VTK  9.1.0
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 
31 class vtkLine;
32 class vtkQuadric;
34 
35 class VTKCOMMONDATAMODEL_EXPORT vtkTriangle : public vtkCell
36 {
37 public:
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 
227 protected:
229  ~vtkTriangle() override;
230 
232 
233 private:
234  vtkTriangle(const vtkTriangle&) = delete;
235  void operator=(const vtkTriangle&) = delete;
236 };
237 
238 //----------------------------------------------------------------------------
239 inline 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 //----------------------------------------------------------------------------
291 inline 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
Definition: vtkCellArray.h:181
represent and manipulate cell attribute data
Definition: vtkCellData.h:33
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
Definition: vtkDataArray.h:50
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
Definition: vtkPointData.h:33
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.
Definition: vtkTriangle.h:247
vtkCell * GetFace(int) override
See the vtkCell API for descriptions of these methods.
Definition: vtkTriangle.h:56
void EvaluateLocation(int &subId, const double pcoords[3], double x[3], double *weights) override
See the vtkCell API for descriptions of these methods.
const vtkIdType * GetEdgeArray(vtkIdType edgeId)
Return the ids of the vertices defining edge (edgeId).
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...
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:239
vtkCell * GetEdge(int edgeId) override
Get the edge specified by edgeId (range 0 to 2) and return that edge's 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
Definition: vtkTriangle.h:231
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.
Definition: vtkTriangle.h:291
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.
static vtkTriangle * New()
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.
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 * GetParametricCoords() override
See the vtkCell API for descriptions of these methods.
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:282
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.
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
@ points
Definition: vtkX3D.h:452
@ length
Definition: vtkX3D.h:399
@ value
Definition: vtkX3D.h:226
@ center
Definition: vtkX3D.h:236
@ index
Definition: vtkX3D.h:252
@ VTK_TRIANGLE
Definition: vtkCellType.h:51
int vtkIdType
Definition: vtkType.h:332