VTK  9.2.5
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=========================================================================*/
26#ifndef vtkTriangle_h
27#define vtkTriangle_h
28
29#include "vtkCell.h"
30#include "vtkCommonDataModelModule.h" // For export macro
31
32#include "vtkMath.h" // Needed for inline methods
33
34class vtkLine;
35class vtkQuadric;
37
38class VTKCOMMONDATAMODEL_EXPORT vtkTriangle : public vtkCell
39{
40public:
41 static vtkTriangle* New();
42 vtkTypeMacro(vtkTriangle, vtkCell);
43 void PrintSelf(ostream& os, vtkIndent indent) override;
44
49 vtkCell* GetEdge(int edgeId) override;
50
52
55 int GetCellType() override { return VTK_TRIANGLE; }
56 int GetCellDimension() override { return 2; }
57 int GetNumberOfEdges() override { return 3; }
58 int GetNumberOfFaces() override { return 0; }
59 vtkCell* GetFace(int) override { return nullptr; }
60 int CellBoundary(int subId, const double pcoords[3], vtkIdList* pts) override;
61 void Contour(double value, vtkDataArray* cellScalars, vtkIncrementalPointLocator* locator,
62 vtkCellArray* verts, vtkCellArray* lines, vtkCellArray* polys, vtkPointData* inPd,
63 vtkPointData* outPd, vtkCellData* inCd, vtkIdType cellId, vtkCellData* outCd) override;
64 int EvaluatePosition(const double x[3], double closestPoint[3], int& subId, double pcoords[3],
65 double& dist2, double weights[]) override;
66 void EvaluateLocation(int& subId, const double pcoords[3], double x[3], double* weights) override;
67 int Triangulate(int index, vtkIdList* ptIds, vtkPoints* pts) override;
69 int subId, const double pcoords[3], const double* values, int dim, double* derivs) override;
70 double* GetParametricCoords() override;
72
76 double ComputeArea();
77
82 void Clip(double value, vtkDataArray* cellScalars, vtkIncrementalPointLocator* locator,
83 vtkCellArray* polys, vtkPointData* inPd, vtkPointData* outPd, vtkCellData* inCd,
84 vtkIdType cellId, vtkCellData* outCd, int insideOut) override;
85
86 static void InterpolationFunctions(const double pcoords[3], double sf[3]);
87 static void InterpolationDerivs(const double pcoords[3], double derivs[6]);
89
93 void InterpolateFunctions(const double pcoords[3], double sf[3]) override
94 {
96 }
97 void InterpolateDerivs(const double pcoords[3], double derivs[6]) override
98 {
99 vtkTriangle::InterpolationDerivs(pcoords, derivs);
100 }
102
111
118 int IntersectWithLine(const double p1[3], const double p2[3], double tol, double& t, double x[3],
119 double pcoords[3], int& subId) override;
120
124 int GetParametricCenter(double pcoords[3]) override;
125
130 double GetParametricDistance(const double pcoords[3]) override;
131
135 static void TriangleCenter(
136 const double p1[3], const double p2[3], const double p3[3], double center[3]);
137
142 static double TriangleArea(const double p1[3], const double p2[3], const double p3[3]);
143
150 static double Circumcircle(
151 const double p1[2], const double p2[2], const double p3[2], double center[2]);
152
165 static int BarycentricCoords(const double x[2], const double x1[2], const double x2[2],
166 const double x3[2], double bcoords[3]);
167
173 static int ProjectTo2D(const double x1[3], const double x2[3], const double x3[3], double v1[2],
174 double v2[2], double v3[2]);
175
180 static void ComputeNormal(vtkPoints* p, int numPts, const vtkIdType* pts, double n[3]);
181
185 static void ComputeNormal(
186 const double v1[3], const double v2[3], const double v3[3], double n[3]);
187
191 static void ComputeNormalDirection(
192 const double v1[3], const double v2[3], const double v3[3], double n[3]);
193
194 // Description:
195 // Determine whether or not triangle (p1,q1,r1) intersects triangle
196 // (p2,q2,r2). This method is adapted from Olivier Devillers, Philippe Guigue.
197 // Faster Triangle-Triangle Intersection Tests. RR-4488, IN-RIA. 2002.
198 // <inria-00072100>.
199 static int TrianglesIntersect(const double p1[3], const double q1[3], const double r1[3],
200 const double p2[3], const double q2[3], const double r2[3]);
201
202 // Description:
203 // Given a point x, determine whether it is inside (within the
204 // tolerance squared, tol2) the triangle defined by the three
205 // coordinate values p1, p2, p3. Method is via comparing dot products.
206 // (Note: in current implementation the tolerance only works in the
207 // neighborhood of the three vertices of the triangle.
208 static int PointInTriangle(const double x[3], const double x1[3], const double x2[3],
209 const double x3[3], const double tol2);
210
212
218 static void ComputeQuadric(
219 const double x1[3], const double x2[3], const double x3[3], double quadric[4][4]);
220 static void ComputeQuadric(
221 const double x1[3], const double x2[3], const double x3[3], vtkQuadric* quadric);
223
228 static bool ComputeCentroid(vtkPoints* points, const vtkIdType* pointIds, double centroid[3]);
229
230protected:
232 ~vtkTriangle() override;
233
235
236private:
237 vtkTriangle(const vtkTriangle&) = delete;
238 void operator=(const vtkTriangle&) = delete;
239};
240
241//----------------------------------------------------------------------------
242inline int vtkTriangle::GetParametricCenter(double pcoords[3])
243{
244 pcoords[0] = pcoords[1] = 1. / 3;
245 pcoords[2] = 0.0;
246 return 0;
247}
248
249//----------------------------------------------------------------------------
251 const double v1[3], const double v2[3], const double v3[3], double n[3])
252{
253 double ax, ay, az, bx, by, bz;
254
255 // order is important!!! maintain consistency with triangle vertex order
256 ax = v3[0] - v2[0];
257 ay = v3[1] - v2[1];
258 az = v3[2] - v2[2];
259 bx = v1[0] - v2[0];
260 by = v1[1] - v2[1];
261 bz = v1[2] - v2[2];
262
263 n[0] = (ay * bz - az * by);
264 n[1] = (az * bx - ax * bz);
265 n[2] = (ax * by - ay * bx);
266}
267
268//----------------------------------------------------------------------------
270 const double v1[3], const double v2[3], const double v3[3], double n[3])
271{
272 double length;
273
275
276 if ((length = sqrt((n[0] * n[0] + n[1] * n[1] + n[2] * n[2]))) != 0.0)
277 {
278 n[0] /= length;
279 n[1] /= length;
280 n[2] /= length;
281 }
282}
283
284//----------------------------------------------------------------------------
286 const double p1[3], const double p2[3], const double p3[3], double center[3])
287{
288 center[0] = (p1[0] + p2[0] + p3[0]) / 3.0;
289 center[1] = (p1[1] + p2[1] + p3[1]) / 3.0;
290 center[2] = (p1[2] + p2[2] + p3[2]) / 3.0;
291}
292
293//----------------------------------------------------------------------------
294inline double vtkTriangle::TriangleArea(const double p1[3], const double p2[3], const double p3[3])
295{
296 double n[3];
298
299 return 0.5 * vtkMath::Norm(n);
300}
301
302#endif
object to represent cell connectivity
Definition: vtkCellArray.h:187
represent and manipulate cell attribute data
Definition: vtkCellData.h:42
abstract class to specify cell behavior
Definition: vtkCell.h:61
virtual int GetParametricCenter(double pcoords[3])
Return center of the cell in parametric coordinates.
abstract superclass for arrays of numeric data
Definition: vtkDataArray.h:56
list of point or cell ids
Definition: vtkIdList.h:34
Abstract class in support of both point location and point insertion.
a simple class to control print indentation
Definition: vtkIndent.h:40
cell represents a 1D line
Definition: vtkLine.h:34
static float Norm(const float *x, int n)
Compute the norm of n-vector.
represent and manipulate point attribute data
Definition: vtkPointData.h:42
represent and manipulate 3D points
Definition: vtkPoints.h:40
evaluate implicit quadric function
Definition: vtkQuadric.h:34
a cell that represents a triangle
Definition: vtkTriangle.h:39
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.
Definition: vtkTriangle.h:250
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.
Definition: vtkTriangle.h:242
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:58
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
Definition: vtkTriangle.h:234
void InterpolateFunctions(const double pcoords[3], double sf[3]) override
Compute the interpolation functions/derivatives (aka shape functions/derivatives)
Definition: vtkTriangle.h:93
static double TriangleArea(const double p1[3], const double p2[3], const double p3[3])
Compute the area of a triangle in 3D.
Definition: vtkTriangle.h:294
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:97
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:56
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.
Definition: vtkTriangle.h:285
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:57
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:59
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:55
@ VTK_TRIANGLE
Definition: vtkCellType.h:51
int vtkIdType
Definition: vtkType.h:332