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Program: Visualization Toolkit
Module: vtkTriangle.h
Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen
All rights reserved.
See Copyright.txt or for details.
This software is distributed WITHOUT ANY WARRANTY; without even
PURPOSE. See the above copyright notice for more information.
// .NAME vtkTriangle - a cell that represents a triangle
// .SECTION Description
// vtkTriangle is a concrete implementation of vtkCell to represent a triangle
// located in 3-space.
#ifndef __vtkTriangle_h
#define __vtkTriangle_h
#include "vtkCell.h"
#include "vtkMath.h" // Needed for inline methods
class vtkLine;
class vtkQuadric;
class vtkIncrementalPointLocator;
class VTK_FILTERING_EXPORT vtkTriangle : public vtkCell
static vtkTriangle *New();
void PrintSelf(ostream& os, vtkIndent indent);
// Description:
// Get the edge specified by edgeId (range 0 to 2) and return that edge's
// coordinates.
vtkCell *GetEdge(int edgeId);
// Description:
// See the vtkCell API for descriptions of these methods.
int GetCellType() {return VTK_TRIANGLE;};
int GetCellDimension() {return 2;};
int GetNumberOfEdges() {return 3;};
int GetNumberOfFaces() {return 0;};
vtkCell *GetFace(int) {return 0;};
int CellBoundary(int subId, double pcoords[3], vtkIdList *pts);
void Contour(double value, vtkDataArray *cellScalars,
vtkIncrementalPointLocator *locator, vtkCellArray *verts,
vtkCellArray *lines, vtkCellArray *polys,
vtkPointData *inPd, vtkPointData *outPd,
vtkCellData *inCd, vtkIdType cellId, vtkCellData *outCd);
int EvaluatePosition(double x[3], double* closestPoint,
int& subId, double pcoords[3],
double& dist2, double *weights);
void EvaluateLocation(int& subId, double pcoords[3], double x[3],
double *weights);
int Triangulate(int index, vtkIdList *ptIds, vtkPoints *pts);
void Derivatives(int subId, double pcoords[3], double *values,
int dim, double *derivs);
virtual double *GetParametricCoords();
// Description:
// A convenience function to compute the area of a vtkTriangle.
double ComputeArea();
// Description:
// Clip this triangle using scalar value provided. Like contouring, except
// that it cuts the triangle to produce other triangles.
void Clip(double value, vtkDataArray *cellScalars,
vtkIncrementalPointLocator *locator, vtkCellArray *polys,
vtkPointData *inPd, vtkPointData *outPd,
vtkCellData *inCd, vtkIdType cellId, vtkCellData *outCd,
int insideOut);
// Description:
// @deprecated Replaced by vtkTriangle::InterpolateFunctions as of VTK 5.2
static void InterpolationFunctions(double pcoords[3], double sf[3]);
// Description:
// @deprecated Replaced by vtkTriangle::InterpolateDerivs as of VTK 5.2
static void InterpolationDerivs(double pcoords[3], double derivs[6]);
// Description:
// Compute the interpolation functions/derivatives
// (aka shape functions/derivatives)
virtual void InterpolateFunctions(double pcoords[3], double sf[3])
virtual void InterpolateDerivs(double pcoords[3], double derivs[6])
// Description:
// Return the ids of the vertices defining edge (`edgeId`).
// Ids are related to the cell, not to the dataset.
int *GetEdgeArray(int edgeId);
// Description:
// Plane intersection plus in/out test on triangle. The in/out test is
// performed using tol as the tolerance.
int IntersectWithLine(double p1[3], double p2[3], double tol, double& t,
double x[3], double pcoords[3], int& subId);
// Description:
// Return the center of the triangle in parametric coordinates.
int GetParametricCenter(double pcoords[3]);
// Description:
// Return the distance of the parametric coordinate provided to the
// cell. If inside the cell, a distance of zero is returned.
double GetParametricDistance(double pcoords[3]);
// Description:
// Compute the center of the triangle.
static void TriangleCenter(double p1[3], double p2[3], double p3[3],
double center[3]);
// Description:
// Compute the area of a triangle in 3D.
// See also vtkTriangle::ComputeArea()
static double TriangleArea(double p1[3], double p2[3], double p3[3]);
// Description:
// Compute the circumcenter (center[3]) and radius squared (method
// return value) of a triangle defined by the three points x1, x2,
// and x3. (Note that the coordinates are 2D. 3D points can be used
// but the z-component will be ignored.)
static double Circumcircle(double p1[2], double p2[2], double p3[2],
double center[2]);
// Description:
// Given a 2D point x[2], determine the barycentric coordinates of the point.
// Barycentric coordinates are a natural coordinate system for simplices that
// express a position as a linear combination of the vertices. For a
// triangle, there are three barycentric coordinates (because there are
// three vertices), and the sum of the coordinates must equal 1. If a
// point x is inside a simplex, then all three coordinates will be strictly
// positive. If two coordinates are zero (so the third =1), then the
// point x is on a vertex. If one coordinates are zero, the point x is on an
// edge. In this method, you must specify the vertex coordinates x1->x3.
// Returns 0 if triangle is degenerate.
static int BarycentricCoords(double x[2], double x1[2], double x2[2],
double x3[2], double bcoords[3]);
// Description:
// Project triangle defined in 3D to 2D coordinates. Returns 0 if
// degenerate triangle; non-zero value otherwise. Input points are x1->x3;
// output 2D points are v1->v3.
static int ProjectTo2D(double x1[3], double x2[3], double x3[3],
double v1[2], double v2[2], double v3[2]);
// Description:
// Compute the triangle normal from a points list, and a list of point ids
// that index into the points list.
static void ComputeNormal(vtkPoints *p, int numPts, vtkIdType *pts,
double n[3]);
// Description:
// Compute the triangle normal from three points.
static void ComputeNormal(double v1[3], double v2[3], double v3[3], double n[3]);
// Description:
// Compute the (unnormalized) triangle normal direction from three points.
static void ComputeNormalDirection(double v1[3], double v2[3], double v3[3],
double n[3]);
// Description:
// Given a point x, determine whether it is inside (within the
// tolerance squared, tol2) the triangle defined by the three
// coordinate values p1, p2, p3. Method is via comparing dot products.
// (Note: in current implementation the tolerance only works in the
// neighborhood of the three vertices of the triangle.
static int PointInTriangle(double x[3], double x1[3],
double x2[3], double x3[3],
double tol2);
// Description:
// Calculate the error quadric for this triangle. Return the
// quadric as a 4x4 matrix or a vtkQuadric. (from Peter
// Lindstrom's Siggraph 2000 paper, "Out-of-Core Simplification of
// Large Polygonal Models")
static void ComputeQuadric(double x1[3], double x2[3], double x3[3],
double quadric[4][4]);
static void ComputeQuadric(double x1[3], double x2[3], double x3[3],
vtkQuadric *quadric);
vtkLine *Line;
vtkTriangle(const vtkTriangle&); // Not implemented.
void operator=(const vtkTriangle&); // Not implemented.
inline int vtkTriangle::GetParametricCenter(double pcoords[3])
pcoords[0] = pcoords[1] = 1./3; pcoords[2] = 0.0;
return 0;
inline void vtkTriangle::ComputeNormalDirection(double v1[3], double v2[3],
double v3[3], double n[3])
double ax, ay, az, bx, by, bz;
// order is important!!! maintain consistency with triangle vertex order
ax = v3[0] - v2[0]; ay = v3[1] - v2[1]; az = v3[2] - v2[2];
bx = v1[0] - v2[0]; by = v1[1] - v2[1]; bz = v1[2] - v2[2];
n[0] = (ay * bz - az * by);
n[1] = (az * bx - ax * bz);
n[2] = (ax * by - ay * bx);
inline void vtkTriangle::ComputeNormal(double v1[3], double v2[3],
double v3[3], double n[3])
double length;
vtkTriangle::ComputeNormalDirection(v1, v2, v3, n);
if ( (length = sqrt((n[0]*n[0] + n[1]*n[1] + n[2]*n[2]))) != 0.0 )
n[0] /= length;
n[1] /= length;
n[2] /= length;
inline void vtkTriangle::TriangleCenter(double p1[3], double p2[3],
double p3[3], double center[3])
center[0] = (p1[0]+p2[0]+p3[0]) / 3.0;
center[1] = (p1[1]+p2[1]+p3[1]) / 3.0;
center[2] = (p1[2]+p2[2]+p3[2]) / 3.0;
inline double vtkTriangle::TriangleArea(double p1[3], double p2[3], double p3[3])
double a,b,c;
a = vtkMath::Distance2BetweenPoints(p1,p2);
b = vtkMath::Distance2BetweenPoints(p2,p3);
c = vtkMath::Distance2BetweenPoints(p3,p1);
return (0.25* sqrt(fabs(4.0*a*c - (a-b+c)*(a-b+c))));