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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 "vtkCommonDataModelModule.h" // For export macro
27 #include "vtkCell.h"
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) VTK_OVERRIDE;
41 
46  vtkCell *GetEdge(int edgeId) VTK_OVERRIDE;
47 
49 
52  int GetCellType() VTK_OVERRIDE {return VTK_TRIANGLE;};
53  int GetCellDimension() VTK_OVERRIDE {return 2;};
54  int GetNumberOfEdges() VTK_OVERRIDE {return 3;};
55  int GetNumberOfFaces() VTK_OVERRIDE {return 0;};
56  vtkCell *GetFace(int) VTK_OVERRIDE {return 0;};
57  int CellBoundary(int subId, double pcoords[3], vtkIdList *pts) VTK_OVERRIDE;
58  void Contour(double value, vtkDataArray *cellScalars,
60  vtkCellArray *lines, vtkCellArray *polys,
61  vtkPointData *inPd, vtkPointData *outPd,
62  vtkCellData *inCd, vtkIdType cellId, vtkCellData *outCd) VTK_OVERRIDE;
63  int EvaluatePosition(double x[3], double* closestPoint,
64  int& subId, double pcoords[3],
65  double& dist2, double *weights) VTK_OVERRIDE;
66  void EvaluateLocation(int& subId, double pcoords[3], double x[3],
67  double *weights) VTK_OVERRIDE;
68  int Triangulate(int index, vtkIdList *ptIds, vtkPoints *pts) VTK_OVERRIDE;
69  void Derivatives(int subId, double pcoords[3], double *values,
70  int dim, double *derivs) VTK_OVERRIDE;
71  double *GetParametricCoords() VTK_OVERRIDE;
73 
77  double ComputeArea();
78 
83  void Clip(double value, vtkDataArray *cellScalars,
85  vtkPointData *inPd, vtkPointData *outPd,
86  vtkCellData *inCd, vtkIdType cellId, vtkCellData *outCd,
87  int insideOut) VTK_OVERRIDE;
88 
92  static void InterpolationFunctions(double pcoords[3], double sf[3]);
96  static void InterpolationDerivs(double pcoords[3], double derivs[6]);
98 
102  void InterpolateFunctions(double pcoords[3], double sf[3]) VTK_OVERRIDE
103  {
105  }
106  void InterpolateDerivs(double pcoords[3], double derivs[6]) VTK_OVERRIDE
107  {
108  vtkTriangle::InterpolationDerivs(pcoords,derivs);
109  }
111 
115  int *GetEdgeArray(int edgeId);
116 
121  int IntersectWithLine(double p1[3], double p2[3], double tol, double& t,
122  double x[3], double pcoords[3], int& subId) VTK_OVERRIDE;
123 
127  int GetParametricCenter(double pcoords[3]) VTK_OVERRIDE;
128 
133  double GetParametricDistance(double pcoords[3]) VTK_OVERRIDE;
134 
138  static void TriangleCenter(double p1[3], double p2[3], double p3[3],
139  double center[3]);
140 
145  static double TriangleArea(double p1[3], double p2[3], double p3[3]);
146 
153  static double Circumcircle(double p1[2], double p2[2], double p3[2],
154  double center[2]);
155 
168  static int BarycentricCoords(double x[2], double x1[2], double x2[2],
169  double x3[2], double bcoords[3]);
170 
171 
177  static int ProjectTo2D(double x1[3], double x2[3], double x3[3],
178  double v1[2], double v2[2], double v3[2]);
179 
184  static void ComputeNormal(vtkPoints *p, int numPts, vtkIdType *pts,
185  double n[3]);
186 
190  static void ComputeNormal(double v1[3], double v2[3], double v3[3], double n[3]);
191 
195  static void ComputeNormalDirection(double v1[3], double v2[3], double v3[3],
196  double n[3]);
197 
198  // Description:
199  // Determine whether or not triangle (p1,q1,r1) intersects triangle
200  // (p2,q2,r2). This method is adapted from Olivier Devillers, Philippe Guigue.
201  // Faster Triangle-Triangle Intersection Tests. RR-4488, IN-RIA. 2002.
202  // <inria-00072100>.
203  static int TrianglesIntersect(double p1[3], double q1[3], double r1[3],
204  double p2[3], double q2[3], double r2[3]);
205 
206  // Description:
207  // Given a point x, determine whether it is inside (within the
208  // tolerance squared, tol2) the triangle defined by the three
209  // coordinate values p1, p2, p3. Method is via comparing dot products.
210  // (Note: in current implementation the tolerance only works in the
211  // neighborhood of the three vertices of the triangle.
212  static int PointInTriangle(double x[3], double x1[3],
213  double x2[3], double x3[3],
214  double tol2);
215 
217 
223  static void ComputeQuadric(double x1[3], double x2[3], double x3[3],
224  double quadric[4][4]);
225  static void ComputeQuadric(double x1[3], double x2[3], double x3[3],
226  vtkQuadric *quadric);
228 
229 
230 protected:
231  vtkTriangle();
232  ~vtkTriangle() VTK_OVERRIDE;
233 
235 
236 private:
237  vtkTriangle(const vtkTriangle&) VTK_DELETE_FUNCTION;
238  void operator=(const vtkTriangle&) VTK_DELETE_FUNCTION;
239 };
240 
241 //----------------------------------------------------------------------------
242 inline int vtkTriangle::GetParametricCenter(double pcoords[3])
243 {
244  pcoords[0] = pcoords[1] = 1./3; pcoords[2] = 0.0;
245  return 0;
246 }
247 
248 //----------------------------------------------------------------------------
249 inline void vtkTriangle::ComputeNormalDirection(double v1[3], double v2[3],
250  double v3[3], double n[3])
251 {
252  double ax, ay, az, bx, by, bz;
253 
254  // order is important!!! maintain consistency with triangle vertex order
255  ax = v3[0] - v2[0]; ay = v3[1] - v2[1]; az = v3[2] - v2[2];
256  bx = v1[0] - v2[0]; by = v1[1] - v2[1]; 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 //----------------------------------------------------------------------------
264 inline void vtkTriangle::ComputeNormal(double v1[3], double v2[3],
265  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 //----------------------------------------------------------------------------
280 inline void vtkTriangle::TriangleCenter(double p1[3], double p2[3],
281  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(double p1[3], double p2[3], double p3[3])
290 {
291  double n[3];
293 
294  return 0.5*vtkMath::Norm(n);
295 }
296 
297 #endif
void PrintSelf(ostream &os, vtkIndent indent) override
Methods invoked by print to print information about the object including superclasses.
static void InterpolationDerivs(double pcoords[3], double derivs[6])
represent and manipulate point attribute data
Definition: vtkPointData.h:31
int GetCellType() override
See the vtkCell API for descriptions of these methods.
Definition: vtkTriangle.h:52
virtual double * GetParametricCoords()
Return a contiguous array of parametric coordinates of the points defining this cell.
represent and manipulate cell attribute data
Definition: vtkCellData.h:32
vtkCell * GetFace(int) override
See the vtkCell API for descriptions of these methods.
Definition: vtkTriangle.h:56
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.
virtual void EvaluateLocation(int &subId, double pcoords[3], double x[3], double *weights)=0
Determine global coordinate (x[3]) from subId and parametric coordinates.
virtual int EvaluatePosition(double x[3], double *closestPoint, 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...
static void ComputeNormalDirection(double v1[3], double v2[3], double v3[3], double n[3])
Compute the (unnormalized) triangle normal direction from three points.
Definition: vtkTriangle.h:249
int vtkIdType
Definition: vtkType.h:345
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:55
static void ComputeNormal(vtkPoints *p, int numPts, 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...
cell represents a 1D line
Definition: vtkLine.h:29
abstract class to specify cell behavior
Definition: vtkCell.h:56
virtual double GetParametricDistance(double pcoords[3])
Return the distance of the parametric coordinate provided to the cell.
static void InterpolationFunctions(double pcoords[3], double sf[3])
a simple class to control print indentation
Definition: vtkIndent.h:33
evaluate implicit quadric function
Definition: vtkQuadric.h:30
list of point or cell ids
Definition: vtkIdList.h:30
virtual void Derivatives(int subId, double pcoords[3], double *values, int dim, double *derivs)=0
Compute derivatives given cell subId and parametric coordinates.
abstract superclass for arrays of numeric data
Definition: vtkDataArray.h:48
virtual int IntersectWithLine(double p1[3], double p2[3], double tol, double &t, double x[3], double pcoords[3], int &subId)=0
Intersect with a ray.
void InterpolateDerivs(double pcoords[3], double derivs[6]) override
Compute the interpolation functions/derivatives (aka shape functions/derivatives) ...
Definition: vtkTriangle.h:106
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.
static void TriangleCenter(double p1[3], double p2[3], double p3[3], double center[3])
Compute the center of the triangle.
Definition: vtkTriangle.h:280
object to represent cell connectivity
Definition: vtkCellArray.h:44
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:54
a cell that represents a triangle
Definition: vtkTriangle.h:35
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 int CellBoundary(int subId, double pcoords[3], vtkIdList *pts)=0
Given parametric coordinates of a point, return the closest cell boundary, and whether the point is i...
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.
int GetCellDimension() override
See the vtkCell API for descriptions of these methods.
Definition: vtkTriangle.h:53
virtual int GetParametricCenter(double pcoords[3])
Return center of the cell in parametric coordinates.
void InterpolateFunctions(double pcoords[3], double sf[3]) override
Compute the interpolation functions/derivatives (aka shape functions/derivatives) ...
Definition: vtkTriangle.h:102
represent and manipulate 3D points
Definition: vtkPoints.h:33
static double TriangleArea(double p1[3], double p2[3], double p3[3])
Compute the area of a triangle in 3D.
Definition: vtkTriangle.h:289