VTK  9.0.20200711
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;
65  void Derivatives(
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 
107  const vtkIdType* GetEdgeArray(vtkIdType edgeId);
108 
113  int IntersectWithLine(const double p1[3], const double p2[3], double tol, double& t, double x[3],
114  double pcoords[3], int& subId) override;
115 
119  int GetParametricCenter(double pcoords[3]) override;
120 
125  double GetParametricDistance(const double pcoords[3]) override;
126 
130  static void TriangleCenter(
131  const double p1[3], const double p2[3], const double p3[3], double center[3]);
132 
137  static double TriangleArea(const double p1[3], const double p2[3], const double p3[3]);
138 
145  static double Circumcircle(
146  const double p1[2], const double p2[2], const double p3[2], double center[2]);
147 
160  static int BarycentricCoords(const double x[2], const double x1[2], const double x2[2],
161  const double x3[2], double bcoords[3]);
162 
168  static int ProjectTo2D(const double x1[3], const double x2[3], const double x3[3], double v1[2],
169  double v2[2], double v3[2]);
170 
175  static void ComputeNormal(vtkPoints* p, int numPts, const vtkIdType* pts, double n[3]);
176 
180  static void ComputeNormal(
181  const double v1[3], const double v2[3], const double v3[3], double n[3]);
182 
186  static void ComputeNormalDirection(
187  const double v1[3], const double v2[3], const double v3[3], double n[3]);
188 
189  // Description:
190  // Determine whether or not triangle (p1,q1,r1) intersects triangle
191  // (p2,q2,r2). This method is adapted from Olivier Devillers, Philippe Guigue.
192  // Faster Triangle-Triangle Intersection Tests. RR-4488, IN-RIA. 2002.
193  // <inria-00072100>.
194  static int TrianglesIntersect(const double p1[3], const double q1[3], const double r1[3],
195  const double p2[3], const double q2[3], const double r2[3]);
196 
197  // Description:
198  // Given a point x, determine whether it is inside (within the
199  // tolerance squared, tol2) the triangle defined by the three
200  // coordinate values p1, p2, p3. Method is via comparing dot products.
201  // (Note: in current implementation the tolerance only works in the
202  // neighborhood of the three vertices of the triangle.
203  static int PointInTriangle(const double x[3], const double x1[3], const double x2[3],
204  const double x3[3], const double tol2);
205 
207 
213  static void ComputeQuadric(
214  const double x1[3], const double x2[3], const double x3[3], double quadric[4][4]);
215  static void ComputeQuadric(
216  const double x1[3], const double x2[3], const double x3[3], vtkQuadric* quadric);
218 
223  static bool ComputeCentroid(vtkPoints* points, const vtkIdType* pointIds, double centroid[3]);
224 
225 protected:
226  vtkTriangle();
227  ~vtkTriangle() override;
228 
230 
231 private:
232  vtkTriangle(const vtkTriangle&) = delete;
233  void operator=(const vtkTriangle&) = delete;
234 };
235 
236 //----------------------------------------------------------------------------
237 inline int vtkTriangle::GetParametricCenter(double pcoords[3])
238 {
239  pcoords[0] = pcoords[1] = 1. / 3;
240  pcoords[2] = 0.0;
241  return 0;
242 }
243 
244 //----------------------------------------------------------------------------
246  const double v1[3], const double v2[3], const double v3[3], double n[3])
247 {
248  double ax, ay, az, bx, by, bz;
249 
250  // order is important!!! maintain consistency with triangle vertex order
251  ax = v3[0] - v2[0];
252  ay = v3[1] - v2[1];
253  az = v3[2] - v2[2];
254  bx = v1[0] - v2[0];
255  by = v1[1] - v2[1];
256  bz = v1[2] - v2[2];
257 
258  n[0] = (ay * bz - az * by);
259  n[1] = (az * bx - ax * bz);
260  n[2] = (ax * by - ay * bx);
261 }
262 
263 //----------------------------------------------------------------------------
265  const double v1[3], const double v2[3], const double v3[3], double n[3])
266 {
267  double length;
268 
270 
271  if ((length = sqrt((n[0] * n[0] + n[1] * n[1] + n[2] * n[2]))) != 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 #endif
vtkPoints
represent and manipulate 3D points
Definition: vtkPoints.h:33
vtkCell::IntersectWithLine
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.
vtkTriangle::ComputeNormal
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...
vtkMath::Norm
static float Norm(const float *x, int n)
Compute the norm of n-vector.
vtkTriangle::TriangleCenter
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
vtkCell::Contour
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.
vtkMath.h
vtkPointData
represent and manipulate point attribute data
Definition: vtkPointData.h:32
vtkX3D::value
Definition: vtkX3D.h:226
vtkIdType
int vtkIdType
Definition: vtkType.h:330
vtkObject::New
static vtkObject * New()
Create an object with Debug turned off, modified time initialized to zero, and reference counting on.
vtkTriangle::InterpolateFunctions
void InterpolateFunctions(const double pcoords[3], double sf[3]) override
Compute the interpolation functions/derivatives (aka shape functions/derivatives)
Definition: vtkTriangle.h:90
vtkTriangle::GetParametricCenter
int GetParametricCenter(double pcoords[3]) override
Return the center of the triangle in parametric coordinates.
Definition: vtkTriangle.h:237
vtkX3D::length
Definition: vtkX3D.h:399
vtkTriangle::GetFace
vtkCell * GetFace(int) override
Return the face cell from the faceId of the cell.
Definition: vtkTriangle.h:56
vtkX3D::center
Definition: vtkX3D.h:236
vtkDataArray
abstract superclass for arrays of numeric data
Definition: vtkDataArray.h:49
vtkCell::EvaluateLocation
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.
vtkTriangle::GetCellType
int GetCellType() override
See the vtkCell API for descriptions of these methods.
Definition: vtkTriangle.h:52
vtkQuadric
evaluate implicit quadric function
Definition: vtkQuadric.h:30
vtkLine
cell represents a 1D line
Definition: vtkLine.h:29
vtkCell.h
vtkX3D::points
Definition: vtkX3D.h:452
vtkCell::Triangulate
virtual int Triangulate(int index, vtkIdList *ptIds, vtkPoints *pts)=0
Generate simplices of proper dimension.
vtkTriangle::GetNumberOfFaces
int GetNumberOfFaces() override
Return the number of faces in the cell.
Definition: vtkTriangle.h:55
vtkTriangle::InterpolationFunctions
static void InterpolationFunctions(const double pcoords[3], double sf[3])
vtkCell
abstract class to specify cell behavior
Definition: vtkCell.h:57
vtkCellData
represent and manipulate cell attribute data
Definition: vtkCellData.h:32
vtkIndent
a simple class to control print indentation
Definition: vtkIndent.h:33
vtkCell::PrintSelf
void PrintSelf(ostream &os, vtkIndent indent) override
Methods invoked by print to print information about the object including superclasses.
vtkCellArray
object to represent cell connectivity
Definition: vtkCellArray.h:180
vtkIncrementalPointLocator
Abstract class in support of both point location and point insertion.
Definition: vtkIncrementalPointLocator.h:51
vtkIdList
list of point or cell ids
Definition: vtkIdList.h:30
vtkTriangle::Line
vtkLine * Line
Definition: vtkTriangle.h:229
vtkTriangle
a cell that represents a triangle
Definition: vtkTriangle.h:35
vtkCell::CellBoundary
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...
vtkTriangle::InterpolateDerivs
void InterpolateDerivs(const double pcoords[3], double derivs[6]) override
Definition: vtkTriangle.h:94
vtkCell::GetParametricDistance
virtual double GetParametricDistance(const double pcoords[3])
Return the distance of the parametric coordinate provided to the cell.
vtkCell::EvaluatePosition
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...
vtkCell::GetParametricCoords
virtual double * GetParametricCoords())
Return a contiguous array of parametric coordinates of the points defining this cell.
vtkCell::Clip
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.
vtkCell::GetEdge
virtual vtkCell * GetEdge(int edgeId)=0
Return the edge cell from the edgeId of the cell.
vtkTriangle::ComputeNormalDirection
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:245
vtkCell::Derivatives
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.
vtkCell::GetParametricCenter
virtual int GetParametricCenter(double pcoords[3])
Return center of the cell in parametric coordinates.
vtkTriangle::GetCellDimension
int GetCellDimension() override
Return the topological dimensional of the cell (0,1,2, or 3).
Definition: vtkTriangle.h:53
vtkTriangle::TriangleArea
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
vtkTriangle::GetNumberOfEdges
int GetNumberOfEdges() override
Return the number of edges in the cell.
Definition: vtkTriangle.h:54
vtkX3D::index
Definition: vtkX3D.h:252
VTK_TRIANGLE
Definition: vtkCellType.h:51
vtkTriangle::InterpolationDerivs
static void InterpolationDerivs(const double pcoords[3], double derivs[6])