VTK  9.3.0
vtkTriangle.h
Go to the documentation of this file.
1 // SPDX-FileCopyrightText: Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen
2 // SPDX-License-Identifier: BSD-3-Clause
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 VTK_ABI_NAMESPACE_BEGIN
32 class vtkLine;
33 class vtkQuadric;
35 
36 class VTKCOMMONDATAMODEL_EXPORT vtkTriangle : public vtkCell
37 {
38 public:
39  static vtkTriangle* New();
40  vtkTypeMacro(vtkTriangle, vtkCell);
41  void PrintSelf(ostream& os, vtkIndent indent) override;
42 
47  vtkCell* GetEdge(int edgeId) override;
48 
50 
53  int GetCellType() override { return VTK_TRIANGLE; }
54  int GetCellDimension() override { return 2; }
55  int GetNumberOfEdges() override { return 3; }
56  int GetNumberOfFaces() override { return 0; }
57  vtkCell* GetFace(int) override { return nullptr; }
58  int CellBoundary(int subId, const double pcoords[3], vtkIdList* pts) override;
59  void Contour(double value, vtkDataArray* cellScalars, vtkIncrementalPointLocator* locator,
60  vtkCellArray* verts, vtkCellArray* lines, vtkCellArray* polys, vtkPointData* inPd,
61  vtkPointData* outPd, vtkCellData* inCd, vtkIdType cellId, vtkCellData* outCd) override;
62  int EvaluatePosition(const double x[3], double closestPoint[3], int& subId, double pcoords[3],
63  double& dist2, double weights[]) override;
64  void EvaluateLocation(int& subId, const double pcoords[3], double x[3], double* weights) override;
65  int Triangulate(int index, vtkIdList* ptIds, vtkPoints* pts) override;
67  int subId, const double pcoords[3], const double* values, int dim, double* derivs) override;
68  double* GetParametricCoords() override;
70 
74  double ComputeArea();
75 
80  void Clip(double value, vtkDataArray* cellScalars, vtkIncrementalPointLocator* locator,
81  vtkCellArray* polys, vtkPointData* inPd, vtkPointData* outPd, vtkCellData* inCd,
82  vtkIdType cellId, vtkCellData* outCd, int insideOut) override;
83 
84  static void InterpolationFunctions(const double pcoords[3], double sf[3]);
85  static void InterpolationDerivs(const double pcoords[3], double derivs[6]);
87 
91  void InterpolateFunctions(const double pcoords[3], double sf[3]) override
92  {
94  }
95  void InterpolateDerivs(const double pcoords[3], double derivs[6]) override
96  {
97  vtkTriangle::InterpolationDerivs(pcoords, derivs);
98  }
100 
109 
116  int IntersectWithLine(const double p1[3], const double p2[3], double tol, double& t, double x[3],
117  double pcoords[3], int& subId) override;
118 
122  int GetParametricCenter(double pcoords[3]) override;
123 
128  double GetParametricDistance(const double pcoords[3]) override;
129 
133  static void TriangleCenter(
134  const double p1[3], const double p2[3], const double p3[3], double center[3]);
135 
140  static double TriangleArea(const double p1[3], const double p2[3], const double p3[3]);
141 
148  static double Circumcircle(
149  const double p1[2], const double p2[2], const double p3[2], double center[2]);
150 
163  static int BarycentricCoords(const double x[2], const double x1[2], const double x2[2],
164  const double x3[2], double bcoords[3]);
165 
171  static int ProjectTo2D(const double x1[3], const double x2[3], const double x3[3], double v1[2],
172  double v2[2], double v3[2]);
173 
178  static void ComputeNormal(vtkPoints* p, int numPts, const vtkIdType* pts, double n[3]);
179 
183  static void ComputeNormal(
184  const double v1[3], const double v2[3], const double v3[3], double n[3]);
185 
189  static void ComputeNormalDirection(
190  const double v1[3], const double v2[3], const double v3[3], double n[3]);
191 
192  // Description:
193  // Determine whether or not triangle (p1,q1,r1) intersects triangle
194  // (p2,q2,r2). This method is adapted from Olivier Devillers, Philippe Guigue.
195  // Faster Triangle-Triangle Intersection Tests. RR-4488, IN-RIA. 2002.
196  // <inria-00072100>.
197  static int TrianglesIntersect(const double p1[3], const double q1[3], const double r1[3],
198  const double p2[3], const double q2[3], const double r2[3]);
199 
200  // Description:
201  // Given a point x, determine whether it is inside (within the
202  // tolerance squared, tol2) the triangle defined by the three
203  // coordinate values p1, p2, p3. Method is via comparing dot products.
204  // (Note: in current implementation the tolerance only works in the
205  // neighborhood of the three vertices of the triangle.
206  static int PointInTriangle(
207  const double x[3], const double x1[3], const double x2[3], const double x3[3], double tol2);
208 
210 
216  static void ComputeQuadric(
217  const double x1[3], const double x2[3], const double x3[3], double quadric[4][4]);
218  static void ComputeQuadric(
219  const double x1[3], const double x2[3], const double x3[3], vtkQuadric* quadric);
221 
226  static bool ComputeCentroid(vtkPoints* points, const vtkIdType* pointIds, double centroid[3]);
227 
228 protected:
230  ~vtkTriangle() override;
231 
233 
234 private:
235  vtkTriangle(const vtkTriangle&) = delete;
236  void operator=(const vtkTriangle&) = delete;
237 };
238 
239 //----------------------------------------------------------------------------
240 inline int vtkTriangle::GetParametricCenter(double pcoords[3])
241 {
242  pcoords[0] = pcoords[1] = 1.0 / 3.0;
243  pcoords[2] = 0.0;
244  return 0;
245 }
246 
247 //----------------------------------------------------------------------------
249  const double v1[3], const double v2[3], const double v3[3], double n[3])
250 {
251  // order is important!!! maintain consistency with triangle vertex order
252  double ax = v3[0] - v2[0];
253  double ay = v3[1] - v2[1];
254  double az = v3[2] - v2[2];
255  double bx = v1[0] - v2[0];
256  double by = v1[1] - v2[1];
257  double bz = v1[2] - v2[2];
258 
259  n[0] = (ay * bz - az * by);
260  n[1] = (az * bx - ax * bz);
261  n[2] = (ax * by - ay * bx);
262 }
263 
264 //----------------------------------------------------------------------------
266  const double v1[3], const double v2[3], const double v3[3], double n[3])
267 {
269 
270  double length = sqrt(n[0] * n[0] + n[1] * n[1] + n[2] * n[2]);
271  if (length != 0.0)
272  {
273  n[0] /= length;
274  n[1] /= length;
275  n[2] /= length;
276  }
277 }
278 
279 //----------------------------------------------------------------------------
281  const double p1[3], const double p2[3], const double p3[3], double center[3])
282 {
283  center[0] = (p1[0] + p2[0] + p3[0]) / 3.0;
284  center[1] = (p1[1] + p2[1] + p3[1]) / 3.0;
285  center[2] = (p1[2] + p2[2] + p3[2]) / 3.0;
286 }
287 
288 //----------------------------------------------------------------------------
289 inline double vtkTriangle::TriangleArea(const double p1[3], const double p2[3], const double p3[3])
290 {
291  double n[3];
293 
294  return 0.5 * vtkMath::Norm(n);
295 }
296 
297 VTK_ABI_NAMESPACE_END
298 #endif
object to represent cell connectivity
Definition: vtkCellArray.h:185
represent and manipulate cell attribute data
Definition: vtkCellData.h:40
abstract class to specify cell behavior
Definition: vtkCell.h:59
virtual int GetParametricCenter(double pcoords[3])
Return center of the cell in parametric coordinates.
abstract superclass for arrays of numeric data
Definition: vtkDataArray.h:54
list of point or cell ids
Definition: vtkIdList.h:32
Abstract class in support of both point location and point insertion.
a simple class to control print indentation
Definition: vtkIndent.h:38
cell represents a 1D line
Definition: vtkLine.h:32
static float Norm(const float *x, int n)
Compute the norm of n-vector.
represent and manipulate point attribute data
Definition: vtkPointData.h:39
represent and manipulate 3D points
Definition: vtkPoints.h:38
evaluate implicit quadric function
Definition: vtkQuadric.h:32
a cell that represents a triangle
Definition: vtkTriangle.h:37
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:248
vtkCell * GetFace(int) override
See the vtkCell API for descriptions of these methods.
Definition: vtkTriangle.h:57
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:240
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:56
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:232
void InterpolateFunctions(const double pcoords[3], double sf[3]) override
Compute the interpolation functions/derivatives (aka shape functions/derivatives)
Definition: vtkTriangle.h:91
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:289
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:95
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:54
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:280
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:55
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:53
@ 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:51
int vtkIdType
Definition: vtkType.h:315