VTK  9.2.6
vtkTriangle.h
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1/*=========================================================================
2
3 Program: Visualization Toolkit
4 Module: vtkTriangle.h
5
6 Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen
7 All rights reserved.
8 See Copyright.txt or http://www.kitware.com/Copyright.htm for details.
9
10 This software is distributed WITHOUT ANY WARRANTY; without even
11 the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
12 PURPOSE. See the above copyright notice for more information.
13
14=========================================================================*/
23#ifndef vtkTriangle_h
24#define vtkTriangle_h
25
26#include "vtkCell.h"
27#include "vtkCommonDataModelModule.h" // For export macro
28
29#include "vtkMath.h" // Needed for inline methods
30
31class vtkLine;
32class vtkQuadric;
34
35class VTKCOMMONDATAMODEL_EXPORT vtkTriangle : public vtkCell
36{
37public:
38 static vtkTriangle* New();
39 vtkTypeMacro(vtkTriangle, vtkCell);
40 void PrintSelf(ostream& os, vtkIndent indent) override;
41
46 vtkCell* GetEdge(int edgeId) override;
47
49
52 int GetCellType() override { return VTK_TRIANGLE; }
53 int GetCellDimension() override { return 2; }
54 int GetNumberOfEdges() override { return 3; }
55 int GetNumberOfFaces() override { return 0; }
56 vtkCell* GetFace(int) override { return nullptr; }
57 int CellBoundary(int subId, const double pcoords[3], vtkIdList* pts) override;
58 void Contour(double value, vtkDataArray* cellScalars, vtkIncrementalPointLocator* locator,
59 vtkCellArray* verts, vtkCellArray* lines, vtkCellArray* polys, vtkPointData* inPd,
60 vtkPointData* outPd, vtkCellData* inCd, vtkIdType cellId, vtkCellData* outCd) override;
61 int EvaluatePosition(const double x[3], double closestPoint[3], int& subId, double pcoords[3],
62 double& dist2, double weights[]) override;
63 void EvaluateLocation(int& subId, const double pcoords[3], double x[3], double* weights) override;
64 int Triangulate(int index, vtkIdList* ptIds, vtkPoints* pts) override;
66 int subId, const double pcoords[3], const double* values, int dim, double* derivs) override;
67 double* GetParametricCoords() override;
69
73 double ComputeArea();
74
79 void Clip(double value, vtkDataArray* cellScalars, vtkIncrementalPointLocator* locator,
80 vtkCellArray* polys, vtkPointData* inPd, vtkPointData* outPd, vtkCellData* inCd,
81 vtkIdType cellId, vtkCellData* outCd, int insideOut) override;
82
83 static void InterpolationFunctions(const double pcoords[3], double sf[3]);
84 static void InterpolationDerivs(const double pcoords[3], double derivs[6]);
86
90 void InterpolateFunctions(const double pcoords[3], double sf[3]) override
91 {
93 }
94 void InterpolateDerivs(const double pcoords[3], double derivs[6]) override
95 {
96 vtkTriangle::InterpolationDerivs(pcoords, derivs);
97 }
99
108
115 int IntersectWithLine(const double p1[3], const double p2[3], double tol, double& t, double x[3],
116 double pcoords[3], int& subId) override;
117
121 int GetParametricCenter(double pcoords[3]) override;
122
127 double GetParametricDistance(const double pcoords[3]) override;
128
132 static void TriangleCenter(
133 const double p1[3], const double p2[3], const double p3[3], double center[3]);
134
139 static double TriangleArea(const double p1[3], const double p2[3], const double p3[3]);
140
147 static double Circumcircle(
148 const double p1[2], const double p2[2], const double p3[2], double center[2]);
149
162 static int BarycentricCoords(const double x[2], const double x1[2], const double x2[2],
163 const double x3[2], double bcoords[3]);
164
170 static int ProjectTo2D(const double x1[3], const double x2[3], const double x3[3], double v1[2],
171 double v2[2], double v3[2]);
172
177 static void ComputeNormal(vtkPoints* p, int numPts, const vtkIdType* pts, double n[3]);
178
182 static void ComputeNormal(
183 const double v1[3], const double v2[3], const double v3[3], double n[3]);
184
188 static void ComputeNormalDirection(
189 const double v1[3], const double v2[3], const double v3[3], double n[3]);
190
191 // Description:
192 // Determine whether or not triangle (p1,q1,r1) intersects triangle
193 // (p2,q2,r2). This method is adapted from Olivier Devillers, Philippe Guigue.
194 // Faster Triangle-Triangle Intersection Tests. RR-4488, IN-RIA. 2002.
195 // <inria-00072100>.
196 static int TrianglesIntersect(const double p1[3], const double q1[3], const double r1[3],
197 const double p2[3], const double q2[3], const double r2[3]);
198
199 // Description:
200 // Given a point x, determine whether it is inside (within the
201 // tolerance squared, tol2) the triangle defined by the three
202 // coordinate values p1, p2, p3. Method is via comparing dot products.
203 // (Note: in current implementation the tolerance only works in the
204 // neighborhood of the three vertices of the triangle.
205 static int PointInTriangle(const double x[3], const double x1[3], const double x2[3],
206 const double x3[3], const double tol2);
207
209
215 static void ComputeQuadric(
216 const double x1[3], const double x2[3], const double x3[3], double quadric[4][4]);
217 static void ComputeQuadric(
218 const double x1[3], const double x2[3], const double x3[3], vtkQuadric* quadric);
220
225 static bool ComputeCentroid(vtkPoints* points, const vtkIdType* pointIds, double centroid[3]);
226
227protected:
229 ~vtkTriangle() override;
230
232
233private:
234 vtkTriangle(const vtkTriangle&) = delete;
235 void operator=(const vtkTriangle&) = delete;
236};
237
238//----------------------------------------------------------------------------
239inline int vtkTriangle::GetParametricCenter(double pcoords[3])
240{
241 pcoords[0] = pcoords[1] = 1. / 3;
242 pcoords[2] = 0.0;
243 return 0;
244}
245
246//----------------------------------------------------------------------------
248 const double v1[3], const double v2[3], const double v3[3], double n[3])
249{
250 double ax, ay, az, bx, by, bz;
251
252 // order is important!!! maintain consistency with triangle vertex order
253 ax = v3[0] - v2[0];
254 ay = v3[1] - v2[1];
255 az = v3[2] - v2[2];
256 bx = v1[0] - v2[0];
257 by = v1[1] - v2[1];
258 bz = v1[2] - v2[2];
259
260 n[0] = (ay * bz - az * by);
261 n[1] = (az * bx - ax * bz);
262 n[2] = (ax * by - ay * bx);
263}
264
265//----------------------------------------------------------------------------
267 const double v1[3], const double v2[3], const double v3[3], double n[3])
268{
269 double length;
270
272
273 if ((length = sqrt((n[0] * n[0] + n[1] * n[1] + n[2] * n[2]))) != 0.0)
274 {
275 n[0] /= length;
276 n[1] /= length;
277 n[2] /= length;
278 }
279}
280
281//----------------------------------------------------------------------------
283 const double p1[3], const double p2[3], const double p3[3], double center[3])
284{
285 center[0] = (p1[0] + p2[0] + p3[0]) / 3.0;
286 center[1] = (p1[1] + p2[1] + p3[1]) / 3.0;
287 center[2] = (p1[2] + p2[2] + p3[2]) / 3.0;
288}
289
290//----------------------------------------------------------------------------
291inline double vtkTriangle::TriangleArea(const double p1[3], const double p2[3], const double p3[3])
292{
293 double n[3];
295
296 return 0.5 * vtkMath::Norm(n);
297}
298
299#endif
object to represent cell connectivity
represent and manipulate cell attribute data
Definition vtkCellData.h:36
abstract class to specify cell behavior
Definition vtkCell.h:58
virtual int GetParametricCenter(double pcoords[3])
Return center of the cell in parametric coordinates.
abstract superclass for arrays of numeric data
list of point or cell ids
Definition vtkIdList.h:31
Abstract class in support of both point location and point insertion.
a simple class to control print indentation
Definition vtkIndent.h:34
cell represents a 1D line
Definition vtkLine.h:31
static float Norm(const float *x, int n)
Compute the norm of n-vector.
represent and manipulate point attribute data
represent and manipulate 3D points
Definition vtkPoints.h:34
evaluate implicit quadric function
Definition vtkQuadric.h:31
a cell that represents a triangle
Definition vtkTriangle.h:36
static int PointInTriangle(const double x[3], const double x1[3], const double x2[3], const double x3[3], const double tol2)
static void ComputeNormalDirection(const double v1[3], const double v2[3], const double v3[3], double n[3])
Compute the (unnormalized) triangle normal direction from three points.
void EvaluateLocation(int &subId, const double pcoords[3], double x[3], double *weights) override
See the vtkCell API for descriptions of these methods.
static int TrianglesIntersect(const double p1[3], const double q1[3], const double r1[3], const double p2[3], const double q2[3], const double r2[3])
static void ComputeQuadric(const double x1[3], const double x2[3], const double x3[3], vtkQuadric *quadric)
Calculate the error quadric for this triangle.
static void ComputeNormal(vtkPoints *p, int numPts, const vtkIdType *pts, double n[3])
Compute the triangle normal from a points list, and a list of point ids that index into the points li...
static vtkTriangle * New()
int EvaluatePosition(const double x[3], double closestPoint[3], int &subId, double pcoords[3], double &dist2, double weights[]) override
See the vtkCell API for descriptions of these methods.
int GetParametricCenter(double pcoords[3]) override
Return the center of the triangle in parametric coordinates.
void Contour(double value, vtkDataArray *cellScalars, vtkIncrementalPointLocator *locator, vtkCellArray *verts, vtkCellArray *lines, vtkCellArray *polys, vtkPointData *inPd, vtkPointData *outPd, vtkCellData *inCd, vtkIdType cellId, vtkCellData *outCd) override
See the vtkCell API for descriptions of these methods.
int GetNumberOfFaces() override
See the vtkCell API for descriptions of these methods.
Definition vtkTriangle.h:55
void Clip(double value, vtkDataArray *cellScalars, vtkIncrementalPointLocator *locator, vtkCellArray *polys, vtkPointData *inPd, vtkPointData *outPd, vtkCellData *inCd, vtkIdType cellId, vtkCellData *outCd, int insideOut) override
Clip this triangle using scalar value provided.
int CellBoundary(int subId, const double pcoords[3], vtkIdList *pts) override
See the vtkCell API for descriptions of these methods.
vtkLine * Line
void InterpolateFunctions(const double pcoords[3], double sf[3]) override
Compute the interpolation functions/derivatives (aka shape functions/derivatives)
Definition vtkTriangle.h:90
static double TriangleArea(const double p1[3], const double p2[3], const double p3[3])
Compute the area of a triangle in 3D.
static int ProjectTo2D(const double x1[3], const double x2[3], const double x3[3], double v1[2], double v2[2], double v3[2])
Project triangle defined in 3D to 2D coordinates.
static bool ComputeCentroid(vtkPoints *points, const vtkIdType *pointIds, double centroid[3])
Get the centroid of the triangle.
double GetParametricDistance(const double pcoords[3]) override
Return the distance of the parametric coordinate provided to the cell.
~vtkTriangle() override
int IntersectWithLine(const double p1[3], const double p2[3], double tol, double &t, double x[3], double pcoords[3], int &subId) override
Given a line defined by two points p1 and p2, determine whether it intersects the triangle.
int Triangulate(int index, vtkIdList *ptIds, vtkPoints *pts) override
See the vtkCell API for descriptions of these methods.
void InterpolateDerivs(const double pcoords[3], double derivs[6]) override
Compute the interpolation functions/derivatives (aka shape functions/derivatives)
Definition vtkTriangle.h:94
void PrintSelf(ostream &os, vtkIndent indent) override
Methods invoked by print to print information about the object including superclasses.
double * GetParametricCoords() override
See the vtkCell API for descriptions of these methods.
static double Circumcircle(const double p1[2], const double p2[2], const double p3[2], double center[2])
Compute the circumcenter (center[3]) and radius squared (method return value) of a triangle defined b...
static void InterpolationDerivs(const double pcoords[3], double derivs[6])
static void ComputeQuadric(const double x1[3], const double x2[3], const double x3[3], double quadric[4][4])
Calculate the error quadric for this triangle.
int GetCellDimension() override
See the vtkCell API for descriptions of these methods.
Definition vtkTriangle.h:53
double ComputeArea()
A convenience function to compute the area of a vtkTriangle.
static void TriangleCenter(const double p1[3], const double p2[3], const double p3[3], double center[3])
Compute the center of the triangle.
const vtkIdType * GetEdgeArray(vtkIdType edgeId)
Return the ids of the vertices defining edge (edgeId).
static int BarycentricCoords(const double x[2], const double x1[2], const double x2[2], const double x3[2], double bcoords[3])
Given a 2D point x[2], determine the barycentric coordinates of the point.
int GetNumberOfEdges() override
See the vtkCell API for descriptions of these methods.
Definition vtkTriangle.h:54
void Derivatives(int subId, const double pcoords[3], const double *values, int dim, double *derivs) override
See the vtkCell API for descriptions of these methods.
vtkCell * GetFace(int) override
See the vtkCell API for descriptions of these methods.
Definition vtkTriangle.h:56
vtkCell * GetEdge(int edgeId) override
Get the edge specified by edgeId (range 0 to 2) and return that edge's coordinates.
static void InterpolationFunctions(const double pcoords[3], double sf[3])
int GetCellType() override
See the vtkCell API for descriptions of these methods.
Definition vtkTriangle.h:52
@ VTK_TRIANGLE
Definition vtkCellType.h:51
int vtkIdType
Definition vtkType.h:332