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239 lines
9.1 KiB
239 lines
9.1 KiB
/*=========================================================================
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Program: Visualization Toolkit
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Module: $RCSfile: vtkTriangle.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 vtkTriangle - a cell that represents a triangle
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// .SECTION Description
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// vtkTriangle is a concrete implementation of vtkCell to represent a triangle
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// located in 3-space.
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#ifndef __vtkTriangle_h
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#define __vtkTriangle_h
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#include "vtkCell.h"
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#include "vtkMath.h" // Needed for inline methods
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class vtkLine;
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class vtkQuadric;
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class VTK_FILTERING_EXPORT vtkTriangle : public vtkCell
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{
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public:
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static vtkTriangle *New();
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vtkTypeRevisionMacro(vtkTriangle,vtkCell);
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void PrintSelf(ostream& os, vtkIndent indent);
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// Description:
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// Get the edge specified by edgeId (range 0 to 2) and return that edge's
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// coordinates.
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vtkCell *GetEdge(int edgeId);
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// Description:
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// See the vtkCell API for descriptions of these methods.
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int GetCellType() {return VTK_TRIANGLE;};
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int GetCellDimension() {return 2;};
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int GetNumberOfEdges() {return 3;};
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int GetNumberOfFaces() {return 0;};
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vtkCell *GetFace(int) {return 0;};
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int CellBoundary(int subId, double pcoords[3], vtkIdList *pts);
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void Contour(double value, vtkDataArray *cellScalars,
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vtkPointLocator *locator, vtkCellArray *verts,
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vtkCellArray *lines, vtkCellArray *polys,
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vtkPointData *inPd, vtkPointData *outPd,
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vtkCellData *inCd, vtkIdType cellId, vtkCellData *outCd);
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int EvaluatePosition(double x[3], double* closestPoint,
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int& subId, double pcoords[3],
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double& dist2, double *weights);
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void EvaluateLocation(int& subId, double pcoords[3], double x[3],
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double *weights);
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int Triangulate(int index, vtkIdList *ptIds, vtkPoints *pts);
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void Derivatives(int subId, double pcoords[3], double *values,
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int dim, double *derivs);
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virtual double *GetParametricCoords();
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// Description:
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// Clip this triangle using scalar value provided. Like contouring, except
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// that it cuts the triangle to produce other triangles.
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void Clip(double value, vtkDataArray *cellScalars,
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vtkPointLocator *locator, vtkCellArray *polys,
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vtkPointData *inPd, vtkPointData *outPd,
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vtkCellData *inCd, vtkIdType cellId, vtkCellData *outCd,
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int insideOut);
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// Description:
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// vtkTriangle specific methods.
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static void InterpolationFunctions(double pcoords[3], double sf[3]);
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static void InterpolationDerivs(double pcoords[3], double derivs[6]);
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// Description:
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// Plane intersection plus in/out test on triangle. The in/out test is
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// performed using tol as the tolerance.
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int IntersectWithLine(double p1[3], double p2[3], double tol, double& t,
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double x[3], double pcoords[3], int& subId);
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// Description:
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// Return the center of the triangle in parametric coordinates.
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int GetParametricCenter(double pcoords[3]);
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// Description:
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// Return the distance of the parametric coordinate provided to the
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// cell. If inside the cell, a distance of zero is returned.
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double GetParametricDistance(double pcoords[3]);
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// Description:
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// Compute the center of the triangle.
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static void TriangleCenter(double p1[3], double p2[3], double p3[3],
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double center[3]);
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// Description:
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// Compute the area of a triangle in 3D.
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static double TriangleArea(double p1[3], double p2[3], double p3[3]);
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// Description:
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// Compute the circumcenter (center[3]) and radius squared (method
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// return value) of a triangle defined by the three points x1, x2,
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// and x3. (Note that the coordinates are 2D. 3D points can be used
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// but the z-component will be ignored.)
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static double Circumcircle(double p1[2], double p2[2], double p3[2],
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double center[2]);
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// Description:
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// Given a 2D point x[2], determine the barycentric coordinates of the point.
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// Barycentric coordinates are a natural coordinate system for simplices that
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// express a position as a linear combination of the vertices. For a
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// triangle, there are three barycentric coordinates (because there are
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// three vertices), and the sum of the coordinates must equal 1. If a
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// point x is inside a simplex, then all three coordinates will be strictly
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// positive. If two coordinates are zero (so the third =1), then the
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// point x is on a vertex. If one coordinates are zero, the point x is on an
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// edge. In this method, you must specify the vertex coordinates x1->x3.
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// Returns 0 if triangle is degenerate.
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static int BarycentricCoords(double x[2], double x1[2], double x2[2],
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double x3[2], double bcoords[3]);
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// Description:
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// Project triangle defined in 3D to 2D coordinates. Returns 0 if
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// degenerate triangle; non-zero value otherwise. Input points are x1->x3;
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// output 2D points are v1->v3.
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static int ProjectTo2D(double x1[3], double x2[3], double x3[3],
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double v1[2], double v2[2], double v3[2]);
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// Description:
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// Compute the triangle normal from a points list, and a list of point ids
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// that index into the points list.
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static void ComputeNormal(vtkPoints *p, int numPts, vtkIdType *pts,
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double n[3]);
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// Description:
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// Compute the triangle normal from three points.
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static void ComputeNormal(double v1[3], double v2[3], double v3[3], double n[3]);
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// Description:
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// Compute the (unnormalized) triangle normal direction from three points.
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static void ComputeNormalDirection(double v1[3], double v2[3], double v3[3],
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double n[3]);
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// Description:
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// Given a point x, determine whether it is inside (within the
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// tolerance squared, tol2) the triangle defined by the three
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// coordinate values p1, p2, p3. Method is via comparing dot products.
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// (Note: in current implementation the tolerance only works in the
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// neighborhood of the three vertices of the triangle.
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static int PointInTriangle(double x[3], double x1[3],
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double x2[3], double x3[3],
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double tol2);
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// Description:
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// Calculate the error quadric for this triangle. Return the
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// quadric as a 4x4 matrix or a vtkQuadric. (from Peter
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// Lindstrom's Siggraph 2000 paper, "Out-of-Core Simplification of
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// Large Polygonal Models")
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static void ComputeQuadric(double x1[3], double x2[3], double x3[3],
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double quadric[4][4]);
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static void ComputeQuadric(double x1[3], double x2[3], double x3[3],
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vtkQuadric *quadric);
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protected:
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vtkTriangle();
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~vtkTriangle();
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vtkLine *Line;
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private:
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vtkTriangle(const vtkTriangle&); // Not implemented.
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void operator=(const vtkTriangle&); // Not implemented.
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};
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//----------------------------------------------------------------------------
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inline int vtkTriangle::GetParametricCenter(double pcoords[3])
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{
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pcoords[0] = pcoords[1] = 1./3; pcoords[2] = 0.0;
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return 0;
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}
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//----------------------------------------------------------------------------
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inline void vtkTriangle::ComputeNormalDirection(double v1[3], double v2[3],
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double v3[3], double n[3])
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{
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double ax, ay, az, bx, by, bz;
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// order is important!!! maintain consistency with triangle vertex order
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ax = v3[0] - v2[0]; ay = v3[1] - v2[1]; az = v3[2] - v2[2];
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bx = v1[0] - v2[0]; by = v1[1] - v2[1]; bz = v1[2] - v2[2];
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n[0] = (ay * bz - az * by);
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n[1] = (az * bx - ax * bz);
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n[2] = (ax * by - ay * bx);
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}
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//----------------------------------------------------------------------------
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inline void vtkTriangle::ComputeNormal(double v1[3], double v2[3],
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double v3[3], double n[3])
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{
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double length;
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vtkTriangle::ComputeNormalDirection(v1, v2, v3, n);
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if ( (length = sqrt((n[0]*n[0] + n[1]*n[1] + n[2]*n[2]))) != 0.0 )
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{
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n[0] /= length;
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n[1] /= length;
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n[2] /= length;
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}
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}
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//----------------------------------------------------------------------------
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inline void vtkTriangle::TriangleCenter(double p1[3], double p2[3],
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double p3[3], double center[3])
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{
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center[0] = (p1[0]+p2[0]+p3[0]) / 3.0;
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center[1] = (p1[1]+p2[1]+p3[1]) / 3.0;
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center[2] = (p1[2]+p2[2]+p3[2]) / 3.0;
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}
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//----------------------------------------------------------------------------
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inline double vtkTriangle::TriangleArea(double p1[3], double p2[3], double p3[3])
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{
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double a,b,c;
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a = vtkMath::Distance2BetweenPoints(p1,p2);
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b = vtkMath::Distance2BetweenPoints(p2,p3);
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c = vtkMath::Distance2BetweenPoints(p3,p1);
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return (0.25* sqrt(fabs(4.0*a*c - (a-b+c)*(a-b+c))));
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}
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#endif
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