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230 lines
10 KiB
230 lines
10 KiB
/*=========================================================================
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Program: Visualization Toolkit
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Module: $RCSfile: vtkDelaunay3D.h,v $
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Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen
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All rights reserved.
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See Copyright.txt or http://www.kitware.com/Copyright.htm for details.
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This software is distributed WITHOUT ANY WARRANTY; without even
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the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
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PURPOSE. See the above copyright notice for more information.
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=========================================================================*/
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// .NAME vtkDelaunay3D - create 3D Delaunay triangulation of input points
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// .SECTION Description
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// vtkDelaunay3D is a filter that constructs a 3D Delaunay
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// triangulation from a list of input points. These points may be
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// represented by any dataset of type vtkPointSet and subclasses. The
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// output of the filter is an unstructured grid dataset. Usually the
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// output is a tetrahedral mesh, but if a non-zero alpha distance
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// value is specified (called the "alpha" value), then only tetrahedra,
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// triangles, edges, and vertices lying within the alpha radius are
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// output. In other words, non-zero alpha values may result in arbitrary
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// combinations of tetrahedra, triangles, lines, and vertices. (The notion
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// of alpha value is derived from Edelsbrunner's work on "alpha shapes".)
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//
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// The 3D Delaunay triangulation is defined as the triangulation that
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// satisfies the Delaunay criterion for n-dimensional simplexes (in
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// this case n=3 and the simplexes are tetrahedra). This criterion
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// states that a circumsphere of each simplex in a triangulation
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// contains only the n+1 defining points of the simplex. (See text for
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// more information.) While in two dimensions this translates into an
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// "optimal" triangulation, this is not true in 3D, since a measurement
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// for optimality in 3D is not agreed on.
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//
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// Delaunay triangulations are used to build topological structures
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// from unorganized (or unstructured) points. The input to this filter
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// is a list of points specified in 3D. (If you wish to create 2D
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// triangulations see vtkDelaunay2D.) The output is an unstructured grid.
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//
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// The Delaunay triangulation can be numerically sensitive. To prevent
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// problems, try to avoid injecting points that will result in
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// triangles with bad aspect ratios (1000:1 or greater). In practice
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// this means inserting points that are "widely dispersed", and
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// enables smooth transition of triangle sizes throughout the
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// mesh. (You may even want to add extra points to create a better
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// point distribution.) If numerical problems are present, you will
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// see a warning message to this effect at the end of the
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// triangulation process.
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// .SECTION Caveats
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// Points arranged on a regular lattice (termed degenerate cases) can be
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// triangulated in more than one way (at least according to the Delaunay
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// criterion). The choice of triangulation (as implemented by
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// this algorithm) depends on the order of the input points. The first four
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// points will form a tetrahedron; other degenerate points (relative to this
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// initial tetrahedron) will not break it.
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//
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// Points that are coincident (or nearly so) may be discarded by the
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// algorithm. This is because the Delaunay triangulation requires
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// unique input points. You can control the definition of coincidence
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// with the "Tolerance" instance variable.
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//
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// The output of the Delaunay triangulation is supposedly a convex hull. In
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// certain cases this implementation may not generate the convex hull. This
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// behavior can be controlled by the Offset instance variable. Offset is a
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// multiplier used to control the size of the initial triangulation. The
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// larger the offset value, the more likely you will generate a convex hull;
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// and the more likely you are to see numerical problems.
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//
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// The implementation of this algorithm varies from the 2D Delaunay
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// algorithm (i.e., vtkDelaunay2D) in an important way. When points are
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// injected into the triangulation, the search for the enclosing tetrahedron
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// is quite different. In the 3D case, the closest previously inserted point
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// point is found, and then the connected tetrahedra are searched to find
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// the containing one. (In 2D, a "walk" towards the enclosing triangle is
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// performed.) If the triangulation is Delaunay, then an enclosing tetrahedron
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// will be found. However, in degenerate cases an enclosing tetrahedron may
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// not be found and the point will be rejected.
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// .SECTION See Also
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// vtkDelaunay2D vtkGaussianSplatter vtkUnstructuredGrid
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#ifndef __vtkDelaunay3D_h
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#define __vtkDelaunay3D_h
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#include "vtkUnstructuredGridAlgorithm.h"
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class vtkIdList;
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class vtkPointLocator;
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class vtkPointSet;
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class vtkPoints;
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class vtkTetraArray;
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class VTK_GRAPHICS_EXPORT vtkDelaunay3D : public vtkUnstructuredGridAlgorithm
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{
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public:
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vtkTypeRevisionMacro(vtkDelaunay3D,vtkUnstructuredGridAlgorithm);
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void PrintSelf(ostream& os, vtkIndent indent);
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// Description:
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// Construct object with Alpha = 0.0; Tolerance = 0.001; Offset = 2.5;
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// BoundingTriangulation turned off.
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static vtkDelaunay3D *New();
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// Description:
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// Specify alpha (or distance) value to control output of this filter.
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// For a non-zero alpha value, only edges, faces, or tetra contained
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// within the circumsphere (of radius alpha) will be output. Otherwise,
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// only tetrahedra will be output.
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vtkSetClampMacro(Alpha,double,0.0,VTK_DOUBLE_MAX);
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vtkGetMacro(Alpha,double);
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// Description:
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// Specify a tolerance to control discarding of closely spaced points.
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// This tolerance is specified as a fraction of the diagonal length of
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// the bounding box of the points.
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vtkSetClampMacro(Tolerance,double,0.0,1.0);
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vtkGetMacro(Tolerance,double);
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// Description:
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// Specify a multiplier to control the size of the initial, bounding
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// Delaunay triangulation.
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vtkSetClampMacro(Offset,double,2.5,VTK_DOUBLE_MAX);
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vtkGetMacro(Offset,double);
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// Description:
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// Boolean controls whether bounding triangulation points (and associated
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// triangles) are included in the output. (These are introduced as an
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// initial triangulation to begin the triangulation process. This feature
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// is nice for debugging output.)
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vtkSetMacro(BoundingTriangulation,int);
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vtkGetMacro(BoundingTriangulation,int);
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vtkBooleanMacro(BoundingTriangulation,int);
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// Description:
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// Set / get a spatial locator for merging points. By default,
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// an instance of vtkPointLocator is used.
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void SetLocator(vtkPointLocator *locator);
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vtkGetObjectMacro(Locator,vtkPointLocator);
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// Description:
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// Create default locator. Used to create one when none is specified. The
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// locator is used to eliminate "coincident" points.
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void CreateDefaultLocator();
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// Description:
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// This is a helper method used with InsertPoint() to create
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// tetrahedronalizations of points. Its purpose is construct an initial
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// Delaunay triangulation into which to inject other points. You must
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// specify the center of a cubical bounding box and its length, as well
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// as the number of points to insert. The method returns a pointer to
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// an unstructured grid. Use this pointer to manipulate the mesh as
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// necessary. You must delete (with Delete()) the mesh when done.
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// Note: This initialization method places points forming bounding octahedron
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// at the end of the Mesh's point list. That is, InsertPoint() assumes that
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// you will be inserting points between (0,numPtsToInsert-1).
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vtkUnstructuredGrid *InitPointInsertion(double center[3], double length,
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vtkIdType numPts, vtkPoints* &pts);
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// Description:
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// This is a helper method used with InitPointInsertion() to create
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// tetrahedronalizations of points. Its purpose is to inject point at
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// coordinates specified into tetrahedronalization. The point id is an index
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// into the list of points in the mesh structure. (See
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// vtkDelaunay3D::InitPointInsertion() for more information.) When you have
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// completed inserting points, traverse the mesh structure to extract desired
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// tetrahedra (or tetra faces and edges).The holeTetras id list lists all the
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// tetrahedra that are deleted (invalid) in the mesh structure.
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void InsertPoint(vtkUnstructuredGrid *Mesh, vtkPoints *points,
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vtkIdType id, double x[3], vtkIdList *holeTetras);
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// Description:
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// Invoke this method after all points have been inserted. The purpose of
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// the method is to clean up internal data structures. Note that the
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// (vtkUnstructuredGrid *)Mesh returned from InitPointInsertion() is NOT
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// deleted, you still are responsible for cleaning that up.
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void EndPointInsertion();
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// Description:
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// Return the MTime also considering the locator.
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unsigned long GetMTime();
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protected:
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vtkDelaunay3D();
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~vtkDelaunay3D();
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int RequestData(vtkInformation *, vtkInformationVector **, vtkInformationVector *);
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double Alpha;
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double Tolerance;
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int BoundingTriangulation;
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double Offset;
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vtkPointLocator *Locator; //help locate points faster
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vtkTetraArray *TetraArray; //used to keep track of circumspheres/neighbors
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int FindTetra(vtkUnstructuredGrid *Mesh, double x[3], vtkIdType tetId,
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int depth);
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int InSphere(double x[3], vtkIdType tetraId);
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void InsertTetra(vtkUnstructuredGrid *Mesh, vtkPoints *pts,
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vtkIdType tetraId);
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int NumberOfDuplicatePoints; //keep track of bad data
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int NumberOfDegeneracies;
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// Keep track of number of references to points to avoid new/delete calls
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int *References;
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vtkIdType FindEnclosingFaces(double x[3], vtkUnstructuredGrid *Mesh,
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vtkIdList *tetras, vtkIdList *faces,
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vtkPointLocator *Locator);
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virtual int FillInputPortInformation(int, vtkInformation*);
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private: //members added for performance
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vtkIdList *Tetras; //used in InsertPoint
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vtkIdList *Faces; //used in InsertPoint
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vtkIdList *BoundaryPts; //used by InsertPoint
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vtkIdList *CheckedTetras; //used by InsertPoint
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vtkIdList *NeiTetras; //used by InsertPoint
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private:
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vtkDelaunay3D(const vtkDelaunay3D&); // Not implemented.
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void operator=(const vtkDelaunay3D&); // Not implemented.
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};
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#endif
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