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 =========================================================================*/
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 
34 class vtkLine;
35 class vtkQuadric;
37 
38 class VTKCOMMONDATAMODEL_EXPORT vtkTriangle : public vtkCell
39 {
40 public:
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;
68  void Derivatives(
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 
110  const vtkIdType* GetEdgeArray(vtkIdType edgeId);
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 
230 protected:
231  vtkTriangle();
232  ~vtkTriangle() override;
233 
235 
236 private:
237  vtkTriangle(const vtkTriangle&) = delete;
238  void operator=(const vtkTriangle&) = delete;
239 };
240 
241 //----------------------------------------------------------------------------
242 inline 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 //----------------------------------------------------------------------------
294 inline 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
static void InterpolationDerivs(const double pcoords[3], double derivs[6])
void PrintSelf(ostream &os, vtkIndent indent) override
Methods invoked by print to print information about the object including superclasses.
represent and manipulate point attribute data
Definition: vtkPointData.h:41
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
int GetCellType() override
See the vtkCell API for descriptions of these methods.
Definition: vtkTriangle.h:55
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...
represent and manipulate cell attribute data
Definition: vtkCellData.h:41
vtkCell * GetFace(int) override
See the vtkCell API for descriptions of these methods.
Definition: vtkTriangle.h:59
Abstract class in support of both point location and point insertion.
virtual int Triangulate(int index, vtkIdList *ptIds, vtkPoints *pts)=0
Generate simplices of proper dimension.
void InterpolateFunctions(const double pcoords[3], double sf[3]) override
Compute the interpolation functions/derivatives (aka shape functions/derivatives) ...
Definition: vtkTriangle.h:93
int vtkIdType
Definition: vtkType.h:332
int GetParametricCenter(double pcoords[3]) override
Return the center of the triangle in parametric coordinates.
Definition: vtkTriangle.h:242
int GetNumberOfFaces() override
See the vtkCell API for descriptions of these methods.
Definition: vtkTriangle.h:58
virtual int CellBoundary(int subId, const double pcoords[3], vtkIdList *pts)=0
Given parametric coordinates of a point, return the closest cell boundary, and whether the point is i...
virtual double GetParametricDistance(const double pcoords[3])
Return the distance of the parametric coordinate provided to the cell.
cell represents a 1D line
Definition: vtkLine.h:33
abstract class to specify cell behavior
Definition: vtkCell.h:60
virtual void EvaluateLocation(int &subId, const double pcoords[3], double x[3], double *weights)=0
Determine global coordinate (x[3]) from subId and parametric coordinates.
a simple class to control print indentation
Definition: vtkIndent.h:39
evaluate implicit quadric function
Definition: vtkQuadric.h:33
list of point or cell ids
Definition: vtkIdList.h:33
void InterpolateDerivs(const double pcoords[3], double derivs[6]) override
Compute the interpolation functions/derivatives (aka shape functions/derivatives) ...
Definition: vtkTriangle.h:97
abstract superclass for arrays of numeric data
Definition: vtkDataArray.h:55
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
static void InterpolationFunctions(const double pcoords[3], double sf[3])
virtual void Clip(double value, vtkDataArray *cellScalars, vtkIncrementalPointLocator *locator, vtkCellArray *connectivity, vtkPointData *inPd, vtkPointData *outPd, vtkCellData *inCd, vtkIdType cellId, vtkCellData *outCd, int insideOut)=0
Cut (or clip) the cell based on the input cellScalars and the specified value.
virtual int EvaluatePosition(const double x[3], double closestPoint[3], int &subId, double pcoords[3], double &dist2, double weights[])=0
Given a point x[3] return inside(=1), outside(=0) cell, or (-1) computational problem encountered; ev...
object to represent cell connectivity
Definition: vtkCellArray.h:186
virtual vtkCell * GetEdge(int edgeId)=0
Return the edge cell from the edgeId of the cell.
int GetNumberOfEdges() override
See the vtkCell API for descriptions of these methods.
Definition: vtkTriangle.h:57
a cell that represents a triangle
Definition: vtkTriangle.h:38
virtual void Contour(double value, vtkDataArray *cellScalars, vtkIncrementalPointLocator *locator, vtkCellArray *verts, vtkCellArray *lines, vtkCellArray *polys, vtkPointData *inPd, vtkPointData *outPd, vtkCellData *inCd, vtkIdType cellId, vtkCellData *outCd)=0
Generate contouring primitives.
vtkLine * Line
Definition: vtkTriangle.h:234
virtual void Derivatives(int subId, const double pcoords[3], const double *values, int dim, double *derivs)=0
Compute derivatives given cell subId and parametric coordinates.
static vtkObject * New()
Create an object with Debug turned off, modified time initialized to zero, and reference counting on...
static float Norm(const float *x, int n)
Compute the norm of n-vector.
virtual double * GetParametricCoords())
Return a contiguous array of parametric coordinates of the points defining this cell.
int GetCellDimension() override
See the vtkCell API for descriptions of these methods.
Definition: vtkTriangle.h:56
virtual int GetParametricCenter(double pcoords[3])
Return center of the cell in parametric coordinates.
virtual int IntersectWithLine(const double p1[3], const double p2[3], double tol, double &t, double x[3], double pcoords[3], int &subId)=0
Intersect with a ray.
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
represent and manipulate 3D points
Definition: vtkPoints.h:39