VTK  9.3.20240329
vtkTriangle.h
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1 // SPDX-FileCopyrightText: Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen
2 // SPDX-License-Identifier: BSD-3-Clause
123 #ifndef vtkTriangle_h
124 #define vtkTriangle_h
125 
126 #include "vtkCell.h"
127 #include "vtkCommonDataModelModule.h" // For export macro
128 
129 #include "vtkMath.h" // Needed for inline methods
130 
131 VTK_ABI_NAMESPACE_BEGIN
132 class vtkLine;
133 class vtkQuadric;
135 
136 class VTKCOMMONDATAMODEL_EXPORT vtkTriangle : public vtkCell
137 {
138 public:
139  static vtkTriangle* New();
140  vtkTypeMacro(vtkTriangle, vtkCell);
141  void PrintSelf(ostream& os, vtkIndent indent) override;
142 
147  vtkCell* GetEdge(int edgeId) override;
148 
150 
153  int GetCellType() override { return VTK_TRIANGLE; }
154  int GetCellDimension() override { return 2; }
155  int GetNumberOfEdges() override { return 3; }
156  int GetNumberOfFaces() override { return 0; }
157  vtkCell* GetFace(int) override { return nullptr; }
158  int CellBoundary(int subId, const double pcoords[3], vtkIdList* pts) override;
159  void Contour(double value, vtkDataArray* cellScalars, vtkIncrementalPointLocator* locator,
160  vtkCellArray* verts, vtkCellArray* lines, vtkCellArray* polys, vtkPointData* inPd,
161  vtkPointData* outPd, vtkCellData* inCd, vtkIdType cellId, vtkCellData* outCd) override;
162  int EvaluatePosition(const double x[3], double closestPoint[3], int& subId, double pcoords[3],
163  double& dist2, double weights[]) override;
164  void EvaluateLocation(int& subId, const double pcoords[3], double x[3], double* weights) override;
165  int TriangulateLocalIds(int index, vtkIdList* ptIds) override;
167  int subId, const double pcoords[3], const double* values, int dim, double* derivs) override;
168  double* GetParametricCoords() override;
170 
174  double ComputeArea();
175 
180  void Clip(double value, vtkDataArray* cellScalars, vtkIncrementalPointLocator* locator,
181  vtkCellArray* polys, vtkPointData* inPd, vtkPointData* outPd, vtkCellData* inCd,
182  vtkIdType cellId, vtkCellData* outCd, int insideOut) override;
183 
184  static void InterpolationFunctions(const double pcoords[3], double sf[3]);
185  static void InterpolationDerivs(const double pcoords[3], double derivs[6]);
187 
191  void InterpolateFunctions(const double pcoords[3], double sf[3]) override
192  {
194  }
195  void InterpolateDerivs(const double pcoords[3], double derivs[6]) override
196  {
197  vtkTriangle::InterpolationDerivs(pcoords, derivs);
198  }
200 
209 
216  int IntersectWithLine(const double p1[3], const double p2[3], double tol, double& t, double x[3],
217  double pcoords[3], int& subId) override;
218 
222  int GetParametricCenter(double pcoords[3]) override;
223 
228  double GetParametricDistance(const double pcoords[3]) override;
229 
233  static void TriangleCenter(
234  const double p1[3], const double p2[3], const double p3[3], double center[3]);
235 
240  static double TriangleArea(const double p1[3], const double p2[3], const double p3[3]);
241 
248  static double Circumcircle(
249  const double p1[2], const double p2[2], const double p3[2], double center[2]);
250 
263  static int BarycentricCoords(const double x[2], const double x1[2], const double x2[2],
264  const double x3[2], double bcoords[3]);
265 
271  static int ProjectTo2D(const double x1[3], const double x2[3], const double x3[3], double v1[2],
272  double v2[2], double v3[2]);
273 
278  static void ComputeNormal(vtkPoints* p, int numPts, const vtkIdType* pts, double n[3]);
279 
283  static void ComputeNormal(
284  const double v1[3], const double v2[3], const double v3[3], double n[3]);
285 
289  static void ComputeNormalDirection(
290  const double v1[3], const double v2[3], const double v3[3], double n[3]);
291 
292  // Description:
293  // Determine whether or not triangle (p1,q1,r1) intersects triangle
294  // (p2,q2,r2). This method is adapted from Olivier Devillers, Philippe Guigue.
295  // Faster Triangle-Triangle Intersection Tests. RR-4488, IN-RIA. 2002.
296  // <inria-00072100>.
297  static int TrianglesIntersect(const double p1[3], const double q1[3], const double r1[3],
298  const double p2[3], const double q2[3], const double r2[3]);
299 
300  // Description:
301  // Given a point x, determine whether it is inside (within the
302  // tolerance squared, tol2) the triangle defined by the three
303  // coordinate values p1, p2, p3. Method is via comparing dot products.
304  // (Note: in current implementation the tolerance only works in the
305  // neighborhood of the three vertices of the triangle.
306  static int PointInTriangle(
307  const double x[3], const double x1[3], const double x2[3], const double x3[3], double tol2);
308 
310 
316  static void ComputeQuadric(
317  const double x1[3], const double x2[3], const double x3[3], double quadric[4][4]);
318  static void ComputeQuadric(
319  const double x1[3], const double x2[3], const double x3[3], vtkQuadric* quadric);
321 
326  static bool ComputeCentroid(vtkPoints* points, const vtkIdType* pointIds, double centroid[3]);
327 
328 protected:
330  ~vtkTriangle() override;
331 
333 
334 private:
335  vtkTriangle(const vtkTriangle&) = delete;
336  void operator=(const vtkTriangle&) = delete;
337 };
338 
339 //----------------------------------------------------------------------------
340 inline int vtkTriangle::GetParametricCenter(double pcoords[3])
341 {
342  pcoords[0] = pcoords[1] = 1.0 / 3.0;
343  pcoords[2] = 0.0;
344  return 0;
345 }
346 
347 //----------------------------------------------------------------------------
349  const double v1[3], const double v2[3], const double v3[3], double n[3])
350 {
351  // order is important!!! maintain consistency with triangle vertex order
352  double ax = v3[0] - v2[0];
353  double ay = v3[1] - v2[1];
354  double az = v3[2] - v2[2];
355  double bx = v1[0] - v2[0];
356  double by = v1[1] - v2[1];
357  double bz = v1[2] - v2[2];
358 
359  n[0] = (ay * bz - az * by);
360  n[1] = (az * bx - ax * bz);
361  n[2] = (ax * by - ay * bx);
362 }
363 
364 //----------------------------------------------------------------------------
366  const double v1[3], const double v2[3], const double v3[3], double n[3])
367 {
369 
370  double length = sqrt(n[0] * n[0] + n[1] * n[1] + n[2] * n[2]);
371  if (length != 0.0)
372  {
373  n[0] /= length;
374  n[1] /= length;
375  n[2] /= length;
376  }
377 }
378 
379 //----------------------------------------------------------------------------
381  const double p1[3], const double p2[3], const double p3[3], double center[3])
382 {
383  center[0] = (p1[0] + p2[0] + p3[0]) / 3.0;
384  center[1] = (p1[1] + p2[1] + p3[1]) / 3.0;
385  center[2] = (p1[2] + p2[2] + p3[2]) / 3.0;
386 }
387 
388 //----------------------------------------------------------------------------
389 inline double vtkTriangle::TriangleArea(const double p1[3], const double p2[3], const double p3[3])
390 {
391  double n[3];
393 
394  return 0.5 * vtkMath::Norm(n);
395 }
396 
397 VTK_ABI_NAMESPACE_END
398 #endif
object to represent cell connectivity
Definition: vtkCellArray.h:286
represent and manipulate cell attribute data
Definition: vtkCellData.h:141
abstract class to specify cell behavior
Definition: vtkCell.h:130
virtual int GetParametricCenter(double pcoords[3])
Return center of the cell in parametric coordinates.
abstract superclass for arrays of numeric data
Definition: vtkDataArray.h:155
list of point or cell ids
Definition: vtkIdList.h:133
Abstract class in support of both point location and point insertion.
a simple class to control print indentation
Definition: vtkIndent.h:108
cell represents a 1D line
Definition: vtkLine.h:132
static float Norm(const float *x, int n)
Compute the norm of n-vector.
represent and manipulate point attribute data
Definition: vtkPointData.h:140
represent and manipulate 3D points
Definition: vtkPoints.h:139
evaluate implicit quadric function
Definition: vtkQuadric.h:112
a cell that represents a triangle
Definition: vtkTriangle.h:137
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:348
vtkCell * GetFace(int) override
See the vtkCell API for descriptions of these methods.
Definition: vtkTriangle.h:157
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:340
vtkCell * GetEdge(int edgeId) override
Get the edge specified by edgeId (range 0 to 2) and return that edge's 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:156
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:332
void InterpolateFunctions(const double pcoords[3], double sf[3]) override
Compute the interpolation functions/derivatives (aka shape functions/derivatives)
Definition: vtkTriangle.h:191
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:389
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.
void InterpolateDerivs(const double pcoords[3], double derivs[6]) override
Compute the interpolation functions/derivatives (aka shape functions/derivatives)
Definition: vtkTriangle.h:195
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:154
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:380
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:155
int TriangulateLocalIds(int index, vtkIdList *ptIds) override
See the vtkCell API for descriptions of these methods.
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:153
const std::string pointIds
@ points
Definition: vtkX3D.h:446
@ length
Definition: vtkX3D.h:393
@ value
Definition: vtkX3D.h:220
@ center
Definition: vtkX3D.h:230
@ index
Definition: vtkX3D.h:246
@ VTK_TRIANGLE
Definition: vtkCellType.h:61
int vtkIdType
Definition: vtkType.h:315