctly.\n"); } } else { printf(" !! !! !! !! %d boundary connection viewed with horror.\n", horrors); } subfaces->pathblock = bakpathblock; subfaces->pathitem = bakpathitem; subfaces->pathitemsleft = bakpathitemsleft; subfaces->alignbytes = bakalignbytes; return horrors; } /////////////////////////////////////////////////////////////////////////////// // // // checksegments() Check the connections between tetrahedra and segments. // // // /////////////////////////////////////////////////////////////////////////////// int tetgenmesh::checksegments() { triface tetloop, neightet, spintet; shellface* segs; face neighsh, spinsh, checksh; face sseg, checkseg; point pa, pb; int miscount; int t1ver; int horrors, i; if (!b->quiet) { printf(" Checking tet->seg connections...\n"); } horrors = 0; tetrahedrons->traversalinit(); tetloop.tet = tetrahedrontraverse(); while (tetloop.tet != NULL) { // Loop the six edges of the tet. if (tetloop.tet[8] != NULL) { segs = (shellface*)tetloop.tet[8]; for (i = 0; i < 6; i++) { sdecode(segs[i], sseg); if (sseg.sh != NULL) { // Get the edge of the tet. tetloop.ver = edge2ver[i]; // Check if they are the same edge. pa = (point)sseg.sh[3]; pb = (point)sseg.sh[4]; if (!(((org(tetloop) == pa) && (dest(tetloop) == pb)) || ((org(tetloop) == pb) && (dest(tetloop) == pa)))) { printf(" !! Wrong tet-seg connection.\n"); printf(" Tet: x%lx (%d, %d, %d, %d) - Seg: x%lx (%d, %d).\n", (uintptr_t)tetloop.tet, pointmark(org(tetloop)), pointmark(dest(tetloop)), pointmark(apex(tetloop)), pointmark(oppo(tetloop)), (uintptr_t)sseg.sh, pointmark(pa), pointmark(pb)); horrors++; } else { // Loop all tets sharing at this edge. neightet = tetloop; do { tsspivot1(neightet, checkseg); if (checkseg.sh != sseg.sh) { printf(" !! Wrong tet->seg connection.\n"); printf(" Tet: x%lx (%d, %d, %d, %d) - ", (uintptr_t)neightet.tet, pointmark(org(neightet)), pointmark(dest(neightet)), pointmark(apex(neightet)), pointmark(oppo(neightet))); if (checkseg.sh != NULL) { printf("Seg x%lx (%d, %d).\n", (uintptr_t)checkseg.sh, pointmark(sorg(checkseg)), pointmark(sdest(checkseg))); } else { printf("Seg: NULL.\n"); } horrors++; } fnextself(neightet); } while (neightet.tet != tetloop.tet); } // Check the seg->tet pointer. sstpivot1(sseg, neightet); if (neightet.tet == NULL) { printf(" !! Wrong seg->tet connection (A NULL tet).\n"); horrors++; } else { if (!(((org(neightet) == pa) && (dest(neightet) == pb)) || ((org(neightet) == pb) && (dest(neightet) == pa)))) { printf(" !! Wrong seg->tet connection (Wrong edge).\n"); printf(" Tet: x%lx (%d, %d, %d, %d) - Seg: x%lx (%d, %d).\n", (uintptr_t)neightet.tet, pointmark(org(neightet)), pointmark(dest(neightet)), pointmark(apex(neightet)), pointmark(oppo(neightet)), (uintptr_t)sseg.sh, pointmark(pa), pointmark(pb)); horrors++; } } } } } // Loop the six edge of this tet. neightet.tet = tetloop.tet; for (i = 0; i < 6; i++) { neightet.ver = edge2ver[i]; if (edgemarked(neightet)) { // A possible bug. Report it. printf(" !! A marked edge: (%d, %d, %d, %d) -- x%lx %d.\n", pointmark(org(neightet)), pointmark(dest(neightet)), pointmark(apex(neightet)), pointmark(oppo(neightet)), (uintptr_t)neightet.tet, neightet.ver); // Check if all tets at the edge are marked. spintet = neightet; while (1) { fnextself(spintet); if (!edgemarked(spintet)) { printf(" !! !! An unmarked edge (%d, %d, %d, %d) -- x%lx %d.\n", pointmark(org(spintet)), pointmark(dest(spintet)), pointmark(apex(spintet)), pointmark(oppo(spintet)), (uintptr_t)spintet.tet, spintet.ver); horrors++; } if (spintet.tet == neightet.tet) break; } } } tetloop.tet = tetrahedrontraverse(); } if (!b->quiet) { printf(" Checking seg->tet connections...\n"); } miscount = 0; // Count the number of unrecovered segments. subsegs->traversalinit(); sseg.shver = 0; sseg.sh = shellfacetraverse(subsegs); while (sseg.sh != NULL) { pa = sorg(sseg); pb = sdest(sseg); spivot(sseg, neighsh); if (neighsh.sh != NULL) { spinsh = neighsh; while (1) { // Check seg-subface bond. if (((sorg(spinsh) == pa) && (sdest(spinsh) == pb)) || ((sorg(spinsh) == pb) && (sdest(spinsh) == pa))) { // Keep the same rotate direction. // if (sorg(spinsh) != pa) { // sesymself(spinsh); // printf(" !! Wrong ori at subface (%d, %d, %d) -- x%lx %d\n", // pointmark(sorg(spinsh)), pointmark(sdest(spinsh)), // pointmark(sapex(spinsh)), (uintptr_t) spinsh.sh, // spinsh.shver); // horrors++; //} stpivot(spinsh, spintet); if (spintet.tet != NULL) { // Check if all tets at this segment. while (1) { tsspivot1(spintet, checkseg); if (checkseg.sh == NULL) { printf(" !! !! No seg at tet (%d, %d, %d, %d) -- x%lx %d\n", pointmark(org(spintet)), pointmark(dest(spintet)), pointmark(apex(spintet)), pointmark(oppo(spintet)), (uintptr_t)spintet.tet, spintet.ver); horrors++; } if (checkseg.sh != sseg.sh) { printf(" !! !! Wrong seg (%d, %d) at tet (%d, %d, %d, %d)\n", pointmark(sorg(checkseg)), pointmark(sdest(checkseg)), pointmark(org(spintet)), pointmark(dest(spintet)), pointmark(apex(spintet)), pointmark(oppo(spintet))); horrors++; } fnextself(spintet); // Stop at the next subface. tspivot(spintet, checksh); if (checksh.sh != NULL) break; } // while (1) } } else { printf(" !! Wrong seg-subface (%d, %d, %d) -- x%lx %d connect\n", pointmark(sorg(spinsh)), pointmark(sdest(spinsh)), pointmark(sapex(spinsh)), (uintptr_t)spinsh.sh, spinsh.shver); horrors++; break; } // if pa, pb spivotself(spinsh); if (spinsh.sh == NULL) break; // A dangling segment. if (spinsh.sh == neighsh.sh) break; } // while (1) } // if (neighsh.sh != NULL) // Count the number of "un-recovered" segments. sstpivot1(sseg, neightet); if (neightet.tet == NULL) { miscount++; } sseg.sh = shellfacetraverse(subsegs); } if (!b->quiet) { printf(" Checking seg->seg connections...\n"); } points->traversalinit(); pa = pointtraverse(); while (pa != NULL) { if (pointtype(pa) == FREESEGVERTEX) { // There should be two subsegments connected at 'pa'. // Get a subsegment containing 'pa'. sdecode(point2sh(pa), sseg); if ((sseg.sh == NULL) || sseg.sh[3] == NULL) { printf(" !! Dead point-to-seg pointer at point %d.\n", pointmark(pa)); horrors++; } else { sseg.shver = 0; if (sorg(sseg) != pa) { if (sdest(sseg) != pa) { printf(" !! Wrong point-to-seg pointer at point %d.\n", pointmark(pa)); horrors++; } else { // Find the next subsegment at 'pa'. senext(sseg, checkseg); if ((checkseg.sh == NULL) || (checkseg.sh[3] == NULL)) { printf(" !! Dead seg-seg connection at point %d.\n", pointmark(pa)); horrors++; } else { spivotself(checkseg); checkseg.shver = 0; if ((sorg(checkseg) != pa) && (sdest(checkseg) != pa)) { printf(" !! Wrong seg-seg connection at point %d.\n", pointmark(pa)); horrors++; } } } } else { // Find the previous subsegment at 'pa'. senext2(sseg, checkseg); if ((checkseg.sh == NULL) || (checkseg.sh[3] == NULL)) { printf(" !! Dead seg-seg connection at point %d.\n", pointmark(pa)); horrors++; } else { spivotself(checkseg); checkseg.shver = 0; if ((sorg(checkseg) != pa) && (sdest(checkseg) != pa)) { printf(" !! Wrong seg-seg connection at point %d.\n", pointmark(pa)); horrors++; } } } } } pa = pointtraverse(); } if (horrors == 0) { printf(" Segments are connected properly.\n"); } else { printf(" !! !! !! !! Found %d missing connections.\n", horrors); } if (miscount > 0) { printf(" !! !! Found %d missing segments.\n", miscount); } return horrors; } /////////////////////////////////////////////////////////////////////////////// // // // checkdelaunay() Ensure that the mesh is (constrained) Delaunay. // // // /////////////////////////////////////////////////////////////////////////////// int tetgenmesh::checkdelaunay(int perturb) { triface tetloop; triface symtet; face checksh; point pa, pb, pc, pd, pe; REAL sign; int ndcount; // Count the non-locally Delaunay faces. int horrors; if (!b->quiet) { printf(" Checking Delaunay property of the mesh...\n"); } ndcount = 0; horrors = 0; tetloop.ver = 0; // Run through the list of triangles, checking each one. tetrahedrons->traversalinit(); tetloop.tet = tetrahedrontraverse(); while (tetloop.tet != (tetrahedron*)NULL) { // Check all four faces of the tetrahedron. for (tetloop.ver = 0; tetloop.ver < 4; tetloop.ver++) { fsym(tetloop, symtet); // Only do test if its adjoining tet is not a hull tet or its pointer // is larger (to ensure that each pair isn't tested twice). if (((point)symtet.tet[7] != dummypoint) && (tetloop.tet < symtet.tet)) { pa = org(tetloop); pb = dest(tetloop); pc = apex(tetloop); pd = oppo(tetloop); pe = oppo(symtet); if (perturb) { sign = insphere_s(pa, pb, pc, pd, pe); } else { sign = insphere(pa, pb, pc, pd, pe); } if (sign < 0.0) { ndcount++; if (checksubfaceflag) { tspivot(tetloop, checksh); } if (checksh.sh == NULL) { printf(" !! Non-locally Delaunay (%d, %d, %d) - %d, %d\n", pointmark(pa), pointmark(pb), pointmark(pc), pointmark(pd), pointmark(pe)); horrors++; } } } } tetloop.tet = tetrahedrontraverse(); } if (horrors == 0) { if (!b->quiet) { if (ndcount > 0) { printf(" The mesh is constrained Delaunay.\n"); } else { printf(" The mesh is Delaunay.\n"); } } } else { printf(" !! !! !! !! Found %d non-Delaunay faces.\n", horrors); } return horrors; } /////////////////////////////////////////////////////////////////////////////// // // // Check if the current tetrahedralization is (constrained) regular. // // // // The parameter 'type' determines which regularity should be checked: // // - 0: check the Delaunay property. // // - 1: check the Delaunay property with symbolic perturbation. // // - 2: check the regular property, the weights are stored in p[3]. // // - 3: check the regular property with symbolic perturbation. // // // /////////////////////////////////////////////////////////////////////////////// int tetgenmesh::checkregular(int type) { triface tetloop; triface symtet; face checksh; point p[5]; REAL sign; int ndcount; // Count the non-locally Delaunay faces. int horrors; if (!b->quiet) { printf(" Checking %s %s property of the mesh...\n", (type & 2) == 0 ? "Delaunay" : "regular", (type & 1) == 0 ? " " : "(s)"); } // Make sure orient3d(p[1], p[0], p[2], p[3]) > 0; // Hence if (insphere(p[1], p[0], p[2], p[3], p[4]) > 0) means that // p[4] lies inside the circumsphere of p[1], p[0], p[2], p[3]. // The same if orient4d(p[1], p[0], p[2], p[3], p[4]) > 0 means that // p[4] lies below the oriented hyperplane passing through // p[1], p[0], p[2], p[3]. ndcount = 0; horrors = 0; tetloop.ver = 0; // Run through the list of triangles, checking each one. tetrahedrons->traversalinit(); tetloop.tet = tetrahedrontraverse(); while (tetloop.tet != (tetrahedron*)NULL) { // Check all four faces of the tetrahedron. for (tetloop.ver = 0; tetloop.ver < 4; tetloop.ver++) { fsym(tetloop, symtet); // Only do test if its adjoining tet is not a hull tet or its pointer // is larger (to ensure that each pair isn't tested twice). if (((point)symtet.tet[7] != dummypoint) && (tetloop.tet < symtet.tet)) { p[0] = org(tetloop); // pa p[1] = dest(tetloop); // pb p[2] = apex(tetloop); // pc p[3] = oppo(tetloop); // pd p[4] = oppo(symtet); // pe if (type == 0) { sign = insphere(p[1], p[0], p[2], p[3], p[4]); } else if (type == 1) { sign = insphere_s(p[1], p[0], p[2], p[3], p[4]); } else if (type == 2) { sign = orient4d(p[1], p[0], p[2], p[3], p[4], p[1][3], p[0][3], p[2][3], p[3][3], p[4][3]); } else { // type == 3 sign = orient4d_s(p[1], p[0], p[2], p[3], p[4], p[1][3], p[0][3], p[2][3], p[3][3], p[4][3]); } if (sign > 0.0) { ndcount++; if (checksubfaceflag) { tspivot(tetloop, checksh); } if (checksh.sh == NULL) { printf(" !! Non-locally %s (%d, %d, %d) - %d, %d\n", (type & 2) == 0 ? "Delaunay" : "regular", pointmark(p[0]), pointmark(p[1]), pointmark(p[2]), pointmark(p[3]), pointmark(p[4])); horrors++; } } } } tetloop.tet = tetrahedrontraverse(); } if (horrors == 0) { if (!b->quiet) { if (ndcount > 0) { printf(" The mesh is constrained %s.\n", (type & 2) == 0 ? "Delaunay" : "regular"); } else { printf(" The mesh is %s.\n", (type & 2) == 0 ? "Delaunay" : "regular"); } } } else { printf(" !! !! !! !! Found %d non-%s faces.\n", horrors, (type & 2) == 0 ? "Delaunay" : "regular"); } return horrors; } /////////////////////////////////////////////////////////////////////////////// // // // checkconforming() Ensure that the mesh is conforming Delaunay. // // // // If 'flag' is 1, only check subsegments. If 'flag' is 2, check subfaces. // // If 'flag' is 3, check both subsegments and subfaces. // // // /////////////////////////////////////////////////////////////////////////////// int tetgenmesh::checkconforming(int flag) { triface searchtet, neightet, spintet; face shloop; face segloop; point eorg, edest, eapex, pa, pb, pc; REAL cent[3], radius, dist, diff, rd, len; bool enq; int encsubsegs, encsubfaces; int t1ver; int i; REAL A[4][4], rhs[4], D; int indx[4]; REAL elen[3]; encsubsegs = 0; if (flag & 1) { if (!b->quiet) { printf(" Checking conforming property of segments...\n"); } encsubsegs = 0; // Run through the list of subsegments, check each one. subsegs->traversalinit(); segloop.sh = shellfacetraverse(subsegs); while (segloop.sh != (shellface*)NULL) { eorg = (point)segloop.sh[3]; edest = (point)segloop.sh[4]; radius = 0.5 * distance(eorg, edest); for (i = 0; i < 3; i++) cent[i] = 0.5 * (eorg[i] + edest[i]); enq = false; sstpivot1(segloop, neightet); if (neightet.tet != NULL) { spintet = neightet; while (1) { eapex = apex(spintet); if (eapex != dummypoint) { dist = distance(eapex, cent); diff = dist - radius; if (fabs(diff) / radius <= b->epsilon) diff = 0.0; // Rounding. if (diff < 0) { enq = true; break; } } fnextself(spintet); if (spintet.tet == neightet.tet) break; } } if (enq) { printf(" !! !! Non-conforming segment: (%d, %d)\n", pointmark(eorg), pointmark(edest)); encsubsegs++; } segloop.sh = shellfacetraverse(subsegs); } if (encsubsegs == 0) { if (!b->quiet) { printf(" The segments are conforming Delaunay.\n"); } } else { printf(" !! !! %d subsegments are non-conforming.\n", encsubsegs); } } // if (flag & 1) encsubfaces = 0; if (flag & 2) { if (!b->quiet) { printf(" Checking conforming property of subfaces...\n"); } // Run through the list of subfaces, check each one. subfaces->traversalinit(); shloop.sh = shellfacetraverse(subfaces); while (shloop.sh != (shellface*)NULL) { pa = (point)shloop.sh[3]; pb = (point)shloop.sh[4]; pc = (point)shloop.sh[5]; // Compute the coefficient matrix A (3x3). A[0][0] = pb[0] - pa[0]; A[0][1] = pb[1] - pa[1]; A[0][2] = pb[2] - pa[2]; // vector V1 (pa->pb) A[1][0] = pc[0] - pa[0]; A[1][1] = pc[1] - pa[1]; A[1][2] = pc[2] - pa[2]; // vector V2 (pa->pc) cross(A[0], A[1], A[2]); // vector V3 (V1 X V2) // Compute the right hand side vector b (3x1). elen[0] = dot(A[0], A[0]); elen[1] = dot(A[1], A[1]); rhs[0] = 0.5 * elen[0]; rhs[1] = 0.5 * elen[1]; rhs[2] = 0.0; if (lu_decmp(A, 3, indx, &D, 0)) { lu_solve(A, 3, indx, rhs, 0); cent[0] = pa[0] + rhs[0]; cent[1] = pa[1] + rhs[1]; cent[2] = pa[2] + rhs[2]; rd = sqrt(rhs[0] * rhs[0] + rhs[1] * rhs[1] + rhs[2] * rhs[2]); // Check if this subface is encroached. for (i = 0; i < 2; i++) { stpivot(shloop, searchtet); if (!ishulltet(searchtet)) { len = distance(oppo(searchtet), cent); if ((fabs(len - rd) / rd) < b->epsilon) len = rd; // Rounding. if (len < rd) { printf(" !! !! Non-conforming subface: (%d, %d, %d)\n", pointmark(pa), pointmark(pb), pointmark(pc)); encsubfaces++; enq = true; break; } } sesymself(shloop); } } shloop.sh = shellfacetraverse(subfaces); } if (encsubfaces == 0) { if (!b->quiet) { printf(" The subfaces are conforming Delaunay.\n"); } } else { printf(" !! !! %d subfaces are non-conforming.\n", encsubfaces); } } // if (flag & 2) return encsubsegs + encsubfaces; } /////////////////////////////////////////////////////////////////////////////// // // // qualitystatistics() Print statistics about the quality of the mesh. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::qualitystatistics() { triface tetloop, neightet; point p[4]; char sbuf[128]; REAL radiusratiotable[12]; REAL aspectratiotable[12]; REAL A[4][4], rhs[4], D; REAL V[6][3], N[4][3], H[4]; // edge-vectors, face-normals, face-heights. REAL edgelength[6], alldihed[6], faceangle[3]; REAL shortest, longest; REAL smallestvolume, biggestvolume; REAL smallestratio, biggestratio; REAL smallestradiusratio, biggestradiusratio; // radius-edge ratio. REAL smallestdiangle, biggestdiangle; REAL smallestfaangle, biggestfaangle; REAL total_tet_vol, total_tetprism_vol; REAL tetvol, minaltitude; REAL cirradius, minheightinv; // insradius; REAL shortlen, longlen; REAL tetaspect, tetradius; REAL smalldiangle, bigdiangle; REAL smallfaangle, bigfaangle; unsigned long radiustable[12]; unsigned long aspecttable[16]; unsigned long dihedangletable[18]; unsigned long faceangletable[18]; int indx[4]; int radiusindex; int aspectindex; int tendegree; int i, j; // Report the tet which has the biggest radius-edge ratio. triface biggestradiusratiotet; printf("Mesh quality statistics:\n\n"); shortlen = longlen = 0.0; smalldiangle = bigdiangle = 0.0; total_tet_vol = 0.0; total_tetprism_vol = 0.0; radiusratiotable[0] = 0.707; radiusratiotable[1] = 1.0; radiusratiotable[2] = 1.1; radiusratiotable[3] = 1.2; radiusratiotable[4] = 1.4; radiusratiotable[5] = 1.6; radiusratiotable[6] = 1.8; radiusratiotable[7] = 2.0; radiusratiotable[8] = 2.5; radiusratiotable[9] = 3.0; radiusratiotable[10] = 10.0; radiusratiotable[11] = 0.0; aspectratiotable[0] = 1.5; aspectratiotable[1] = 2.0; aspectratiotable[2] = 2.5; aspectratiotable[3] = 3.0; aspectratiotable[4] = 4.0; aspectratiotable[5] = 6.0; aspectratiotable[6] = 10.0; aspectratiotable[7] = 15.0; aspectratiotable[8] = 25.0; aspectratiotable[9] = 50.0; aspectratiotable[10] = 100.0; aspectratiotable[11] = 0.0; for (i = 0; i < 12; i++) radiustable[i] = 0l; for (i = 0; i < 12; i++) aspecttable[i] = 0l; for (i = 0; i < 18; i++) dihedangletable[i] = 0l; for (i = 0; i < 18; i++) faceangletable[i] = 0l; minaltitude = xmax - xmin + ymax - ymin + zmax - zmin; minaltitude = minaltitude * minaltitude; shortest = minaltitude; longest = 0.0; smallestvolume = minaltitude; biggestvolume = 0.0; smallestratio = smallestradiusratio = 1e+16; // minaltitude; biggestratio = biggestradiusratio = 0.0; smallestdiangle = smallestfaangle = 180.0; biggestdiangle = biggestfaangle = 0.0; int attrnum = numelemattrib - 1; // Loop all elements, calculate quality parameters for each element. tetrahedrons->traversalinit(); tetloop.tet = tetrahedrontraverse(); while (tetloop.tet != (tetrahedron*)NULL) { if (b->convex) { // Skip tets in the exterior. if (elemattribute(tetloop.tet, attrnum) == -1.0) { tetloop.tet = tetrahedrontraverse(); continue; } } // Get four vertices: p0, p1, p2, p3. for (i = 0; i < 4; i++) p[i] = (point)tetloop.tet[4 + i]; // Get the tet volume. tetvol = orient3dfast(p[1], p[0], p[2], p[3]) / 6.0; total_tet_vol += tetvol; total_tetprism_vol += tetprismvol(p[0], p[1], p[2], p[3]); // Calculate the largest and smallest volume. if (tetvol < smallestvolume) { smallestvolume = tetvol; } if (tetvol > biggestvolume) { biggestvolume = tetvol; } // Set the edge vectors: V[0], ..., V[5] for (i = 0; i < 3; i++) V[0][i] = p[0][i] - p[3][i]; // V[0]: p3->p0. for (i = 0; i < 3; i++) V[1][i] = p[1][i] - p[3][i]; // V[1]: p3->p1. for (i = 0; i < 3; i++) V[2][i] = p[2][i] - p[3][i]; // V[2]: p3->p2. for (i = 0; i < 3; i++) V[3][i] = p[1][i] - p[0][i]; // V[3]: p0->p1. for (i = 0; i < 3; i++) V[4][i] = p[2][i] - p[1][i]; // V[4]: p1->p2. for (i = 0; i < 3; i++) V[5][i] = p[0][i] - p[2][i]; // V[5]: p2->p0. // Get the squares of the edge lengths. for (i = 0; i < 6; i++) edgelength[i] = dot(V[i], V[i]); // Calculate the longest and shortest edge length. for (i = 0; i < 6; i++) { if (i == 0) { shortlen = longlen = edgelength[i]; } else { shortlen = edgelength[i] < shortlen ? edgelength[i] : shortlen; longlen = edgelength[i] > longlen ? edgelength[i] : longlen; } if (edgelength[i] > longest) { longest = edgelength[i]; } if (edgelength[i] < shortest) { shortest = edgelength[i]; } } // Set the matrix A = [V[0], V[1], V[2]]^T. for (j = 0; j < 3; j++) { for (i = 0; i < 3; i++) A[j][i] = V[j][i]; } // Decompose A just once. if (lu_decmp(A, 3, indx, &D, 0)) { // Get the three faces normals. for (j = 0; j < 3; j++) { for (i = 0; i < 3; i++) rhs[i] = 0.0; rhs[j] = 1.0; // Positive means the inside direction lu_solve(A, 3, indx, rhs, 0); for (i = 0; i < 3; i++) N[j][i] = rhs[i]; } // Get the fourth face normal by summing up the first three. for (i = 0; i < 3; i++) N[3][i] = -N[0][i] - N[1][i] - N[2][i]; // Get the radius of the circumsphere. for (i = 0; i < 3; i++) rhs[i] = 0.5 * dot(V[i], V[i]); lu_solve(A, 3, indx, rhs, 0); cirradius = sqrt(dot(rhs, rhs)); // Normalize the face normals. for (i = 0; i < 4; i++) { // H[i] is the inverse of height of its corresponding face. H[i] = sqrt(dot(N[i], N[i])); for (j = 0; j < 3; j++) N[i][j] /= H[i]; } // Get the radius of the inscribed sphere. // insradius = 1.0 / (H[0] + H[1] + H[2] + H[3]); // Get the biggest H[i] (corresponding to the smallest height). minheightinv = H[0]; for (i = 1; i < 4; i++) { if (H[i] > minheightinv) minheightinv = H[i]; } } else { // A nearly degenerated tet. if (tetvol <= 0.0) { printf(" !! Warning: A %s tet (%d,%d,%d,%d).\n", tetvol < 0 ? "inverted" : "degenerated", pointmark(p[0]), pointmark(p[1]), pointmark(p[2]), pointmark(p[3])); // Skip it. tetloop.tet = tetrahedrontraverse(); continue; } // Calculate the four face normals. facenormal(p[2], p[1], p[3], N[0], 1, NULL); facenormal(p[0], p[2], p[3], N[1], 1, NULL); facenormal(p[1], p[0], p[3], N[2], 1, NULL); facenormal(p[0], p[1], p[2], N[3], 1, NULL); // Normalize the face normals. for (i = 0; i < 4; i++) { // H[i] is the twice of the area of the face. H[i] = sqrt(dot(N[i], N[i])); for (j = 0; j < 3; j++) N[i][j] /= H[i]; } // Get the biggest H[i] / tetvol (corresponding to the smallest height). minheightinv = (H[0] / tetvol); for (i = 1; i < 4; i++) { if ((H[i] / tetvol) > minheightinv) minheightinv = (H[i] / tetvol); } // Let the circumradius to be the half of its longest edge length. cirradius = 0.5 * sqrt(longlen); } // Get the dihedrals (in degree) at each edges. j = 0; for (i = 1; i < 4; i++) { alldihed[j] = -dot(N[0], N[i]); // Edge cd, bd, bc. if (alldihed[j] < -1.0) alldihed[j] = -1; // Rounding. else if (alldihed[j] > 1.0) alldihed[j] = 1; alldihed[j] = acos(alldihed[j]) / PI * 180.0; j++; } for (i = 2; i < 4; i++) { alldihed[j] = -dot(N[1], N[i]); // Edge ad, ac. if (alldihed[j] < -1.0) alldihed[j] = -1; // Rounding. else if (alldihed[j] > 1.0) alldihed[j] = 1; alldihed[j] = acos(alldihed[j]) / PI * 180.0; j++; } alldihed[j] = -dot(N[2], N[3]); // Edge ab. if (alldihed[j] < -1.0) alldihed[j] = -1; // Rounding. else if (alldihed[j] > 1.0) alldihed[j] = 1; alldihed[j] = acos(alldihed[j]) / PI * 180.0; // Calculate the largest and smallest dihedral angles. for (i = 0; i < 6; i++) { if (i == 0) { smalldiangle = bigdiangle = alldihed[i]; } else { smalldiangle = alldihed[i] < smalldiangle ? alldihed[i] : smalldiangle; bigdiangle = alldihed[i] > bigdiangle ? alldihed[i] : bigdiangle; } if (alldihed[i] < smallestdiangle) { smallestdiangle = alldihed[i]; } if (alldihed[i] > biggestdiangle) { biggestdiangle = alldihed[i]; } // Accumulate the corresponding number in the dihedral angle histogram. if (alldihed[i] < 5.0) { tendegree = 0; } else if (alldihed[i] >= 5.0 && alldihed[i] < 10.0) { tendegree = 1; } else if (alldihed[i] >= 80.0 && alldihed[i] < 110.0) { tendegree = 9; // Angles between 80 to 110 degree are in one entry. } else if (alldihed[i] >= 170.0 && alldihed[i] < 175.0) { tendegree = 16; } else if (alldihed[i] >= 175.0) { tendegree = 17; } else { tendegree = (int)(alldihed[i] / 10.); if (alldihed[i] < 80.0) { tendegree++; // In the left column. } else { tendegree--; // In the right column. } } dihedangletable[tendegree]++; } // Calculate the largest and smallest face angles. for (tetloop.ver = 0; tetloop.ver < 4; tetloop.ver++) { fsym(tetloop, neightet); // Only do the calulation once for a face. if (((point)neightet.tet[7] == dummypoint) || (tetloop.tet < neightet.tet)) { p[0] = org(tetloop); p[1] = dest(tetloop); p[2] = apex(tetloop); faceangle[0] = interiorangle(p[0], p[1], p[2], NULL); faceangle[1] = interiorangle(p[1], p[2], p[0], NULL); faceangle[2] = PI - (faceangle[0] + faceangle[1]); // Translate angles into degrees. for (i = 0; i < 3; i++) { faceangle[i] = (faceangle[i] * 180.0) / PI; } // Calculate the largest and smallest face angles. for (i = 0; i < 3; i++) { if (i == 0) { smallfaangle = bigfaangle = faceangle[i]; } else { smallfaangle = faceangle[i] < smallfaangle ? faceangle[i] : smallfaangle; bigfaangle = faceangle[i] > bigfaangle ? faceangle[i] : bigfaangle; } if (faceangle[i] < smallestfaangle) { smallestfaangle = faceangle[i]; } if (faceangle[i] > biggestfaangle) { biggestfaangle = faceangle[i]; } tendegree = (int)(faceangle[i] / 10.); faceangletable[tendegree]++; } } } // Calculate aspect ratio and radius-edge ratio for this element. tetradius = cirradius / sqrt(shortlen); if (tetradius < smallestradiusratio) { smallestradiusratio = tetradius; } if (tetradius > biggestradiusratio) { biggestradiusratio = tetradius; biggestradiusratiotet.tet = tetloop.tet; } // tetaspect = sqrt(longlen) / (2.0 * insradius); tetaspect = sqrt(longlen) * minheightinv; // Remember the largest and smallest aspect ratio. if (tetaspect < smallestratio) { smallestratio = tetaspect; } if (tetaspect > biggestratio) { biggestratio = tetaspect; } // Accumulate the corresponding number in the aspect ratio histogram. aspectindex = 0; while ((tetaspect > aspectratiotable[aspectindex]) && (aspectindex < 11)) { aspectindex++; } aspecttable[aspectindex]++; radiusindex = 0; while ((tetradius > radiusratiotable[radiusindex]) && (radiusindex < 11)) { radiusindex++; } radiustable[radiusindex]++; tetloop.tet = tetrahedrontraverse(); } shortest = sqrt(shortest); longest = sqrt(longest); minaltitude = sqrt(minaltitude); printf(" Smallest volume: %16.5g | Largest volume: %16.5g\n", smallestvolume, biggestvolume); printf(" Shortest edge: %16.5g | Longest edge: %16.5g\n", shortest, longest); printf(" Smallest asp.ratio: %13.5g | Largest asp.ratio: %13.5g\n", smallestratio, biggestratio); sprintf(sbuf, "%.17g", biggestfaangle); if (strlen(sbuf) > 8) { sbuf[8] = '\0'; } printf(" Smallest facangle: %14.5g | Largest facangle: %s\n", smallestfaangle, sbuf); sprintf(sbuf, "%.17g", biggestdiangle); if (strlen(sbuf) > 8) { sbuf[8] = '\0'; } printf(" Smallest dihedral: %14.5g | Largest dihedral: %s\n\n", smallestdiangle, sbuf); printf(" Aspect ratio histogram:\n"); printf(" < %-6.6g : %8ld | %6.6g - %-6.6g : %8ld\n", aspectratiotable[0], aspecttable[0], aspectratiotable[5], aspectratiotable[6], aspecttable[6]); for (i = 1; i < 5; i++) { printf(" %6.6g - %-6.6g : %8ld | %6.6g - %-6.6g : %8ld\n", aspectratiotable[i - 1], aspectratiotable[i], aspecttable[i], aspectratiotable[i + 5], aspectratiotable[i + 6], aspecttable[i + 6]); } printf(" %6.6g - %-6.6g : %8ld | %6.6g - : %8ld\n", aspectratiotable[4], aspectratiotable[5], aspecttable[5], aspectratiotable[10], aspecttable[11]); printf(" (A tetrahedron's aspect ratio is its longest edge length"); printf(" divided by its\n"); printf(" smallest side height)\n\n"); printf(" Face angle histogram:\n"); for (i = 0; i < 9; i++) { printf(" %3d - %3d degrees: %8ld | %3d - %3d degrees: %8ld\n", i * 10, i * 10 + 10, faceangletable[i], i * 10 + 90, i * 10 + 100, faceangletable[i + 9]); } if (minfaceang != PI) { printf(" Minimum input face angle is %g (degree).\n", minfaceang / PI * 180.0); } printf("\n"); printf(" Dihedral angle histogram:\n"); // Print the three two rows: printf(" %3d - %2d degrees: %8ld | %3d - %3d degrees: %8ld\n", 0, 5, dihedangletable[0], 80, 110, dihedangletable[9]); printf(" %3d - %2d degrees: %8ld | %3d - %3d degrees: %8ld\n", 5, 10, dihedangletable[1], 110, 120, dihedangletable[10]); // Print the third to seventh rows. for (i = 2; i < 7; i++) { printf(" %3d - %2d degrees: %8ld | %3d - %3d degrees: %8ld\n", (i - 1) * 10, (i - 1) * 10 + 10, dihedangletable[i], (i - 1) * 10 + 110, (i - 1) * 10 + 120, dihedangletable[i + 9]); } // Print the last two rows. printf(" %3d - %2d degrees: %8ld | %3d - %3d degrees: %8ld\n", 60, 70, dihedangletable[7], 170, 175, dihedangletable[16]); printf(" %3d - %2d degrees: %8ld | %3d - %3d degrees: %8ld\n", 70, 80, dihedangletable[8], 175, 180, dihedangletable[17]); if (minfacetdihed != PI) { printf(" Minimum input dihedral angle is %g (degree).\n", minfacetdihed / PI * 180.0); } printf("\n"); printf("\n"); } /////////////////////////////////////////////////////////////////////////////// // // // memorystatistics() Report the memory usage. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::memorystatistics() { printf("Memory usage statistics:\n\n"); // Count the number of blocks of tetrahedra. int tetblocks = 0; tetrahedrons->pathblock = tetrahedrons->firstblock; while (tetrahedrons->pathblock != NULL) { tetblocks++; tetrahedrons->pathblock = (void**)*(tetrahedrons->pathblock); } // Calculate the total memory (in bytes) used by storing meshes. unsigned long totalmeshmemory = 0l, totalt2shmemory = 0l; totalmeshmemory = points->maxitems * points->itembytes + tetrahedrons->maxitems * tetrahedrons->itembytes; if (b->plc || b->refine) { totalmeshmemory += (subfaces->maxitems * subfaces->itembytes + subsegs->maxitems * subsegs->itembytes); totalt2shmemory = (tet2subpool->maxitems * tet2subpool->itembytes + tet2segpool->maxitems * tet2segpool->itembytes); } unsigned long totalalgomemory = 0l; totalalgomemory = cavetetlist->totalmemory + cavebdrylist->totalmemory + caveoldtetlist->totalmemory + flippool->maxitems * flippool->itembytes; if (b->plc || b->refine) { totalalgomemory += (subsegstack->totalmemory + subfacstack->totalmemory + subvertstack->totalmemory + caveshlist->totalmemory + caveshbdlist->totalmemory + cavesegshlist->totalmemory + cavetetshlist->totalmemory + cavetetseglist->totalmemory + caveencshlist->totalmemory + caveencseglist->totalmemory + cavetetvertlist->totalmemory + unflipqueue->totalmemory); } printf(" Maximum number of tetrahedra: %ld\n", tetrahedrons->maxitems); printf(" Maximum number of tet blocks (blocksize = %d): %d\n", b->tetrahedraperblock, tetblocks); /* if (b->plc || b->refine) { printf(" Approximate memory for tetrahedral mesh (bytes): %ld\n", totalmeshmemory); printf(" Approximate memory for extra pointers (bytes): %ld\n", totalt2shmemory); } else { printf(" Approximate memory for tetrahedralization (bytes): %ld\n", totalmeshmemory); } printf(" Approximate memory for algorithms (bytes): %ld\n", totalalgomemory); printf(" Approximate memory for working arrays (bytes): %ld\n", totalworkmemory); printf(" Approximate total used memory (bytes): %ld\n", totalmeshmemory + totalt2shmemory + totalalgomemory + totalworkmemory); */ if (b->plc || b->refine) { printf(" Approximate memory for tetrahedral mesh (bytes): "); printfcomma(totalmeshmemory); printf("\n"); printf(" Approximate memory for extra pointers (bytes): "); printfcomma(totalt2shmemory); printf("\n"); } else { printf(" Approximate memory for tetrahedralization (bytes): "); printfcomma(totalmeshmemory); printf("\n"); } printf(" Approximate memory for algorithms (bytes): "); printfcomma(totalalgomemory); printf("\n"); printf(" Approximate memory for working arrays (bytes): "); printfcomma(totalworkmemory); printf("\n"); printf(" Approximate total used memory (bytes): "); printfcomma(totalmeshmemory + totalt2shmemory + totalalgomemory + totalworkmemory); printf("\n"); printf("\n"); } /////////////////////////////////////////////////////////////////////////////// // // // statistics() Print all sorts of cool facts. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::statistics() { long tetnumber, facenumber; printf("\nStatistics:\n\n"); printf(" Input points: %d\n", in->numberofpoints); if (b->refine) { printf(" Input tetrahedra: %d\n", in->numberoftetrahedra); if (in->numberoftrifaces > 0) { printf(" Input triangles: %d\n", in->numberoftrifaces); } if (in->numberofedges > 0) { printf(" Input edges: %d\n", in->numberofedges); } } else if (b->plc) { printf(" Input facets: %d\n", in->numberoffacets); printf(" Input segments: %ld\n", insegments); if (in->numberofedges > 0) { printf(" Input edges: %d\n", in->numberofedges); } printf(" Input holes: %d\n", in->numberofholes); printf(" Input regions: %d\n", in->numberofregions); } tetnumber = tetrahedrons->items - hullsize; facenumber = (tetnumber * 4l + hullsize) / 2l; if (b->weighted) { // -w option printf("\n Mesh points: %ld\n", points->items - nonregularcount); } else { printf("\n Mesh points: %ld\n", points->items); } printf(" Mesh tetrahedra: %ld\n", tetnumber); printf(" Mesh faces: %ld\n", facenumber); if (meshedges > 0l) { printf(" Mesh edges: %ld\n", meshedges); } else { if (!nonconvex) { long vsize = points->items - dupverts - unuverts; if (b->weighted) vsize -= nonregularcount; meshedges = vsize + facenumber - tetnumber - 1; printf(" Mesh edges: %ld\n", meshedges); } } if (b->plc || b->refine) { printf(" Mesh faces on exterior boundary: %ld\n", hullsize); if (meshhulledges > 0l) { printf(" Mesh edges on exterior boundary: %ld\n", meshhulledges); } printf(" Mesh faces on input facets: %ld\n", subfaces->items); printf(" Mesh edges on input segments: %ld\n", subsegs->items); if (st_facref_count > 0l) { printf(" Steiner points on input facets: %ld\n", st_facref_count); } if (st_segref_count > 0l) { printf(" Steiner points on input segments: %ld\n", st_segref_count); } if (st_volref_count > 0l) { printf(" Steiner points inside domain: %ld\n", st_volref_count); } } else { printf(" Convex hull faces: %ld\n", hullsize); if (meshhulledges > 0l) { printf(" Convex hull edges: %ld\n", meshhulledges); } } if (b->weighted) { // -w option printf(" Skipped non-regular points: %ld\n", nonregularcount); } printf("\n"); if (b->verbose > 0) { if (b->plc || b->refine) { // -p or -r if (tetrahedrons->items > 0l) { qualitystatistics(); } } if (tetrahedrons->items > 0l) { memorystatistics(); } } } //// //// //// //// //// meshstat_cxx ///////////////////////////////////////////////////////////// //// output_cxx /////////////////////////////////////////////////////////////// //// //// //// //// /////////////////////////////////////////////////////////////////////////////// // // // jettisonnodes() Jettison unused or duplicated vertices. // // // // Unused points are those input points which are outside the mesh domain or // // have no connection (isolated) to the mesh. Duplicated points exist for // // example if the input PLC is read from a .stl mesh file (marked during the // // Delaunay tetrahedralization step. This routine remove these points from // // points list. All existing points are reindexed. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::jettisonnodes() { point pointloop; bool jetflag; int oldidx, newidx; int remcount; if (!b->quiet) { printf("Jettisoning redundant points.\n"); } points->traversalinit(); pointloop = pointtraverse(); oldidx = newidx = 0; // in->firstnumber; remcount = 0; while (pointloop != (point)NULL) { jetflag = (pointtype(pointloop) == DUPLICATEDVERTEX) || (pointtype(pointloop) == UNUSEDVERTEX); if (jetflag) { // It is a duplicated or unused point, delete it. pointdealloc(pointloop); remcount++; } else { // Re-index it. setpointmark(pointloop, newidx + in->firstnumber); if (in->pointmarkerlist != (int*)NULL) { if (oldidx < in->numberofpoints) { // Re-index the point marker as well. in->pointmarkerlist[newidx] = in->pointmarkerlist[oldidx]; } } newidx++; } oldidx++; pointloop = pointtraverse(); } if (b->verbose) { printf(" %ld duplicated vertices are removed.\n", dupverts); printf(" %ld unused vertices are removed.\n", unuverts); } dupverts = 0l; unuverts = 0l; // The following line ensures that dead items in the pool of nodes cannot // be allocated for the new created nodes. This ensures that the input // nodes will occur earlier in the output files, and have lower indices. points->deaditemstack = (void*)NULL; } /////////////////////////////////////////////////////////////////////////////// // // // highorder() Create extra nodes for quadratic subparametric elements. // // // // 'highordertable' is an array (size = numberoftetrahedra * 6) for storing // // high-order nodes of each tetrahedron. This routine is used only when -o2 // // switch is used. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::highorder() { triface tetloop, worktet, spintet; point *extralist, *adjextralist; point torg, tdest, newpoint; int highorderindex; int t1ver; int i, j; if (!b->quiet) { printf("Adding vertices for second-order tetrahedra.\n"); } // Initialize the 'highordertable'. highordertable = new point[tetrahedrons->items * 6]; if (highordertable == (point*)NULL) { terminatetetgen(this, 1); } // This will overwrite the slot for element markers. highorderindex = 11; // The following line ensures that dead items in the pool of nodes cannot // be allocated for the extra nodes associated with high order elements. // This ensures that the primary nodes (at the corners of elements) will // occur earlier in the output files, and have lower indices, than the // extra nodes. points->deaditemstack = (void*)NULL; // Assign an entry for each tetrahedron to find its extra nodes. At the // mean while, initialize all extra nodes be NULL. i = 0; tetrahedrons->traversalinit(); tetloop.tet = tetrahedrontraverse(); while (tetloop.tet != (tetrahedron*)NULL) { tetloop.tet[highorderindex] = (tetrahedron)&highordertable[i]; for (j = 0; j < 6; j++) { highordertable[i + j] = (point)NULL; } i += 6; tetloop.tet = tetrahedrontraverse(); } // To create a unique node on each edge. Loop over all tetrahedra, and // look at the six edges of each tetrahedron. If the extra node in // the tetrahedron corresponding to this edge is NULL, create a node // for this edge, at the same time, set the new node into the extra // node lists of all other tetrahedra sharing this edge. tetrahedrons->traversalinit(); tetloop.tet = tetrahedrontraverse(); while (tetloop.tet != (tetrahedron*)NULL) { // Get the list of extra nodes. extralist = (point*)tetloop.tet[highorderindex]; worktet.tet = tetloop.tet; for (i = 0; i < 6; i++) { if (extralist[i] == (point)NULL) { // Go to the ith-edge. worktet.ver = edge2ver[i]; // Create a new point in the middle of this edge. torg = org(worktet); tdest = dest(worktet); makepoint(&newpoint, FREEVOLVERTEX); for (j = 0; j < 3 + numpointattrib; j++) { newpoint[j] = 0.5 * (torg[j] + tdest[j]); } // Interpolate its metrics. for (j = 0; j < in->numberofpointmtrs; j++) { newpoint[pointmtrindex + j] = 0.5 * (torg[pointmtrindex + j] + tdest[pointmtrindex + j]); } // Set this point into all extra node lists at this edge. spintet = worktet; while (1) { if (!ishulltet(spintet)) { adjextralist = (point*)spintet.tet[highorderindex]; adjextralist[ver2edge[spintet.ver]] = newpoint; } fnextself(spintet); if (spintet.tet == worktet.tet) break; } } // if (!extralist[i]) } // i tetloop.tet = tetrahedrontraverse(); } } /////////////////////////////////////////////////////////////////////////////// // // // indexelements() Index all tetrahedra. // // // // Many output functions require that the tetrahedra are indexed. This // // routine is called when -E option is used. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::indexelements() { triface worktet; int eindex = b->zeroindex ? 0 : in->firstnumber; // firstindex; tetrahedrons->traversalinit(); worktet.tet = tetrahedrontraverse(); while (worktet.tet != NULL) { setelemindex(worktet.tet, eindex); eindex++; if (b->metric) { // -m option // Update the point-to-tet map, so that every point is pointing // to a real tet, not a fictious one. Used by .p2t file. tetrahedron tptr = encode(worktet); for (int i = 0; i < 4; i++) { setpoint2tet((point)(worktet.tet[4 + i]), tptr); } } worktet.tet = tetrahedrontraverse(); } } /////////////////////////////////////////////////////////////////////////////// // // // numberedges() Count the number of edges, save in "meshedges". // // // // This routine is called when '-p' or '-r', and '-E' options are used. The // // total number of edges depends on the genus of the input surface mesh. // // // // NOTE: This routine must be called after outelements(). So all elements // // have been indexed. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::numberedges() { triface worktet, spintet; int ishulledge; int t1ver; int i; meshedges = meshhulledges = 0l; tetrahedrons->traversalinit(); worktet.tet = tetrahedrontraverse(); while (worktet.tet != NULL) { for (i = 0; i < 6; i++) { worktet.ver = edge2ver[i]; ishulledge = 0; fnext(worktet, spintet); do { if (!ishulltet(spintet)) { if (elemindex(spintet.tet) < elemindex(worktet.tet)) break; } else { ishulledge = 1; } fnextself(spintet); } while (spintet.tet != worktet.tet); if (spintet.tet == worktet.tet) { meshedges++; if (ishulledge) meshhulledges++; } } infect(worktet); worktet.tet = tetrahedrontraverse(); } } /////////////////////////////////////////////////////////////////////////////// // // // outnodes() Output the points to a .node file or a tetgenio structure. // // // // Note: each point has already been numbered on input (the first index is // // 'in->firstnumber'). // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::outnodes(tetgenio* out) { FILE* outfile = NULL; char outnodefilename[FILENAMESIZE]; face parentsh; point pointloop; int nextras, bmark, marker = 0, weightDT = 0; int coordindex, attribindex; int pointnumber, firstindex; int index, i; if (out == (tetgenio*)NULL) { strcpy(outnodefilename, b->outfilename); strcat(outnodefilename, ".node"); } if (!b->quiet) { if (out == (tetgenio*)NULL) { printf("Writing %s.\n", outnodefilename); } else { printf("Writing nodes.\n"); } } nextras = numpointattrib; if (b->weighted) { // -w if (b->weighted_param == 0) weightDT = 1; // Weighted DT. } bmark = !b->nobound && in->pointmarkerlist; if (out == (tetgenio*)NULL) { outfile = fopen(outnodefilename, "w"); if (outfile == (FILE*)NULL) { printf("File I/O Error: Cannot create file %s.\n", outnodefilename); terminatetetgen(this, 1); } // Number of points, number of dimensions, number of point attributes, // and number of boundary markers (zero or one). fprintf(outfile, "%ld %d %d %d\n", points->items, 3, nextras, bmark); } else { // Allocate space for 'pointlist'; out->pointlist = new REAL[points->items * 3]; if (out->pointlist == (REAL*)NULL) { printf("Error: Out of memory.\n"); terminatetetgen(this, 1); } // Allocate space for 'pointattributelist' if necessary; if (nextras > 0) { out->pointattributelist = new REAL[points->items * nextras]; if (out->pointattributelist == (REAL*)NULL) { printf("Error: Out of memory.\n"); terminatetetgen(this, 1); } } // Allocate space for 'pointmarkerlist' if necessary; if (bmark) { out->pointmarkerlist = new int[points->items]; if (out->pointmarkerlist == (int*)NULL) { printf("Error: Out of memory.\n"); terminatetetgen(this, 1); } } if (b->psc) { out->pointparamlist = new tetgenio::pointparam[points->items]; if (out->pointparamlist == NULL) { printf("Error: Out of memory.\n"); terminatetetgen(this, 1); } } out->numberofpoints = points->items; out->numberofpointattributes = nextras; coordindex = 0; attribindex = 0; } // Determine the first index (0 or 1). firstindex = b->zeroindex ? 0 : in->firstnumber; points->traversalinit(); pointloop = pointtraverse(); pointnumber = firstindex; // in->firstnumber; index = 0; while (pointloop != (point)NULL) { if (bmark) { // Default the vertex has a zero marker. marker = 0; // Is it an input vertex? if (index < in->numberofpoints) { // Input point's marker is directly copied to output. marker = in->pointmarkerlist[index]; } else { if ((pointtype(pointloop) == FREESEGVERTEX) || (pointtype(pointloop) == FREEFACETVERTEX)) { sdecode(point2sh(pointloop), parentsh); if (parentsh.sh != NULL) { marker = shellmark(parentsh); } } // if (pointtype(...)) } } if (out == (tetgenio*)NULL) { // Point number, x, y and z coordinates. fprintf(outfile, "%4d %.17g %.17g %.17g", pointnumber, pointloop[0], pointloop[1], pointloop[2]); for (i = 0; i < nextras; i++) { // Write an attribute. if ((i == 0) && weightDT) { fprintf(outfile, " %.17g", pointloop[0] * pointloop[0] + pointloop[1] * pointloop[1] + pointloop[2] * pointloop[2] - pointloop[3 + i]); } else { fprintf(outfile, " %.17g", pointloop[3 + i]); } } if (bmark) { // Write the boundary marker. fprintf(outfile, " %d", marker); } if (b->psc) { fprintf(outfile, " %.8g %.8g %d", pointgeomuv(pointloop, 0), pointgeomuv(pointloop, 1), pointgeomtag(pointloop)); if (pointtype(pointloop) == RIDGEVERTEX) { fprintf(outfile, " 0"); } else if (pointtype(pointloop) == ACUTEVERTEX) { fprintf(outfile, " 0"); } else if (pointtype(pointloop) == FREESEGVERTEX) { fprintf(outfile, " 1"); } else if (pointtype(pointloop) == FREEFACETVERTEX) { fprintf(outfile, " 2"); } else if (pointtype(pointloop) == FREEVOLVERTEX) { fprintf(outfile, " 3"); } else { fprintf(outfile, " -1"); // Unknown type. } } fprintf(outfile, "\n"); } else { // X, y, and z coordinates. out->pointlist[coordindex++] = pointloop[0]; out->pointlist[coordindex++] = pointloop[1]; out->pointlist[coordindex++] = pointloop[2]; // Point attributes. for (i = 0; i < nextras; i++) { // Output an attribute. if ((i == 0) && weightDT) { out->pointattributelist[attribindex++] = pointloop[0] * pointloop[0] + pointloop[1] * pointloop[1] + pointloop[2] * pointloop[2] - pointloop[3 + i]; } else { out->pointattributelist[attribindex++] = pointloop[3 + i]; } } if (bmark) { // Output the boundary marker. out->pointmarkerlist[index] = marker; } if (b->psc) { out->pointparamlist[index].uv[0] = pointgeomuv(pointloop, 0); out->pointparamlist[index].uv[1] = pointgeomuv(pointloop, 1); out->pointparamlist[index].tag = pointgeomtag(pointloop); if (pointtype(pointloop) == RIDGEVERTEX) { out->pointparamlist[index].type = 0; } else if (pointtype(pointloop) == ACUTEVERTEX) { out->pointparamlist[index].type = 0; } else if (pointtype(pointloop) == FREESEGVERTEX) { out->pointparamlist[index].type = 1; } else if (pointtype(pointloop) == FREEFACETVERTEX) { out->pointparamlist[index].type = 2; } else if (pointtype(pointloop) == FREEVOLVERTEX) { out->pointparamlist[index].type = 3; } else { out->pointparamlist[index].type = -1; // Unknown type. } } } pointloop = pointtraverse(); pointnumber++; index++; } if (out == (tetgenio*)NULL) { fprintf(outfile, "# Generated by %s\n", b->commandline); fclose(outfile); } } /////////////////////////////////////////////////////////////////////////////// // // // outmetrics() Output the metric to a file (*.mtr) or a tetgenio obj. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::outmetrics(tetgenio* out) { FILE* outfile = NULL; char outmtrfilename[FILENAMESIZE]; point ptloop; int mtrindex = 0; int i; int msize = (sizeoftensor - useinsertradius); if (msize == 0) { return; } if (out == (tetgenio*)NULL) { strcpy(outmtrfilename, b->outfilename); strcat(outmtrfilename, ".mtr"); } if (!b->quiet) { if (out == (tetgenio*)NULL) { printf("Writing %s.\n", outmtrfilename); } else { printf("Writing metrics.\n"); } } if (out == (tetgenio*)NULL) { outfile = fopen(outmtrfilename, "w"); if (outfile == (FILE*)NULL) { printf("File I/O Error: Cannot create file %s.\n", outmtrfilename); terminatetetgen(this, 3); } // Number of points, number of point metrices, fprintf(outfile, "%ld %d\n", points->items, msize); } else { // Allocate space for 'pointmtrlist'. out->numberofpointmtrs = msize; out->pointmtrlist = new REAL[points->items * msize]; if (out->pointmtrlist == (REAL*)NULL) { terminatetetgen(this, 1); } } points->traversalinit(); ptloop = pointtraverse(); while (ptloop != (point)NULL) { if (out == (tetgenio*)NULL) { for (i = 0; i < msize; i++) { fprintf(outfile, " %-16.8e", ptloop[pointmtrindex + i]); } fprintf(outfile, "\n"); } else { for (i = 0; i < msize; i++) { out->pointmtrlist[mtrindex++] = ptloop[pointmtrindex + i]; } } ptloop = pointtraverse(); } // Output the point-to-tet map. if (out == (tetgenio*)NULL) { strcpy(outmtrfilename, b->outfilename); strcat(outmtrfilename, ".p2t"); } if (!b->quiet) { if (out == (tetgenio*)NULL) { printf("Writing %s.\n", outmtrfilename); } else { printf("Writing point-to-tet map.\n"); } } if (out == (tetgenio*)NULL) { outfile = fopen(outmtrfilename, "w"); if (outfile == (FILE*)NULL) { printf("File I/O Error: Cannot create file %s.\n", outmtrfilename); terminatetetgen(this, 3); } // Number of points, // fprintf(outfile, "%ld\n", points->items); } else { // Allocate space for 'point2tetlist'. out->point2tetlist = new int[points->items]; if (out->point2tetlist == (int*)NULL) { terminatetetgen(this, 1); } } // The list of tetrahedra must be indexed. if (bgm != NULL) { bgm->indexelements(); } // Determine the first index (0 or 1). int firstindex = b->zeroindex ? 0 : in->firstnumber; int pointindex = firstindex; i = 0; triface parenttet; points->traversalinit(); ptloop = pointtraverse(); while (ptloop != (point)NULL) { if (bgm != NULL) { bgm->decode(point2bgmtet(ptloop), parenttet); } else { decode(point2tet(ptloop), parenttet); } if (out == (tetgenio*)NULL) { fprintf(outfile, "%d %d\n", pointindex, elemindex(parenttet.tet)); } else { out->point2tetlist[i] = elemindex(parenttet.tet); } pointindex++; i++; ptloop = pointtraverse(); } if (out == (tetgenio*)NULL) { fprintf(outfile, "# Generated by %s\n", b->commandline); fclose(outfile); } } /////////////////////////////////////////////////////////////////////////////// // // // outelements() Output the tetrahedra to an .ele file or a tetgenio // // structure. // // // // This routine also indexes all tetrahedra (exclusing hull tets) (from in-> // // firstnumber). The total number of mesh edges is counted in 'meshedges'. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::outelements(tetgenio* out) { FILE* outfile = NULL; char outelefilename[FILENAMESIZE]; tetrahedron* tptr; point p1, p2, p3, p4; point* extralist; REAL* talist = NULL; int* tlist = NULL; long ntets; int firstindex, shift; int pointindex, attribindex; int highorderindex = 11; int elementnumber; int eextras; int i; if (out == (tetgenio*)NULL) { strcpy(outelefilename, b->outfilename); strcat(outelefilename, ".ele"); } if (!b->quiet) { if (out == (tetgenio*)NULL) { printf("Writing %s.\n", outelefilename); } else { printf("Writing elements.\n"); } } // The number of tets excluding hull tets. ntets = tetrahedrons->items - hullsize; eextras = numelemattrib; if (out == (tetgenio*)NULL) { outfile = fopen(outelefilename, "w"); if (outfile == (FILE*)NULL) { printf("File I/O Error: Cannot create file %s.\n", outelefilename); terminatetetgen(this, 1); } // Number of tetras, points per tetra, attributes per tetra. fprintf(outfile, "%ld %d %d\n", ntets, b->order == 1 ? 4 : 10, eextras); } else { // Allocate memory for output tetrahedra. out->tetrahedronlist = new int[ntets * (b->order == 1 ? 4 : 10)]; if (out->tetrahedronlist == (int*)NULL) { printf("Error: Out of memory.\n"); terminatetetgen(this, 1); } // Allocate memory for output tetrahedron attributes if necessary. if (eextras > 0) { out->tetrahedronattributelist = new REAL[ntets * eextras]; if (out->tetrahedronattributelist == (REAL*)NULL) { printf("Error: Out of memory.\n"); terminatetetgen(this, 1); } } out->numberoftetrahedra = ntets; out->numberofcorners = b->order == 1 ? 4 : 10; out->numberoftetrahedronattributes = eextras; tlist = out->tetrahedronlist; talist = out->tetrahedronattributelist; pointindex = 0; attribindex = 0; } // Determine the first index (0 or 1). firstindex = b->zeroindex ? 0 : in->firstnumber; shift = 0; // Default no shift. if ((in->firstnumber == 1) && (firstindex == 0)) { shift = 1; // Shift the output indices by 1. } tetrahedrons->traversalinit(); tptr = tetrahedrontraverse(); elementnumber = firstindex; // in->firstnumber; while (tptr != (tetrahedron*)NULL) { if (!b->reversetetori) { p1 = (point)tptr[4]; p2 = (point)tptr[5]; } else { p1 = (point)tptr[5]; p2 = (point)tptr[4]; } p3 = (point)tptr[6]; p4 = (point)tptr[7]; if (out == (tetgenio*)NULL) { // Tetrahedron number, indices for four points. fprintf(outfile, "%5d %5d %5d %5d %5d", elementnumber, pointmark(p1) - shift, pointmark(p2) - shift, pointmark(p3) - shift, pointmark(p4) - shift); if (b->order == 2) { extralist = (point*)tptr[highorderindex]; // indices for six extra points. fprintf(outfile, " %5d %5d %5d %5d %5d %5d", pointmark(extralist[0]) - shift, pointmark(extralist[1]) - shift, pointmark(extralist[2]) - shift, pointmark(extralist[3]) - shift, pointmark(extralist[4]) - shift, pointmark(extralist[5]) - shift); } for (i = 0; i < eextras; i++) { fprintf(outfile, " %.17g", elemattribute(tptr, i)); } fprintf(outfile, "\n"); } else { tlist[pointindex++] = pointmark(p1) - shift; tlist[pointindex++] = pointmark(p2) - shift; tlist[pointindex++] = pointmark(p3) - shift; tlist[pointindex++] = pointmark(p4) - shift; if (b->order == 2) { extralist = (point*)tptr[highorderindex]; tlist[pointindex++] = pointmark(extralist[0]) - shift; tlist[pointindex++] = pointmark(extralist[1]) - shift; tlist[pointindex++] = pointmark(extralist[2]) - shift; tlist[pointindex++] = pointmark(extralist[3]) - shift; tlist[pointindex++] = pointmark(extralist[4]) - shift; tlist[pointindex++] = pointmark(extralist[5]) - shift; } for (i = 0; i < eextras; i++) { talist[attribindex++] = elemattribute(tptr, i); } } // Remember the index of this element (for counting edges). setelemindex(tptr, elementnumber); if (b->metric) { // -m option // Update the point-to-tet map, so that every point is pointing // to a real tet, not a fictious one. Used by .p2t file. for (int i = 0; i < 4; i++) { setpoint2tet((point)(tptr[4 + i]), (tetrahedron)tptr); } } tptr = tetrahedrontraverse(); elementnumber++; } if (out == (tetgenio*)NULL) { fprintf(outfile, "# Generated by %s\n", b->commandline); fclose(outfile); } } /////////////////////////////////////////////////////////////////////////////// // // // outfaces() Output all faces to a .face file or a tetgenio object. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::outfaces(tetgenio* out) { FILE* outfile = NULL; char facefilename[FILENAMESIZE]; triface tface, tsymface; face checkmark; point torg, tdest, tapex; long ntets, faces; int *elist = NULL, *emlist = NULL; int neigh1 = 0, neigh2 = 0; int marker = 0; int firstindex, shift; int facenumber; int index = 0; // For -o2 option. triface workface; point *extralist, pp[3] = {0, 0, 0}; int highorderindex = 11; int o2index = 0, i; // For -nn option. int* tet2facelist = NULL; int tidx; if (out == (tetgenio*)NULL) { strcpy(facefilename, b->outfilename); strcat(facefilename, ".face"); } if (!b->quiet) { if (out == (tetgenio*)NULL) { printf("Writing %s.\n", facefilename); } else { printf("Writing faces.\n"); } } ntets = tetrahedrons->items - hullsize; faces = (ntets * 4l + hullsize) / 2l; if (out == (tetgenio*)NULL) { outfile = fopen(facefilename, "w"); if (outfile == (FILE*)NULL) { printf("File I/O Error: Cannot create file %s.\n", facefilename); terminatetetgen(this, 1); } fprintf(outfile, "%ld %d\n", faces, !b->nobound); } else { // Allocate memory for 'trifacelist'. out->trifacelist = new int[faces * 3]; if (out->trifacelist == (int*)NULL) { printf("Error: Out of memory.\n"); terminatetetgen(this, 1); } if (b->order == 2) { out->o2facelist = new int[faces * 3]; } // Allocate memory for 'trifacemarkerlist' if necessary. if (!b->nobound) { out->trifacemarkerlist = new int[faces]; if (out->trifacemarkerlist == (int*)NULL) { printf("Error: Out of memory.\n"); terminatetetgen(this, 1); } } if (b->neighout > 1) { // '-nn' switch. out->face2tetlist = new int[faces * 2]; if (out->face2tetlist == (int*)NULL) { printf("Error: Out of memory.\n"); terminatetetgen(this, 1); } } out->numberoftrifaces = faces; elist = out->trifacelist; emlist = out->trifacemarkerlist; } if (b->neighout > 1) { // -nn option // Output the tetrahedron-to-face map. tet2facelist = new int[ntets * 4]; } // Determine the first index (0 or 1). firstindex = b->zeroindex ? 0 : in->firstnumber; shift = 0; // Default no shiftment. if ((in->firstnumber == 1) && (firstindex == 0)) { shift = 1; // Shift the output indices by 1. } tetrahedrons->traversalinit(); tface.tet = tetrahedrontraverse(); facenumber = firstindex; // in->firstnumber; // To loop over the set of faces, loop over all tetrahedra, and look at // the four faces of each one. If its adjacent tet is a hull tet, // operate on the face, otherwise, operate on the face only if the // current tet has a smaller index than its neighbor. while (tface.tet != (tetrahedron*)NULL) { for (tface.ver = 0; tface.ver < 4; tface.ver++) { fsym(tface, tsymface); if (ishulltet(tsymface) || (elemindex(tface.tet) < elemindex(tsymface.tet))) { torg = org(tface); tdest = dest(tface); tapex = apex(tface); if (b->order == 2) { // -o2 // Get the three extra vertices on edges. extralist = (point*)(tface.tet[highorderindex]); // The extra vertices are on edges opposite the corners. enext(tface, workface); for (i = 0; i < 3; i++) { pp[i] = extralist[ver2edge[workface.ver]]; enextself(workface); } } if (!b->nobound) { // Get the boundary marker of this face. if (b->plc || b->refine) { // Shell face is used. tspivot(tface, checkmark); if (checkmark.sh == NULL) { marker = 0; // It is an inner face. It's marker is 0. } else { marker = shellmark(checkmark); } } else { // Shell face is not used, only distinguish outer and inner face. marker = (int)ishulltet(tsymface); } } if (b->neighout > 1) { // '-nn' switch. Output adjacent tets indices. if (!ishulltet(tface)) { neigh1 = elemindex(tface.tet); } else { neigh1 = -1; } if (!ishulltet(tsymface)) { neigh2 = elemindex(tsymface.tet); } else { neigh2 = -1; } // Fill the tetrahedron-to-face map. tidx = elemindex(tface.tet) - firstindex; tet2facelist[tidx * 4 + tface.ver] = facenumber; if (!ishulltet(tsymface)) { tidx = elemindex(tsymface.tet) - firstindex; tet2facelist[tidx * 4 + (tsymface.ver & 3)] = facenumber; } } if (out == (tetgenio*)NULL) { // Face number, indices of three vertices. fprintf(outfile, "%5d %4d %4d %4d", facenumber, pointmark(torg) - shift, pointmark(tdest) - shift, pointmark(tapex) - shift); if (b->order == 2) { // -o2 fprintf(outfile, " %4d %4d %4d", pointmark(pp[0]) - shift, pointmark(pp[1]) - shift, pointmark(pp[2]) - shift); } if (!b->nobound) { // Output a boundary marker. fprintf(outfile, " %d", marker); } if (b->neighout > 1) { fprintf(outfile, " %5d %5d", neigh1, neigh2); } fprintf(outfile, "\n"); } else { // Output indices of three vertices. elist[index++] = pointmark(torg) - shift; elist[index++] = pointmark(tdest) - shift; elist[index++] = pointmark(tapex) - shift; if (b->order == 2) { // -o2 out->o2facelist[o2index++] = pointmark(pp[0]) - shift; out->o2facelist[o2index++] = pointmark(pp[1]) - shift; out->o2facelist[o2index++] = pointmark(pp[2]) - shift; } if (!b->nobound) { emlist[facenumber - in->firstnumber] = marker; } if (b->neighout > 1) { out->face2tetlist[(facenumber - in->firstnumber) * 2] = neigh1; out->face2tetlist[(facenumber - in->firstnumber) * 2 + 1] = neigh2; } } facenumber++; } } tface.tet = tetrahedrontraverse(); } if (out == (tetgenio*)NULL) { fprintf(outfile, "# Generated by %s\n", b->commandline); fclose(outfile); } if (b->neighout > 1) { // -nn option // Output the tetrahedron-to-face map. if (out == (tetgenio*)NULL) { strcpy(facefilename, b->outfilename); strcat(facefilename, ".t2f"); } if (!b->quiet) { if (out == (tetgenio*)NULL) { printf("Writing %s.\n", facefilename); } else { printf("Writing tetrahedron-to-face map.\n"); } } if (out == (tetgenio*)NULL) { outfile = fopen(facefilename, "w"); for (tidx = 0; tidx < ntets; tidx++) { index = tidx * 4; fprintf(outfile, "%4d %d %d %d %d\n", tidx + in->firstnumber, tet2facelist[index], tet2facelist[index + 1], tet2facelist[index + 2], tet2facelist[index + 3]); } fclose(outfile); delete[] tet2facelist; } else { // Simply copy the address of the list to the output. out->tet2facelist = tet2facelist; } } } /////////////////////////////////////////////////////////////////////////////// // // // outhullfaces() Output hull faces to a .face file or a tetgenio object. // // // // The normal of each face is pointing to the outside of the domain. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::outhullfaces(tetgenio* out) { FILE* outfile = NULL; char facefilename[FILENAMESIZE]; triface hulltet; point torg, tdest, tapex; int* elist = NULL; int firstindex, shift; int facenumber; int index; if (out == (tetgenio*)NULL) { strcpy(facefilename, b->outfilename); strcat(facefilename, ".face"); } if (!b->quiet) { if (out == (tetgenio*)NULL) { printf("Writing %s.\n", facefilename); } else { printf("Writing faces.\n"); } } if (out == (tetgenio*)NULL) { outfile = fopen(facefilename, "w"); if (outfile == (FILE*)NULL) { printf("File I/O Error: Cannot create file %s.\n", facefilename); terminatetetgen(this, 1); } fprintf(outfile, "%ld 0\n", hullsize); } else { // Allocate memory for 'trifacelist'. out->trifacelist = new int[hullsize * 3]; if (out->trifacelist == (int*)NULL) { printf("Error: Out of memory.\n"); terminatetetgen(this, 1); } out->numberoftrifaces = hullsize; elist = out->trifacelist; index = 0; } // Determine the first index (0 or 1). firstindex = b->zeroindex ? 0 : in->firstnumber; shift = 0; // Default no shiftment. if ((in->firstnumber == 1) && (firstindex == 0)) { shift = 1; // Shift the output indices by 1. } tetrahedrons->traversalinit(); hulltet.tet = alltetrahedrontraverse(); facenumber = firstindex; while (hulltet.tet != (tetrahedron*)NULL) { if (ishulltet(hulltet)) { torg = (point)hulltet.tet[4]; tdest = (point)hulltet.tet[5]; tapex = (point)hulltet.tet[6]; if (out == (tetgenio*)NULL) { // Face number, indices of three vertices. fprintf(outfile, "%5d %4d %4d %4d", facenumber, pointmark(torg) - shift, pointmark(tdest) - shift, pointmark(tapex) - shift); fprintf(outfile, "\n"); } else { // Output indices of three vertices. elist[index++] = pointmark(torg) - shift; elist[index++] = pointmark(tdest) - shift; elist[index++] = pointmark(tapex) - shift; } facenumber++; } hulltet.tet = alltetrahedrontraverse(); } if (out == (tetgenio*)NULL) { fprintf(outfile, "# Generated by %s\n", b->commandline); fclose(outfile); } } /////////////////////////////////////////////////////////////////////////////// // // // outsubfaces() Output subfaces (i.e. boundary faces) to a .face file or // // a tetgenio structure. // // // // The boundary faces are found in 'subfaces'. For listing triangle vertices // // in the same sense for all triangles in the mesh, the direction determined // // by right-hand rule is pointer to the inside of the volume. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::outsubfaces(tetgenio* out) { FILE* outfile = NULL; char facefilename[FILENAMESIZE]; int* elist = NULL; int* emlist = NULL; int index = 0, index1 = 0, index2 = 0; triface abuttingtet; face faceloop; point torg, tdest, tapex; int marker = 0; int firstindex, shift; int neigh1 = 0, neigh2 = 0; int facenumber; // For -o2 option. triface workface; point *extralist, pp[3] = {0, 0, 0}; int highorderindex = 11; int o2index = 0, i; int t1ver; // used by fsymself() if (out == (tetgenio*)NULL) { strcpy(facefilename, b->outfilename); strcat(facefilename, ".face"); } if (!b->quiet) { if (out == (tetgenio*)NULL) { printf("Writing %s.\n", facefilename); } else { printf("Writing faces.\n"); } } if (out == (tetgenio*)NULL) { outfile = fopen(facefilename, "w"); if (outfile == (FILE*)NULL) { printf("File I/O Error: Cannot create file %s.\n", facefilename); terminatetetgen(this, 3); } // Number of subfaces. fprintf(outfile, "%ld %d\n", subfaces->items, !b->nobound); } else { // Allocate memory for 'trifacelist'. out->trifacelist = new int[subfaces->items * 3]; if (out->trifacelist == (int*)NULL) { terminatetetgen(this, 1); } if (b->order == 2) { out->o2facelist = new int[subfaces->items * 3]; } if (!b->nobound) { // Allocate memory for 'trifacemarkerlist'. out->trifacemarkerlist = new int[subfaces->items]; if (out->trifacemarkerlist == (int*)NULL) { terminatetetgen(this, 1); } } if (b->neighout > 1) { // '-nn' switch. out->face2tetlist = new int[subfaces->items * 2]; if (out->face2tetlist == (int*)NULL) { terminatetetgen(this, 1); } } out->numberoftrifaces = subfaces->items; elist = out->trifacelist; emlist = out->trifacemarkerlist; } // Determine the first index (0 or 1). firstindex = b->zeroindex ? 0 : in->firstnumber; shift = 0; // Default no shiftment. if ((in->firstnumber == 1) && (firstindex == 0)) { shift = 1; // Shift the output indices by 1. } subfaces->traversalinit(); faceloop.sh = shellfacetraverse(subfaces); facenumber = firstindex; // in->firstnumber; while (faceloop.sh != (shellface*)NULL) { stpivot(faceloop, abuttingtet); // If there is a tetrahedron containing this subface, orient it so // that the normal of this face points to inside of the volume by // right-hand rule. if (abuttingtet.tet != NULL) { if (ishulltet(abuttingtet)) { fsymself(abuttingtet); } } if (abuttingtet.tet != NULL) { torg = org(abuttingtet); tdest = dest(abuttingtet); tapex = apex(abuttingtet); if (b->order == 2) { // -o2 // Get the three extra vertices on edges. extralist = (point*)(abuttingtet.tet[highorderindex]); workface = abuttingtet; for (i = 0; i < 3; i++) { pp[i] = extralist[ver2edge[workface.ver]]; enextself(workface); } } } else { // This may happen when only a surface mesh be generated. torg = sorg(faceloop); tdest = sdest(faceloop); tapex = sapex(faceloop); if (b->order == 2) { // -o2 // There is no extra node list available. pp[0] = torg; pp[1] = tdest; pp[2] = tapex; } } if (!b->nobound) { marker = shellmark(faceloop); } if (b->neighout > 1) { // '-nn' switch. Output adjacent tets indices. neigh1 = -1; neigh2 = -1; stpivot(faceloop, abuttingtet); if (abuttingtet.tet != NULL) { if (!ishulltet(abuttingtet)) { neigh1 = elemindex(abuttingtet.tet); } fsymself(abuttingtet); if (!ishulltet(abuttingtet)) { neigh2 = elemindex(abuttingtet.tet); } } } if (out == (tetgenio*)NULL) { fprintf(outfile, "%5d %4d %4d %4d", facenumber, pointmark(torg) - shift, pointmark(tdest) - shift, pointmark(tapex) - shift); if (b->order == 2) { // -o2 fprintf(outfile, " %4d %4d %4d", pointmark(pp[0]) - shift, pointmark(pp[1]) - shift, pointmark(pp[2]) - shift); } if (!b->nobound) { fprintf(outfile, " %d", marker); } if (b->neighout > 1) { fprintf(outfile, " %5d %5d", neigh1, neigh2); } fprintf(outfile, "\n"); } else { // Output three vertices of this face; elist[index++] = pointmark(torg) - shift; elist[index++] = pointmark(tdest) - shift; elist[index++] = pointmark(tapex) - shift; if (b->order == 2) { // -o2 out->o2facelist[o2index++] = pointmark(pp[0]) - shift; out->o2facelist[o2index++] = pointmark(pp[1]) - shift; out->o2facelist[o2index++] = pointmark(pp[2]) - shift; } if (!b->nobound) { emlist[index1++] = marker; } if (b->neighout > 1) { out->face2tetlist[index2++] = neigh1; out->face2tetlist[index2++] = neigh2; } } facenumber++; faceloop.sh = shellfacetraverse(subfaces); } if (out == (tetgenio*)NULL) { fprintf(outfile, "# Generated by %s\n", b->commandline); fclose(outfile); } } /////////////////////////////////////////////////////////////////////////////// // // // outedges() Output all edges to a .edge file or a tetgenio object. // // // // Note: This routine must be called after outelements(), so that the total // // number of edges 'meshedges' has been counted. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::outedges(tetgenio* out) { FILE* outfile = NULL; char edgefilename[FILENAMESIZE]; triface tetloop, worktet, spintet; face checkseg; point torg, tdest; int ishulledge; int firstindex, shift; int edgenumber, marker; int index = 0, index1 = 0, index2 = 0; int t1ver; int i; // For -o2 option. point *extralist, pp = NULL; int highorderindex = 11; int o2index = 0; // For -nn option. int* tet2edgelist = NULL; int tidx; if (out == (tetgenio*)NULL) { strcpy(edgefilename, b->outfilename); strcat(edgefilename, ".edge"); } if (!b->quiet) { if (out == (tetgenio*)NULL) { printf("Writing %s.\n", edgefilename); } else { printf("Writing edges.\n"); } } if (meshedges == 0l) { if (nonconvex) { numberedges(); // Count the edges. } else { // Use Euler's characteristic to get the numbe of edges. // It states V - E + F - C = 1, hence E = V + F - C - 1. long tsize = tetrahedrons->items - hullsize; long fsize = (tsize * 4l + hullsize) / 2l; long vsize = points->items - dupverts - unuverts; if (b->weighted) vsize -= nonregularcount; meshedges = vsize + fsize - tsize - 1; } } meshhulledges = 0l; // It will be counted. if (out == (tetgenio*)NULL) { outfile = fopen(edgefilename, "w"); if (outfile == (FILE*)NULL) { printf("File I/O Error: Cannot create file %s.\n", edgefilename); terminatetetgen(this, 1); } // Write the number of edges, boundary markers (0 or 1). fprintf(outfile, "%ld %d\n", meshedges, !b->nobound); } else { // Allocate memory for 'edgelist'. out->numberofedges = meshedges; out->edgelist = new int[meshedges * 2]; if (out->edgelist == (int*)NULL) { printf("Error: Out of memory.\n"); terminatetetgen(this, 1); } if (b->order == 2) { // -o2 switch out->o2edgelist = new int[meshedges]; } if (!b->nobound) { out->edgemarkerlist = new int[meshedges]; } if (b->neighout > 1) { // '-nn' switch. out->edge2tetlist = new int[meshedges]; } } if (b->neighout > 1) { // -nn option // Output the tetrahedron-to-edge map. long tsize = tetrahedrons->items - hullsize; tet2edgelist = new int[tsize * 6]; } // Determine the first index (0 or 1). firstindex = b->zeroindex ? 0 : in->firstnumber; shift = 0; // Default no shiftment. if ((in->firstnumber == 1) && (firstindex == 0)) { shift = 1; // Shift (reduce) the output indices by 1. } tetrahedrons->traversalinit(); tetloop.tet = tetrahedrontraverse(); edgenumber = firstindex; // in->firstnumber; while (tetloop.tet != (tetrahedron*)NULL) { // Count the number of Voronoi faces. worktet.tet = tetloop.tet; for (i = 0; i < 6; i++) { worktet.ver = edge2ver[i]; ishulledge = 0; fnext(worktet, spintet); do { if (!ishulltet(spintet)) { if (elemindex(spintet.tet) < elemindex(worktet.tet)) break; } else { ishulledge = 1; } fnextself(spintet); } while (spintet.tet != worktet.tet); if (spintet.tet == worktet.tet) { // Found a new edge. if (ishulledge) meshhulledges++; torg = org(worktet); tdest = dest(worktet); if (b->order == 2) { // -o2 // Get the extra vertex on this edge. extralist = (point*)worktet.tet[highorderindex]; pp = extralist[ver2edge[worktet.ver]]; } if (out == (tetgenio*)NULL) { fprintf(outfile, "%5d %4d %4d", edgenumber, pointmark(torg) - shift, pointmark(tdest) - shift); if (b->order == 2) { // -o2 fprintf(outfile, " %4d", pointmark(pp) - shift); } } else { // Output three vertices of this face; out->edgelist[index++] = pointmark(torg) - shift; out->edgelist[index++] = pointmark(tdest) - shift; if (b->order == 2) { // -o2 out->o2edgelist[o2index++] = pointmark(pp) - shift; } } if (!b->nobound) { if (b->plc || b->refine) { // Check if the edge is a segment. tsspivot1(worktet, checkseg); if (checkseg.sh != NULL) { marker = shellmark(checkseg); } else { marker = 0; // It's not a segment. } } else { // Mark it if it is a hull edge. marker = ishulledge ? 1 : 0; } if (out == (tetgenio*)NULL) { fprintf(outfile, " %d", marker); } else { out->edgemarkerlist[index1++] = marker; } } if (b->neighout > 1) { // '-nn' switch. if (out == (tetgenio*)NULL) { fprintf(outfile, " %d", elemindex(tetloop.tet)); } else { out->edge2tetlist[index2++] = elemindex(tetloop.tet); } // Fill the tetrahedron-to-edge map. spintet = worktet; while (1) { if (!ishulltet(spintet)) { tidx = elemindex(spintet.tet) - firstindex; tet2edgelist[tidx * 6 + ver2edge[spintet.ver]] = edgenumber; } fnextself(spintet); if (spintet.tet == worktet.tet) break; } } if (out == (tetgenio*)NULL) { fprintf(outfile, "\n"); } edgenumber++; } } tetloop.tet = tetrahedrontraverse(); } if (out == (tetgenio*)NULL) { fprintf(outfile, "# Generated by %s\n", b->commandline); fclose(outfile); } if (b->neighout > 1) { // -nn option long tsize = tetrahedrons->items - hullsize; if (b->facesout) { // -f option // Build the face-to-edge map (use the tet-to-edge map). long fsize = (tsize * 4l + hullsize) / 2l; int* face2edgelist = new int[fsize * 3]; tetrahedrons->traversalinit(); tetloop.tet = tetrahedrontraverse(); int facenumber = 0; // firstindex; // in->firstnumber; while (tetloop.tet != (tetrahedron*)NULL) { for (tetloop.ver = 0; tetloop.ver < 4; tetloop.ver++) { fsym(tetloop, spintet); if (ishulltet(spintet) || (elemindex(tetloop.tet) < elemindex(spintet.tet))) { // The three edges of this face are ordered such that the // first edge is opposite to the first vertex of this face // that appears in the .face file, and so on. tidx = elemindex(tetloop.tet) - firstindex; worktet = tetloop; for (i = 0; i < 3; i++) { enextself(worktet); // The edge opposite to vertex i. int eidx = tet2edgelist[tidx * 6 + ver2edge[worktet.ver]]; face2edgelist[facenumber * 3 + i] = eidx; } facenumber++; } } tetloop.tet = tetrahedrontraverse(); } // Output the face-to-edge map. if (out == (tetgenio*)NULL) { strcpy(edgefilename, b->outfilename); strcat(edgefilename, ".f2e"); } if (!b->quiet) { if (out == (tetgenio*)NULL) { printf("Writing %s.\n", edgefilename); } else { printf("Writing face-to-edge map.\n"); } } if (out == (tetgenio*)NULL) { outfile = fopen(edgefilename, "w"); for (tidx = 0; tidx < fsize; tidx++) { // Re-use `tidx' i = tidx * 3; fprintf(outfile, "%4d %d %d %d\n", tidx + in->firstnumber, face2edgelist[i], face2edgelist[i + 1], face2edgelist[i + 2]); } fclose(outfile); delete[] face2edgelist; } else { // Simply copy the address of the list to the output. out->face2edgelist = face2edgelist; } } // if (b->facesout) // Output the tetrahedron-to-edge map. if (out == (tetgenio*)NULL) { strcpy(edgefilename, b->outfilename); strcat(edgefilename, ".t2e"); } if (!b->quiet) { if (out == (tetgenio*)NULL) { printf("Writing %s.\n", edgefilename); } else { printf("Writing tetrahedron-to-edge map.\n"); } } if (out == (tetgenio*)NULL) { outfile = fopen(edgefilename, "w"); for (tidx = 0; tidx < tsize; tidx++) { i = tidx * 6; fprintf(outfile, "%4d %d %d %d %d %d %d\n", tidx + in->firstnumber, tet2edgelist[i], tet2edgelist[i + 1], tet2edgelist[i + 2], tet2edgelist[i + 3], tet2edgelist[i + 4], tet2edgelist[i + 5]); } fclose(outfile); delete[] tet2edgelist; } else { // Simply copy the address of the list to the output. out->tet2edgelist = tet2edgelist; } } } /////////////////////////////////////////////////////////////////////////////// // // // outsubsegments() Output segments to a .edge file or a structure. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::outsubsegments(tetgenio* out) { FILE* outfile = NULL; char edgefilename[FILENAMESIZE]; int* elist = NULL; int index, i; face edgeloop; point torg, tdest; int firstindex, shift; int marker; int edgenumber; // For -o2 option. triface workface, spintet; point *extralist, pp = NULL; int highorderindex = 11; int o2index = 0; // For -nn option. int neigh = -1; int index2 = 0; int t1ver; // used by fsymself() if (out == (tetgenio*)NULL) { strcpy(edgefilename, b->outfilename); strcat(edgefilename, ".edge"); } if (!b->quiet) { if (out == (tetgenio*)NULL) { printf("Writing %s.\n", edgefilename); } else { printf("Writing edges.\n"); } } if (out == (tetgenio*)NULL) { outfile = fopen(edgefilename, "w"); if (outfile == (FILE*)NULL) { printf("File I/O Error: Cannot create file %s.\n", edgefilename); terminatetetgen(this, 3); } // Number of subsegments. fprintf(outfile, "%ld 1\n", subsegs->items); } else { // Allocate memory for 'edgelist'. out->edgelist = new int[subsegs->items * (b->order == 1 ? 2 : 3)]; if (out->edgelist == (int*)NULL) { terminatetetgen(this, 1); } if (b->order == 2) { out->o2edgelist = new int[subsegs->items]; } out->edgemarkerlist = new int[subsegs->items]; if (out->edgemarkerlist == (int*)NULL) { terminatetetgen(this, 1); } if (b->neighout > 1) { out->edge2tetlist = new int[subsegs->items]; } out->numberofedges = subsegs->items; elist = out->edgelist; } // Determine the first index (0 or 1). firstindex = b->zeroindex ? 0 : in->firstnumber; shift = 0; // Default no shiftment. if ((in->firstnumber == 1) && (firstindex == 0)) { shift = 1; // Shift the output indices by 1. } index = 0; i = 0; subsegs->traversalinit(); edgeloop.sh = shellfacetraverse(subsegs); edgenumber = firstindex; // in->firstnumber; while (edgeloop.sh != (shellface*)NULL) { torg = sorg(edgeloop); tdest = sdest(edgeloop); if ((b->order == 2) || (b->neighout > 1)) { sstpivot1(edgeloop, workface); if (workface.tet != NULL) { // We must find a non-hull tet. if (ishulltet(workface)) { spintet = workface; while (1) { fnextself(spintet); if (!ishulltet(spintet)) break; if (spintet.tet == workface.tet) break; } workface = spintet; } } } if (b->order == 2) { // -o2 // Get the extra vertex on this edge. if (workface.tet != NULL) { extralist = (point*)workface.tet[highorderindex]; pp = extralist[ver2edge[workface.ver]]; } else { pp = torg; // There is no extra node available. } } if (b->neighout > 1) { // -nn if (workface.tet != NULL) { neigh = elemindex(workface.tet); } else { neigh = -1; } } marker = shellmark(edgeloop); if (marker == 0) { marker = 1; // Default marker of a boundary edge is 1. } if (out == (tetgenio*)NULL) { fprintf(outfile, "%5d %4d %4d", edgenumber, pointmark(torg) - shift, pointmark(tdest) - shift); if (b->order == 2) { // -o2 fprintf(outfile, " %4d", pointmark(pp) - shift); } fprintf(outfile, " %d", marker); if (b->neighout > 1) { // -nn fprintf(outfile, " %4d", neigh); } fprintf(outfile, "\n"); } else { // Output three vertices of this face; elist[index++] = pointmark(torg) - shift; elist[index++] = pointmark(tdest) - shift; if (b->order == 2) { // -o2 out->o2edgelist[o2index++] = pointmark(pp) - shift; } out->edgemarkerlist[i++] = marker; if (b->neighout > 1) { // -nn out->edge2tetlist[index2++] = neigh; } } edgenumber++; edgeloop.sh = shellfacetraverse(subsegs); } if (out == (tetgenio*)NULL) { fprintf(outfile, "# Generated by %s\n", b->commandline); fclose(outfile); } } /////////////////////////////////////////////////////////////////////////////// // // // outneighbors() Output tet neighbors to a .neigh file or a structure. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::outneighbors(tetgenio* out) { FILE* outfile = NULL; char neighborfilename[FILENAMESIZE]; int* nlist = NULL; int index = 0; triface tetloop, tetsym; int neighbori[4]; int firstindex; int elementnumber; long ntets; if (out == (tetgenio*)NULL) { strcpy(neighborfilename, b->outfilename); strcat(neighborfilename, ".neigh"); } if (!b->quiet) { if (out == (tetgenio*)NULL) { printf("Writing %s.\n", neighborfilename); } else { printf("Writing neighbors.\n"); } } ntets = tetrahedrons->items - hullsize; if (out == (tetgenio*)NULL) { outfile = fopen(neighborfilename, "w"); if (outfile == (FILE*)NULL) { printf("File I/O Error: Cannot create file %s.\n", neighborfilename); terminatetetgen(this, 1); } // Number of tetrahedra, four faces per tetrahedron. fprintf(outfile, "%ld %d\n", ntets, 4); } else { // Allocate memory for 'neighborlist'. out->neighborlist = new int[ntets * 4]; if (out->neighborlist == (int*)NULL) { printf("Error: Out of memory.\n"); terminatetetgen(this, 1); } nlist = out->neighborlist; } // Determine the first index (0 or 1). firstindex = b->zeroindex ? 0 : in->firstnumber; tetrahedrons->traversalinit(); tetloop.tet = tetrahedrontraverse(); elementnumber = firstindex; // in->firstnumber; while (tetloop.tet != (tetrahedron*)NULL) { for (tetloop.ver = 0; tetloop.ver < 4; tetloop.ver++) { fsym(tetloop, tetsym); if (!ishulltet(tetsym)) { neighbori[tetloop.ver] = elemindex(tetsym.tet); } else { neighbori[tetloop.ver] = -1; } } if (out == (tetgenio*)NULL) { // Tetrahedra number, neighboring tetrahedron numbers. fprintf(outfile, "%4d %4d %4d %4d %4d\n", elementnumber, neighbori[0], neighbori[1], neighbori[2], neighbori[3]); } else { nlist[index++] = neighbori[0]; nlist[index++] = neighbori[1]; nlist[index++] = neighbori[2]; nlist[index++] = neighbori[3]; } tetloop.tet = tetrahedrontraverse(); elementnumber++; } if (out == (tetgenio*)NULL) { fprintf(outfile, "# Generated by %s\n", b->commandline); fclose(outfile); } } /////////////////////////////////////////////////////////////////////////////// // // // outvoronoi() Output the Voronoi diagram to .v.node, .v.edge, v.face, // // and .v.cell. // // // // The Voronoi diagram is the geometric dual of the Delaunay triangulation. // // The Voronoi vertices are the circumcenters of Delaunay tetrahedra. Each // // Voronoi edge connects two Voronoi vertices at two sides of a common Dela- // // unay face. At a face of convex hull, it becomes a ray (goto the infinity).// // A Voronoi face is the convex hull of all Voronoi vertices around a common // // Delaunay edge. It is a closed polygon for any internal Delaunay edge. At a// // ridge, it is unbounded. Each Voronoi cell is the convex hull of all Vor- // // onoi vertices around a common Delaunay vertex. It is a polytope for any // // internal Delaunay vertex. It is an unbounded polyhedron for a Delaunay // // vertex belonging to the convex hull. // // // // NOTE: This routine is only used when the input is only a set of point. // // Comment: Special thanks to Victor Liu for finding and fixing few bugs. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::outvoronoi(tetgenio* out) { FILE* outfile = NULL; char outfilename[FILENAMESIZE]; tetgenio::voroedge* vedge = NULL; tetgenio::vorofacet* vfacet = NULL; arraypool *tetlist, *ptlist; triface tetloop, worktet, spintet, firsttet; point pt[4], ploop, neipt; REAL ccent[3], infvec[3], vec1[3], vec2[3], L; long ntets, faces, edges; int *indexarray, *fidxs, *eidxs; int arraysize, *vertarray = NULL; int vpointcount, vedgecount, vfacecount, tcount; int ishullvert, ishullface; int index, shift, end1, end2; int i, j; int t1ver; // used by fsymself() // Output Voronoi vertices to .v.node file. if (out == (tetgenio*)NULL) { strcpy(outfilename, b->outfilename); strcat(outfilename, ".v.node"); } if (!b->quiet) { if (out == (tetgenio*)NULL) { printf("Writing %s.\n", outfilename); } else { printf("Writing Voronoi vertices.\n"); } } // Determine the first index (0 or 1). shift = (b->zeroindex ? 0 : in->firstnumber); // Each face and edge of the tetrahedral mesh will be indexed for indexing // the Voronoi edges and facets. Indices of faces and edges are saved in // each tetrahedron (including hull tets). // Allocate the total space once. indexarray = new int[tetrahedrons->items * 10]; // Allocate space (10 integers) into each tetrahedron. It re-uses the slot // for element markers, flags. i = 0; tetrahedrons->traversalinit(); tetloop.tet = alltetrahedrontraverse(); while (tetloop.tet != NULL) { tetloop.tet[11] = (tetrahedron) & (indexarray[i * 10]); i++; tetloop.tet = alltetrahedrontraverse(); } // The number of tetrahedra (excluding hull tets) (Voronoi vertices). ntets = tetrahedrons->items - hullsize; // The number of Delaunay faces (Voronoi edges). faces = (4l * ntets + hullsize) / 2l; // The number of Delaunay edges (Voronoi faces). long vsize = points->items - dupverts - unuverts; if (b->weighted) vsize -= nonregularcount; if (!nonconvex) { edges = vsize + faces - ntets - 1; } else { if (meshedges == 0l) { numberedges(); // Count edges. } edges = meshedges; } if (out == (tetgenio*)NULL) { outfile = fopen(outfilename, "w"); if (outfile == (FILE*)NULL) { printf("File I/O Error: Cannot create file %s.\n", outfilename); terminatetetgen(this, 3); } // Number of voronoi points, 3 dim, no attributes, no marker. fprintf(outfile, "%ld 3 0 0\n", ntets); } else { // Allocate space for 'vpointlist'. out->numberofvpoints = (int)ntets; out->vpointlist = new REAL[out->numberofvpoints * 3]; if (out->vpointlist == (REAL*)NULL) { terminatetetgen(this, 1); } } // Output Voronoi vertices (the circumcenters of tetrahedra). tetrahedrons->traversalinit(); tetloop.tet = tetrahedrontraverse(); vpointcount = 0; // The (internal) v-index always starts from 0. index = 0; while (tetloop.tet != (tetrahedron*)NULL) { for (i = 0; i < 4; i++) { pt[i] = (point)tetloop.tet[4 + i]; setpoint2tet(pt[i], encode(tetloop)); } if (b->weighted) { orthosphere(pt[0], pt[1], pt[2], pt[3], pt[0][3], pt[1][3], pt[2][3], pt[3][3], ccent, NULL); } else { circumsphere(pt[0], pt[1], pt[2], pt[3], ccent, NULL); } if (out == (tetgenio*)NULL) { fprintf(outfile, "%4d %16.8e %16.8e %16.8e\n", vpointcount + shift, ccent[0], ccent[1], ccent[2]); } else { out->vpointlist[index++] = ccent[0]; out->vpointlist[index++] = ccent[1]; out->vpointlist[index++] = ccent[2]; } setelemindex(tetloop.tet, vpointcount); vpointcount++; tetloop.tet = tetrahedrontraverse(); } if (out == (tetgenio*)NULL) { fprintf(outfile, "# Generated by %s\n", b->commandline); fclose(outfile); } // Output Voronoi edges to .v.edge file. if (out == (tetgenio*)NULL) { strcpy(outfilename, b->outfilename); strcat(outfilename, ".v.edge"); } if (!b->quiet) { if (out == (tetgenio*)NULL) { printf("Writing %s.\n", outfilename); } else { printf("Writing Voronoi edges.\n"); } } if (out == (tetgenio*)NULL) { outfile = fopen(outfilename, "w"); if (outfile == (FILE*)NULL) { printf("File I/O Error: Cannot create file %s.\n", outfilename); terminatetetgen(this, 3); } // Number of Voronoi edges, no marker. fprintf(outfile, "%ld 0\n", faces); } else { // Allocate space for 'vpointlist'. out->numberofvedges = (int)faces; out->vedgelist = new tetgenio::voroedge[out->numberofvedges]; } // Output the Voronoi edges. tetrahedrons->traversalinit(); tetloop.tet = tetrahedrontraverse(); vedgecount = 0; // D-Face (V-edge) index (from zero). index = 0; // The Delaunay-face index. while (tetloop.tet != (tetrahedron*)NULL) { // Count the number of Voronoi edges. Look at the four faces of each // tetrahedron. Count the face if the tetrahedron's index is // smaller than its neighbor's or the neighbor is outside. end1 = elemindex(tetloop.tet); for (tetloop.ver = 0; tetloop.ver < 4; tetloop.ver++) { fsym(tetloop, worktet); if (ishulltet(worktet) || (elemindex(tetloop.tet) < elemindex(worktet.tet))) { // Found a Voronoi edge. Operate on it. if (out == (tetgenio*)NULL) { fprintf(outfile, "%4d %4d", vedgecount + shift, end1 + shift); } else { vedge = &(out->vedgelist[index++]); vedge->v1 = end1 + shift; } if (!ishulltet(worktet)) { end2 = elemindex(worktet.tet); } else { end2 = -1; } // Note that end2 may be -1 (worktet.tet is outside). if (end2 == -1) { // Calculate the out normal of this hull face. pt[0] = dest(worktet); pt[1] = org(worktet); pt[2] = apex(worktet); for (j = 0; j < 3; j++) vec1[j] = pt[1][j] - pt[0][j]; for (j = 0; j < 3; j++) vec2[j] = pt[2][j] - pt[0][j]; cross(vec1, vec2, infvec); // Normalize it. L = sqrt(infvec[0] * infvec[0] + infvec[1] * infvec[1] + infvec[2] * infvec[2]); if (L > 0) for (j = 0; j < 3; j++) infvec[j] /= L; if (out == (tetgenio*)NULL) { fprintf(outfile, " -1"); fprintf(outfile, " %g %g %g\n", infvec[0], infvec[1], infvec[2]); } else { vedge->v2 = -1; vedge->vnormal[0] = infvec[0]; vedge->vnormal[1] = infvec[1]; vedge->vnormal[2] = infvec[2]; } } else { if (out == (tetgenio*)NULL) { fprintf(outfile, " %4d\n", end2 + shift); } else { vedge->v2 = end2 + shift; vedge->vnormal[0] = 0.0; vedge->vnormal[1] = 0.0; vedge->vnormal[2] = 0.0; } } // Save the V-edge index in this tet and its neighbor. fidxs = (int*)(tetloop.tet[11]); fidxs[tetloop.ver] = vedgecount; fidxs = (int*)(worktet.tet[11]); fidxs[worktet.ver & 3] = vedgecount; vedgecount++; } } // tetloop.ver tetloop.tet = tetrahedrontraverse(); } if (out == (tetgenio*)NULL) { fprintf(outfile, "# Generated by %s\n", b->commandline); fclose(outfile); } // Output Voronoi faces to .v.face file. if (out == (tetgenio*)NULL) { strcpy(outfilename, b->outfilename); strcat(outfilename, ".v.face"); } if (!b->quiet) { if (out == (tetgenio*)NULL) { printf("Writing %s.\n", outfilename); } else { printf("Writing Voronoi faces.\n"); } } if (out == (tetgenio*)NULL) { outfile = fopen(outfilename, "w"); if (outfile == (FILE*)NULL) { printf("File I/O Error: Cannot create file %s.\n", outfilename); terminatetetgen(this, 3); } // Number of Voronoi faces. fprintf(outfile, "%ld 0\n", edges); } else { out->numberofvfacets = edges; out->vfacetlist = new tetgenio::vorofacet[out->numberofvfacets]; if (out->vfacetlist == (tetgenio::vorofacet*)NULL) { terminatetetgen(this, 1); } } // Output the Voronoi facets. tetrahedrons->traversalinit(); tetloop.tet = tetrahedrontraverse(); vfacecount = 0; // D-edge (V-facet) index (from zero). while (tetloop.tet != (tetrahedron*)NULL) { // Count the number of Voronoi faces. Look at the six edges of each // tetrahedron. Count the edge only if the tetrahedron's index is // smaller than those of all other tetrahedra that share the edge. worktet.tet = tetloop.tet; for (i = 0; i < 6; i++) { worktet.ver = edge2ver[i]; // Count the number of faces at this edge. If the edge is a hull edge, // the face containing dummypoint is also counted. // ishulledge = 0; // Is it a hull edge. tcount = 0; firsttet = worktet; spintet = worktet; while (1) { tcount++; fnextself(spintet); if (spintet.tet == worktet.tet) break; if (!ishulltet(spintet)) { if (elemindex(spintet.tet) < elemindex(worktet.tet)) break; } else { // ishulledge = 1; if (apex(spintet) == dummypoint) { // We make this V-edge appear in the end of the edge list. fnext(spintet, firsttet); } } } // while (1) if (spintet.tet == worktet.tet) { // Found a Voronoi facet. Operate on it. pt[0] = org(worktet); pt[1] = dest(worktet); end1 = pointmark(pt[0]) - in->firstnumber; // V-cell index end2 = pointmark(pt[1]) - in->firstnumber; if (out == (tetgenio*)NULL) { fprintf(outfile, "%4d %4d %4d %-2d ", vfacecount + shift, end1 + shift, end2 + shift, tcount); } else { vfacet = &(out->vfacetlist[vfacecount]); vfacet->c1 = end1 + shift; vfacet->c2 = end2 + shift; vfacet->elist = new int[tcount + 1]; vfacet->elist[0] = tcount; index = 1; } // Output V-edges of this V-facet. spintet = firsttet; // worktet; while (1) { fidxs = (int*)(spintet.tet[11]); if (apex(spintet) != dummypoint) { vedgecount = fidxs[spintet.ver & 3]; ishullface = 0; } else { ishullface = 1; // It's not a real face. } if (out == (tetgenio*)NULL) { fprintf(outfile, " %d", !ishullface ? (vedgecount + shift) : -1); } else { vfacet->elist[index++] = !ishullface ? (vedgecount + shift) : -1; } // Save the V-facet index in this tet at this edge. eidxs = &(fidxs[4]); eidxs[ver2edge[spintet.ver]] = vfacecount; // Go to the next face. fnextself(spintet); if (spintet.tet == firsttet.tet) break; } // while (1) if (out == (tetgenio*)NULL) { fprintf(outfile, "\n"); } vfacecount++; } // if (spintet.tet == worktet.tet) } // if (i = 0; i < 6; i++) tetloop.tet = tetrahedrontraverse(); } if (out == (tetgenio*)NULL) { fprintf(outfile, "# Generated by %s\n", b->commandline); fclose(outfile); } // Output Voronoi cells to .v.cell file. if (out == (tetgenio*)NULL) { strcpy(outfilename, b->outfilename); strcat(outfilename, ".v.cell"); } if (!b->quiet) { if (out == (tetgenio*)NULL) { printf("Writing %s.\n", outfilename); } else { printf("Writing Voronoi cells.\n"); } } if (out == (tetgenio*)NULL) { outfile = fopen(outfilename, "w"); if (outfile == (FILE*)NULL) { printf("File I/O Error: Cannot create file %s.\n", outfilename); terminatetetgen(this, 3); } // Number of Voronoi cells. fprintf(outfile, "%ld\n", points->items - unuverts - dupverts); } else { out->numberofvcells = points->items - unuverts - dupverts; out->vcelllist = new int*[out->numberofvcells]; if (out->vcelllist == (int**)NULL) { terminatetetgen(this, 1); } } // Output Voronoi cells. tetlist = cavetetlist; ptlist = cavetetvertlist; points->traversalinit(); ploop = pointtraverse(); vpointcount = 0; while (ploop != (point)NULL) { if ((pointtype(ploop) != UNUSEDVERTEX) && (pointtype(ploop) != DUPLICATEDVERTEX) && (pointtype(ploop) != NREGULARVERTEX)) { getvertexstar(1, ploop, tetlist, ptlist, NULL); // Mark all vertices. Check if it is a hull vertex. ishullvert = 0; for (i = 0; i < ptlist->objects; i++) { neipt = *(point*)fastlookup(ptlist, i); if (neipt != dummypoint) { pinfect(neipt); } else { ishullvert = 1; } } tcount = (int)ptlist->objects; if (out == (tetgenio*)NULL) { fprintf(outfile, "%4d %-2d ", vpointcount + shift, tcount); } else { arraysize = tcount; vertarray = new int[arraysize + 1]; out->vcelllist[vpointcount] = vertarray; vertarray[0] = tcount; index = 1; } // List Voronoi facets bounding this cell. for (i = 0; i < tetlist->objects; i++) { worktet = *(triface*)fastlookup(tetlist, i); // Let 'worktet' be [a,b,c,d] where d = ploop. for (j = 0; j < 3; j++) { neipt = org(worktet); // neipt is a, or b, or c // Skip the dummypoint. if (neipt != dummypoint) { if (pinfected(neipt)) { // It's not processed yet. puninfect(neipt); // Go to the DT edge [a,d], or [b,d], or [c,d]. esym(worktet, spintet); enextself(spintet); // Get the V-face dual to this edge. eidxs = (int*)spintet.tet[11]; vfacecount = eidxs[4 + ver2edge[spintet.ver]]; if (out == (tetgenio*)NULL) { fprintf(outfile, " %d", vfacecount + shift); } else { vertarray[index++] = vfacecount + shift; } } } enextself(worktet); } // j } // i if (ishullvert) { // Add a hull facet (-1) to the facet list. if (out == (tetgenio*)NULL) { fprintf(outfile, " -1"); } else { vertarray[index++] = -1; } } if (out == (tetgenio*)NULL) { fprintf(outfile, "\n"); } tetlist->restart(); ptlist->restart(); vpointcount++; } ploop = pointtraverse(); } // Delete the space for face/edge indices. delete[] indexarray; if (out == (tetgenio*)NULL) { fprintf(outfile, "# Generated by %s\n", b->commandline); fclose(outfile); } } /////////////////////////////////////////////////////////////////////////////// // // // outsmesh() Write surface mesh to a .smesh file, which can be read and // // tetrahedralized by TetGen. // // // // You can specify a filename (without suffix) in 'smfilename'. If you don't // // supply a filename (let smfilename be NULL), the default name stored in // // 'tetgenbehavior' will be used. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::outsmesh(char* smfilename) { FILE* outfile; char nodfilename[FILENAMESIZE]; char smefilename[FILENAMESIZE]; face faceloop; point p1, p2, p3; int firstindex, shift; int bmark; int marker; int i; if (smfilename != (char*)NULL && smfilename[0] != '\0') { strcpy(smefilename, smfilename); } else if (b->outfilename[0] != '\0') { strcpy(smefilename, b->outfilename); } else { strcpy(smefilename, "unnamed"); } strcpy(nodfilename, smefilename); strcat(smefilename, ".smesh"); strcat(nodfilename, ".node"); if (!b->quiet) { printf("Writing %s.\n", smefilename); } outfile = fopen(smefilename, "w"); if (outfile == (FILE*)NULL) { printf("File I/O Error: Cannot create file %s.\n", smefilename); return; } // Determine the first index (0 or 1). firstindex = b->zeroindex ? 0 : in->firstnumber; shift = 0; // Default no shiftment. if ((in->firstnumber == 1) && (firstindex == 0)) { shift = 1; // Shift the output indices by 1. } fprintf(outfile, "# %s. TetGen's input file.\n", smefilename); fprintf(outfile, "\n# part 1: node list.\n"); fprintf(outfile, "0 3 0 0 # nodes are found in %s.\n", nodfilename); marker = 0; // avoid compile warning. bmark = !b->nobound && (in->facetmarkerlist || in->trifacemarkerlist); fprintf(outfile, "\n# part 2: facet list.\n"); // Number of facets, boundary marker. fprintf(outfile, "%ld %d\n", subfaces->items, bmark); subfaces->traversalinit(); faceloop.sh = shellfacetraverse(subfaces); while (faceloop.sh != (shellface*)NULL) { p1 = sorg(faceloop); p2 = sdest(faceloop); p3 = sapex(faceloop); if (bmark) { marker = shellmark(faceloop); } fprintf(outfile, "3 %4d %4d %4d", pointmark(p1) - shift, pointmark(p2) - shift, pointmark(p3) - shift); if (bmark) { fprintf(outfile, " %d", marker); } fprintf(outfile, "\n"); faceloop.sh = shellfacetraverse(subfaces); } // Copy input holelist. fprintf(outfile, "\n# part 3: hole list.\n"); fprintf(outfile, "%d\n", in->numberofholes); for (i = 0; i < in->numberofholes; i++) { fprintf(outfile, "%d %g %g %g\n", i + in->firstnumber, in->holelist[i * 3], in->holelist[i * 3 + 1], in->holelist[i * 3 + 2]); } // Copy input regionlist. fprintf(outfile, "\n# part 4: region list.\n"); fprintf(outfile, "%d\n", in->numberofregions); for (i = 0; i < in->numberofregions; i++) { fprintf(outfile, "%d %g %g %g %d %g\n", i + in->firstnumber, in->regionlist[i * 5], in->regionlist[i * 5 + 1], in->regionlist[i * 5 + 2], (int)in->regionlist[i * 5 + 3], in->regionlist[i * 5 + 4]); } fprintf(outfile, "# Generated by %s\n", b->commandline); fclose(outfile); } /////////////////////////////////////////////////////////////////////////////// // // // outmesh2medit() Write mesh to a .mesh file, which can be read and // // rendered by Medit (a free mesh viewer from INRIA). // // // // You can specify a filename (without suffix) in 'mfilename'. If you don't // // supply a filename (let mfilename be NULL), the default name stored in // // 'tetgenbehavior' will be used. The output file will have the suffix .mesh.// // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::outmesh2medit(char* mfilename) { FILE* outfile; char mefilename[FILENAMESIZE]; tetrahedron* tetptr; triface tface, tsymface; face segloop, checkmark; point ptloop, p1, p2, p3, p4; long ntets, faces; int pointnumber; int marker; int i; if (mfilename != (char*)NULL && mfilename[0] != '\0') { strcpy(mefilename, mfilename); } else if (b->outfilename[0] != '\0') { strcpy(mefilename, b->outfilename); } else { strcpy(mefilename, "unnamed"); } strcat(mefilename, ".mesh"); if (!b->quiet) { printf("Writing %s.\n", mefilename); } outfile = fopen(mefilename, "w"); if (outfile == (FILE*)NULL) { printf("File I/O Error: Cannot create file %s.\n", mefilename); return; } fprintf(outfile, "MeshVersionFormatted 1\n"); fprintf(outfile, "\n"); fprintf(outfile, "Dimension\n"); fprintf(outfile, "3\n"); fprintf(outfile, "\n"); fprintf(outfile, "\n# Set of mesh vertices\n"); fprintf(outfile, "Vertices\n"); fprintf(outfile, "%ld\n", points->items); points->traversalinit(); ptloop = pointtraverse(); pointnumber = 1; // Medit need start number form 1. while (ptloop != (point)NULL) { // Point coordinates. fprintf(outfile, "%.17g %.17g %.17g", ptloop[0], ptloop[1], ptloop[2]); if (in->numberofpointattributes > 0) { // Write an attribute, ignore others if more than one. fprintf(outfile, " %.17g\n", ptloop[3]); } else { fprintf(outfile, " 0\n"); } setpointmark(ptloop, pointnumber); ptloop = pointtraverse(); pointnumber++; } // Compute the number of faces. ntets = tetrahedrons->items - hullsize; faces = (ntets * 4l + hullsize) / 2l; fprintf(outfile, "\n# Set of Triangles\n"); fprintf(outfile, "Triangles\n"); fprintf(outfile, "%ld\n", faces); tetrahedrons->traversalinit(); tface.tet = tetrahedrontraverse(); while (tface.tet != (tetrahedron*)NULL) { for (tface.ver = 0; tface.ver < 4; tface.ver++) { fsym(tface, tsymface); if (ishulltet(tsymface) || (elemindex(tface.tet) < elemindex(tsymface.tet))) { p1 = org(tface); p2 = dest(tface); p3 = apex(tface); fprintf(outfile, "%5d %5d %5d", pointmark(p1), pointmark(p2), pointmark(p3)); // Check if it is a subface. tspivot(tface, checkmark); if (checkmark.sh == NULL) { marker = 0; // It is an inner face. It's marker is 0. } else { marker = shellmark(checkmark); } fprintf(outfile, " %d\n", marker); } } tface.tet = tetrahedrontraverse(); } fprintf(outfile, "\n# Set of Tetrahedra\n"); fprintf(outfile, "Tetrahedra\n"); fprintf(outfile, "%ld\n", ntets); tetrahedrons->traversalinit(); tetptr = tetrahedrontraverse(); while (tetptr != (tetrahedron*)NULL) { if (!b->reversetetori) { p1 = (point)tetptr[4]; p2 = (point)tetptr[5]; } else { p1 = (point)tetptr[5]; p2 = (point)tetptr[4]; } p3 = (point)tetptr[6]; p4 = (point)tetptr[7]; fprintf(outfile, "%5d %5d %5d %5d", pointmark(p1), pointmark(p2), pointmark(p3), pointmark(p4)); if (numelemattrib > 0) { fprintf(outfile, " %.17g", elemattribute(tetptr, 0)); } else { fprintf(outfile, " 0"); } fprintf(outfile, "\n"); tetptr = tetrahedrontraverse(); } fprintf(outfile, "\nCorners\n"); fprintf(outfile, "%d\n", in->numberofpoints); for (i = 0; i < in->numberofpoints; i++) { fprintf(outfile, "%4d\n", i + 1); } if (b->plc || b->refine) { fprintf(outfile, "\nEdges\n"); fprintf(outfile, "%ld\n", subsegs->items); subsegs->traversalinit(); segloop.sh = shellfacetraverse(subsegs); while (segloop.sh != (shellface*)NULL) { p1 = sorg(segloop); p2 = sdest(segloop); fprintf(outfile, "%5d %5d", pointmark(p1), pointmark(p2)); marker = shellmark(segloop); fprintf(outfile, " %d\n", marker); segloop.sh = shellfacetraverse(subsegs); } } fprintf(outfile, "\nEnd\n"); fclose(outfile); } /////////////////////////////////////////////////////////////////////////////// // // // outmesh2vtk() Save mesh to file in VTK Legacy format. // // // // This function was contributed by Bryn Llyod from ETH, 2007. // // // /////////////////////////////////////////////////////////////////////////////// void tetgenmesh::outmesh2vtk(char* ofilename) { FILE* outfile; char vtkfilename[FILENAMESIZE]; point pointloop, p1, p2, p3, p4; tetrahedron* tptr; double x, y, z; int n1, n2, n3, n4; int nnodes = 4; int celltype = 10; if (b->order == 2) { printf(" Write VTK not implemented for order 2 elements \n"); return; } int NEL = tetrahedrons->items - hullsize; int NN = points->items; if (ofilename != (char*)NULL && ofilename[0] != '\0') { strcpy(vtkfilename, ofilename); } else if (b->outfilename[0] != '\0') { strcpy(vtkfilename, b->outfilename); } else { strcpy(vtkfilename, "unnamed"); } strcat(vtkfilename, ".vtk"); if (!b->quiet) { printf("Writing %s.\n", vtkfilename); } outfile = fopen(vtkfilename, "w"); if (outfile == (FILE*)NULL) { printf("File I/O Error: Cannot create file %s.\n", vtkfilename); return; } // always write big endian // bool ImALittleEndian = !testIsBigEndian(); fprintf(outfile, "# vtk DataFile Version 2.0\n"); fprintf(outfile, "Unstructured Grid\n"); fprintf(outfile, "ASCII\n"); // BINARY fprintf(outfile, "DATASET UNSTRUCTURED_GRID\n"); fprintf(outfile, "POINTS %d double\n", NN); points->traversalinit(); pointloop = pointtraverse(); for (int id = 0; id < NN && pointloop != (point)NULL; id++) { x = pointloop[0]; y = pointloop[1]; z = pointloop[2]; fprintf(outfile, "%.17g %.17g %.17g\n", x, y, z); pointloop = pointtraverse(); } fprintf(outfile, "\n"); fprintf(outfile, "CELLS %d %d\n", NEL, NEL * (4 + 1)); // NEL rows, each has 1 type id + 4 node id's tetrahedrons->traversalinit(); tptr = tetrahedrontraverse(); // elementnumber = firstindex; // in->firstnumber; while (tptr != (tetrahedron*)NULL) { if (!b->reversetetori) { p1 = (point)tptr[4]; p2 = (point)tptr[5]; } else { p1 = (point)tptr[5]; p2 = (point)tptr[4]; } p3 = (point)tptr[6]; p4 = (point)tptr[7]; n1 = pointmark(p1) - in->firstnumber; n2 = pointmark(p2) - in->firstnumber; n3 = pointmark(p3) - in->firstnumber; n4 = pointmark(p4) - in->firstnumber; fprintf(outfile, "%d %4d %4d %4d %4d\n", nnodes, n1, n2, n3, n4); tptr = tetrahedrontraverse(); } fprintf(outfile, "\n"); fprintf(outfile, "CELL_TYPES %d\n", NEL); for (int tid = 0; tid < NEL; tid++) { fprintf(outfile, "%d\n", celltype); } fprintf(outfile, "\n"); if (numelemattrib > 0) { // Output tetrahedra region attributes. fprintf(outfile, "CELL_DATA %d\n", NEL); fprintf(outfile, "SCALARS cell_scalars int 1\n"); fprintf(outfile, "LOOKUP_TABLE default\n"); tetrahedrons->traversalinit(); tptr = tetrahedrontraverse(); while (tptr != (tetrahedron*)NULL) { fprintf(outfile, "%d\n", (int)elemattribute(tptr, numelemattrib - 1)); tptr = tetrahedrontraverse(); } fprintf(outfile, "\n"); } fclose(outfile); } //// //// //// //// //// output_cxx /////////////////////////////////////////////////////////////// //// main_cxx ///////////////////////////////////////////////////////////////// //// //// //// //// /////////////////////////////////////////////////////////////////////////////// // // // tetrahedralize() The interface for users using TetGen library to // // generate tetrahedral meshes with all features. // // // // The sequence is roughly as follows. Many of these steps can be skipped, // // depending on the command line switches. // // // // - Initialize constants and parse the command line. // // - Read the vertices from a file and either // // - tetrahedralize them (no -r), or // // - read an old mesh from files and reconstruct it (-r). // // - Insert the boundary segments and facets (-p or -Y). // // - Read the holes (-p), regional attributes (-pA), and regional volume // // constraints (-pa). Carve the holes and concavities, and spread the // // regional attributes and volume constraints. // // - Enforce the constraints on minimum quality bound (-q) and maximum // // volume (-a), and a mesh size function (-m). // // - Optimize the mesh wrt. specified quality measures (-O and -o). // // - Write the output files and print the statistics. // // - Check the consistency of the mesh (-C). // // // /////////////////////////////////////////////////////////////////////////////// void tetrahedralize(tetgenbehavior* b, tetgenio* in, tetgenio* out, tetgenio* addin, tetgenio* bgmin) { tetgenmesh m; clock_t tv[12], ts[5]; // Timing informations (defined in time.h) REAL cps = (REAL)CLOCKS_PER_SEC; tv[0] = clock(); m.b = b; m.in = in; m.addin = addin; if (b->metric && bgmin && (bgmin->numberofpoints > 0)) { m.bgm = new tetgenmesh(); // Create an empty background mesh. m.bgm->b = b; m.bgm->in = bgmin; } m.initializepools(); m.transfernodes(); exactinit(b->verbose, b->noexact, b->nostaticfilter, m.xmax - m.xmin, m.ymax - m.ymin, m.zmax - m.zmin); tv[1] = clock(); if (b->refine) { // -r m.reconstructmesh(); } else { // -p m.incrementaldelaunay(ts[0]); } tv[2] = clock(); if (!b->quiet) { if (b->refine) { printf("Mesh reconstruction seconds: %g\n", ((REAL)(tv[2] - tv[1])) / cps); } else { printf("Delaunay seconds: %g\n", ((REAL)(tv[2] - tv[1])) / cps); if (b->verbose) { printf(" Point sorting seconds: %g\n", ((REAL)(ts[0] - tv[1])) / cps); } } } if (b->plc && !b->refine) { // -p m.meshsurface(); ts[0] = clock(); if (!b->quiet) { printf("Surface mesh seconds: %g\n", ((REAL)(ts[0] - tv[2])) / cps); } if (b->diagnose) { // -d m.detectinterfaces(); ts[1] = clock(); if (!b->quiet) { printf("Self-intersection seconds: %g\n", ((REAL)(ts[1] - ts[0])) / cps); } // Only output when self-intersecting faces exist. if (m.subfaces->items > 0l) { m.outnodes(out); m.outsubfaces(out); } return; } } tv[3] = clock(); if ((b->metric) && (m.bgm != NULL)) { // -m m.bgm->initializepools(); m.bgm->transfernodes(); m.bgm->reconstructmesh(); ts[0] = clock(); if (!b->quiet) { printf("Background mesh reconstruct seconds: %g\n", ((REAL)(ts[0] - tv[3])) / cps); } if (b->metric) { // -m m.interpolatemeshsize(); ts[1] = clock(); if (!b->quiet) { printf("Size interpolating seconds: %g\n", ((REAL)(ts[1] - ts[0])) / cps); } } } tv[4] = clock(); if (b->plc && !b->refine) { // -p if (b->nobisect) { // -Y m.recoverboundary(ts[0]); } else { m.constraineddelaunay(ts[0]); } ts[1] = clock(); if (!b->quiet) { if (b->nobisect) { printf("Boundary recovery "); } else { printf("Constrained Delaunay "); } printf("seconds: %g\n", ((REAL)(ts[1] - tv[4])) / cps); if (b->verbose) { printf(" Segment recovery seconds: %g\n", ((REAL)(ts[0] - tv[4])) / cps); printf(" Facet recovery seconds: %g\n", ((REAL)(ts[1] - ts[0])) / cps); } } m.carveholes(); ts[2] = clock(); if (!b->quiet) { printf("Exterior tets removal seconds: %g\n", ((REAL)(ts[2] - ts[1])) / cps); } if (b->nobisect) { // -Y if (m.subvertstack->objects > 0l) { m.suppresssteinerpoints(); ts[3] = clock(); if (!b->quiet) { printf("Steiner suppression seconds: %g\n", ((REAL)(ts[3] - ts[2])) / cps); } } } } tv[5] = clock(); if (b->coarsen) { // -R m.meshcoarsening(); } tv[6] = clock(); if (!b->quiet) { if (b->coarsen) { printf("Mesh coarsening seconds: %g\n", ((REAL)(tv[6] - tv[5])) / cps); } } if ((b->plc && b->nobisect) || b->coarsen) { m.recoverdelaunay(); } tv[7] = clock(); if (!b->quiet) { if ((b->plc && b->nobisect) || b->coarsen) { printf("Delaunay recovery seconds: %g\n", ((REAL)(tv[7] - tv[6])) / cps); } } if ((b->plc || b->refine) && b->insertaddpoints) { // -i if ((addin != NULL) && (addin->numberofpoints > 0)) { m.insertconstrainedpoints(addin); } } tv[8] = clock(); if (!b->quiet) { if ((b->plc || b->refine) && b->insertaddpoints) { // -i if ((addin != NULL) && (addin->numberofpoints > 0)) { printf("Constrained points seconds: %g\n", ((REAL)(tv[8] - tv[7])) / cps); } } } if (b->quality) { m.delaunayrefinement(); } tv[9] = clock(); if (!b->quiet) { if (b->quality) { printf("Refinement seconds: %g\n", ((REAL)(tv[9] - tv[8])) / cps); } } if ((b->plc || b->refine) && (b->optlevel > 0)) { m.optimizemesh(); } tv[10] = clock(); if (!b->quiet) { if ((b->plc || b->refine) && (b->optlevel > 0)) { printf("Optimization seconds: %g\n", ((REAL)(tv[10] - tv[9])) / cps); } } if (!b->nojettison && ((m.dupverts > 0) || (m.unuverts > 0) || (b->refine && (in->numberofcorners == 10)))) { m.jettisonnodes(); } if ((b->order == 2) && !b->convex) { m.highorder(); } if (!b->quiet) { printf("\n"); } if (out != (tetgenio*)NULL) { out->firstnumber = in->firstnumber; out->mesh_dim = in->mesh_dim; } if (b->nonodewritten || b->noiterationnum) { if (!b->quiet) { printf("NOT writing a .node file.\n"); } } else { m.outnodes(out); } if (b->noelewritten) { if (!b->quiet) { printf("NOT writing an .ele file.\n"); } m.indexelements(); } else { if (m.tetrahedrons->items > 0l) { m.outelements(out); } } if (b->nofacewritten) { if (!b->quiet) { printf("NOT writing an .face file.\n"); } } else { if (b->facesout) { if (m.tetrahedrons->items > 0l) { m.outfaces(out); // Output all faces. } } else { if (b->plc || b->refine) { if (m.subfaces->items > 0l) { m.outsubfaces(out); // Output boundary faces. } } else { if (m.tetrahedrons->items > 0l) { m.outhullfaces(out); // Output convex hull faces. } } } } if (b->nofacewritten) { if (!b->quiet) { printf("NOT writing an .edge file.\n"); } } else { if (b->edgesout) { // -e m.outedges(out); // output all mesh edges. } else { if (b->plc || b->refine) { m.outsubsegments(out); // output subsegments. } } } if ((b->plc || b->refine) && b->metric) { // -m m.outmetrics(out); } if (!out && b->plc && ((b->object == tetgenbehavior::OFF) || (b->object == tetgenbehavior::PLY) || (b->object == tetgenbehavior::STL))) { m.outsmesh(b->outfilename); } if (!out && b->meditview) { m.outmesh2medit(b->outfilename); } if (!out && b->vtkview) { m.outmesh2vtk(b->outfilename); } if (b->neighout) { m.outneighbors(out); } if (b->voroout) { m.outvoronoi(out); } tv[11] = clock(); if (!b->quiet) { printf("\nOutput seconds: %g\n", ((REAL)(tv[11] - tv[10])) / cps); printf("Total running seconds: %g\n", ((REAL)(tv[11] - tv[0])) / cps); } if (b->docheck) { m.checkmesh(0); if (b->plc || b->refine) { m.checkshells(); m.checksegments(); } if (b->docheck > 1) { m.checkdelaunay(); } } if (!b->quiet) { m.statistics(); } } #ifndef TETLIBRARY /////////////////////////////////////////////////////////////////////////////// // // // main() The command line interface of TetGen. // // // /////////////////////////////////////////////////////////////////////////////// int main(int argc, char* argv[]) #else // with TETLIBRARY /////////////////////////////////////////////////////////////////////////////// // // // tetrahedralize() The library interface of TetGen. // // // /////////////////////////////////////////////////////////////////////////////// void tetrahedralize(char* switches, tetgenio* in, tetgenio* out, tetgenio* addin, tetgenio* bgmin) #endif // not TETLIBRARY { tetgenbehavior b; #ifndef TETLIBRARY tetgenio in, addin, bgmin; if (!b.parse_commandline(argc, argv)) { terminatetetgen(NULL, 10); } // Read input files. if (b.refine) { // -r if (!in.load_tetmesh(b.infilename, (int)b.object)) { terminatetetgen(NULL, 10); } } else { // -p if (!in.load_plc(b.infilename, (int)b.object)) { terminatetetgen(NULL, 10); } } if (b.insertaddpoints) { // -i // Try to read a .a.node file. addin.load_node(b.addinfilename); } if (b.metric) { // -m // Try to read a background mesh in files .b.node, .b.ele. bgmin.load_tetmesh(b.bgmeshfilename, (int)b.object); } tetrahedralize(&b, &in, NULL, &addin, &bgmin); return 0; #else // with TETLIBRARY if (!b.parse_commandline(switches)) { terminatetetgen(NULL, 10); } tetrahedralize(&b, in, out, addin, bgmin); #endif // not TETLIBRARY } //// //// //// //// //// main_cxx /////////////////////////////////////////////////////////////////