VTK  9.3.0
vtkTriangle.h
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1// SPDX-FileCopyrightText: Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen
2// SPDX-License-Identifier: BSD-3-Clause
14#ifndef vtkTriangle_h
15#define vtkTriangle_h
16
17#include "vtkCell.h"
18#include "vtkCommonDataModelModule.h" // For export macro
19
20#include "vtkMath.h" // Needed for inline methods
21
22VTK_ABI_NAMESPACE_BEGIN
23class vtkLine;
24class vtkQuadric;
26
27class VTKCOMMONDATAMODEL_EXPORT vtkTriangle : public vtkCell
28{
29public:
30 static vtkTriangle* New();
31 vtkTypeMacro(vtkTriangle, vtkCell);
32 void PrintSelf(ostream& os, vtkIndent indent) override;
33
38 vtkCell* GetEdge(int edgeId) override;
39
41
44 int GetCellType() override { return VTK_TRIANGLE; }
45 int GetCellDimension() override { return 2; }
46 int GetNumberOfEdges() override { return 3; }
47 int GetNumberOfFaces() override { return 0; }
48 vtkCell* GetFace(int) override { return nullptr; }
49 int CellBoundary(int subId, const double pcoords[3], vtkIdList* pts) override;
50 void Contour(double value, vtkDataArray* cellScalars, vtkIncrementalPointLocator* locator,
51 vtkCellArray* verts, vtkCellArray* lines, vtkCellArray* polys, vtkPointData* inPd,
52 vtkPointData* outPd, vtkCellData* inCd, vtkIdType cellId, vtkCellData* outCd) override;
53 int EvaluatePosition(const double x[3], double closestPoint[3], int& subId, double pcoords[3],
54 double& dist2, double weights[]) override;
55 void EvaluateLocation(int& subId, const double pcoords[3], double x[3], double* weights) override;
56 int Triangulate(int index, vtkIdList* ptIds, vtkPoints* pts) override;
58 int subId, const double pcoords[3], const double* values, int dim, double* derivs) override;
59 double* GetParametricCoords() override;
61
65 double ComputeArea();
66
71 void Clip(double value, vtkDataArray* cellScalars, vtkIncrementalPointLocator* locator,
72 vtkCellArray* polys, vtkPointData* inPd, vtkPointData* outPd, vtkCellData* inCd,
73 vtkIdType cellId, vtkCellData* outCd, int insideOut) override;
74
75 static void InterpolationFunctions(const double pcoords[3], double sf[3]);
76 static void InterpolationDerivs(const double pcoords[3], double derivs[6]);
78
82 void InterpolateFunctions(const double pcoords[3], double sf[3]) override
83 {
85 }
86 void InterpolateDerivs(const double pcoords[3], double derivs[6]) override
87 {
88 vtkTriangle::InterpolationDerivs(pcoords, derivs);
89 }
91
100
107 int IntersectWithLine(const double p1[3], const double p2[3], double tol, double& t, double x[3],
108 double pcoords[3], int& subId) override;
109
113 int GetParametricCenter(double pcoords[3]) override;
114
119 double GetParametricDistance(const double pcoords[3]) override;
120
124 static void TriangleCenter(
125 const double p1[3], const double p2[3], const double p3[3], double center[3]);
126
131 static double TriangleArea(const double p1[3], const double p2[3], const double p3[3]);
132
139 static double Circumcircle(
140 const double p1[2], const double p2[2], const double p3[2], double center[2]);
141
154 static int BarycentricCoords(const double x[2], const double x1[2], const double x2[2],
155 const double x3[2], double bcoords[3]);
156
162 static int ProjectTo2D(const double x1[3], const double x2[3], const double x3[3], double v1[2],
163 double v2[2], double v3[2]);
164
169 static void ComputeNormal(vtkPoints* p, int numPts, const vtkIdType* pts, double n[3]);
170
174 static void ComputeNormal(
175 const double v1[3], const double v2[3], const double v3[3], double n[3]);
176
180 static void ComputeNormalDirection(
181 const double v1[3], const double v2[3], const double v3[3], double n[3]);
182
183 // Description:
184 // Determine whether or not triangle (p1,q1,r1) intersects triangle
185 // (p2,q2,r2). This method is adapted from Olivier Devillers, Philippe Guigue.
186 // Faster Triangle-Triangle Intersection Tests. RR-4488, IN-RIA. 2002.
187 // <inria-00072100>.
188 static int TrianglesIntersect(const double p1[3], const double q1[3], const double r1[3],
189 const double p2[3], const double q2[3], const double r2[3]);
190
191 // Description:
192 // Given a point x, determine whether it is inside (within the
193 // tolerance squared, tol2) the triangle defined by the three
194 // coordinate values p1, p2, p3. Method is via comparing dot products.
195 // (Note: in current implementation the tolerance only works in the
196 // neighborhood of the three vertices of the triangle.
197 static int PointInTriangle(
198 const double x[3], const double x1[3], const double x2[3], const double x3[3], double tol2);
199
201
207 static void ComputeQuadric(
208 const double x1[3], const double x2[3], const double x3[3], double quadric[4][4]);
209 static void ComputeQuadric(
210 const double x1[3], const double x2[3], const double x3[3], vtkQuadric* quadric);
212
217 static bool ComputeCentroid(vtkPoints* points, const vtkIdType* pointIds, double centroid[3]);
218
219protected:
221 ~vtkTriangle() override;
222
224
225private:
226 vtkTriangle(const vtkTriangle&) = delete;
227 void operator=(const vtkTriangle&) = delete;
228};
229
230//----------------------------------------------------------------------------
231inline int vtkTriangle::GetParametricCenter(double pcoords[3])
232{
233 pcoords[0] = pcoords[1] = 1.0 / 3.0;
234 pcoords[2] = 0.0;
235 return 0;
236}
237
238//----------------------------------------------------------------------------
240 const double v1[3], const double v2[3], const double v3[3], double n[3])
241{
242 // order is important!!! maintain consistency with triangle vertex order
243 double ax = v3[0] - v2[0];
244 double ay = v3[1] - v2[1];
245 double az = v3[2] - v2[2];
246 double bx = v1[0] - v2[0];
247 double by = v1[1] - v2[1];
248 double bz = v1[2] - v2[2];
249
250 n[0] = (ay * bz - az * by);
251 n[1] = (az * bx - ax * bz);
252 n[2] = (ax * by - ay * bx);
253}
254
255//----------------------------------------------------------------------------
257 const double v1[3], const double v2[3], const double v3[3], double n[3])
258{
260
261 double length = sqrt(n[0] * n[0] + n[1] * n[1] + n[2] * n[2]);
262 if (length != 0.0)
263 {
264 n[0] /= length;
265 n[1] /= length;
266 n[2] /= length;
267 }
268}
269
270//----------------------------------------------------------------------------
272 const double p1[3], const double p2[3], const double p3[3], double center[3])
273{
274 center[0] = (p1[0] + p2[0] + p3[0]) / 3.0;
275 center[1] = (p1[1] + p2[1] + p3[1]) / 3.0;
276 center[2] = (p1[2] + p2[2] + p3[2]) / 3.0;
277}
278
279//----------------------------------------------------------------------------
280inline double vtkTriangle::TriangleArea(const double p1[3], const double p2[3], const double p3[3])
281{
282 double n[3];
284
285 return 0.5 * vtkMath::Norm(n);
286}
287
288VTK_ABI_NAMESPACE_END
289#endif
object to represent cell connectivity
represent and manipulate cell attribute data
Definition vtkCellData.h:31
abstract class to specify cell behavior
Definition vtkCell.h:50
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:23
Abstract class in support of both point location and point insertion.
a simple class to control print indentation
Definition vtkIndent.h:29
cell represents a 1D line
Definition vtkLine.h:23
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:29
evaluate implicit quadric function
Definition vtkQuadric.h:23
a cell that represents a triangle
Definition vtkTriangle.h:28
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.
static int PointInTriangle(const double x[3], const double x1[3], const double x2[3], const double x3[3], double tol2)
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:47
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:82
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:86
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:45
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:46
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:48
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:44
@ VTK_TRIANGLE
Definition vtkCellType.h:42
int vtkIdType
Definition vtkType.h:315