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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 =========================================================================*/
29 #ifndef vtkTriangle_h
30 #define vtkTriangle_h
31 
32 #include "vtkCommonDataModelModule.h" // For export macro
33 #include "vtkCell.h"
34 
35 #include "vtkMath.h" // Needed for inline methods
36 
37 class vtkLine;
38 class vtkQuadric;
40 
41 class VTKCOMMONDATAMODEL_EXPORT vtkTriangle : public vtkCell
42 {
43 public:
44  static vtkTriangle *New();
45  vtkTypeMacro(vtkTriangle,vtkCell);
46  void PrintSelf(ostream& os, vtkIndent indent) VTK_OVERRIDE;
47 
52  vtkCell *GetEdge(int edgeId) VTK_OVERRIDE;
53 
55 
58  int GetCellType() VTK_OVERRIDE {return VTK_TRIANGLE;};
59  int GetCellDimension() VTK_OVERRIDE {return 2;};
60  int GetNumberOfEdges() VTK_OVERRIDE {return 3;};
61  int GetNumberOfFaces() VTK_OVERRIDE {return 0;};
62  vtkCell *GetFace(int) VTK_OVERRIDE {return 0;};
63  int CellBoundary(int subId, double pcoords[3], vtkIdList *pts) VTK_OVERRIDE;
64  void Contour(double value, vtkDataArray *cellScalars,
66  vtkCellArray *lines, vtkCellArray *polys,
67  vtkPointData *inPd, vtkPointData *outPd,
68  vtkCellData *inCd, vtkIdType cellId, vtkCellData *outCd) VTK_OVERRIDE;
69  int EvaluatePosition(double x[3], double* closestPoint,
70  int& subId, double pcoords[3],
71  double& dist2, double *weights) VTK_OVERRIDE;
72  void EvaluateLocation(int& subId, double pcoords[3], double x[3],
73  double *weights) VTK_OVERRIDE;
74  int Triangulate(int index, vtkIdList *ptIds, vtkPoints *pts) VTK_OVERRIDE;
75  void Derivatives(int subId, double pcoords[3], double *values,
76  int dim, double *derivs) VTK_OVERRIDE;
77  double *GetParametricCoords() VTK_OVERRIDE;
79 
83  double ComputeArea();
84 
89  void Clip(double value, vtkDataArray *cellScalars,
91  vtkPointData *inPd, vtkPointData *outPd,
92  vtkCellData *inCd, vtkIdType cellId, vtkCellData *outCd,
93  int insideOut) VTK_OVERRIDE;
94 
98  static void InterpolationFunctions(double pcoords[3], double sf[3]);
102  static void InterpolationDerivs(double pcoords[3], double derivs[6]);
104 
108  void InterpolateFunctions(double pcoords[3], double sf[3]) VTK_OVERRIDE
109  {
111  }
112  void InterpolateDerivs(double pcoords[3], double derivs[6]) VTK_OVERRIDE
113  {
114  vtkTriangle::InterpolationDerivs(pcoords,derivs);
115  }
117 
121  int *GetEdgeArray(int edgeId);
122 
127  int IntersectWithLine(double p1[3], double p2[3], double tol, double& t,
128  double x[3], double pcoords[3], int& subId) VTK_OVERRIDE;
129 
133  int GetParametricCenter(double pcoords[3]) VTK_OVERRIDE;
134 
139  double GetParametricDistance(double pcoords[3]) VTK_OVERRIDE;
140 
144  static void TriangleCenter(double p1[3], double p2[3], double p3[3],
145  double center[3]);
146 
151  static double TriangleArea(double p1[3], double p2[3], double p3[3]);
152 
159  static double Circumcircle(double p1[2], double p2[2], double p3[2],
160  double center[2]);
161 
174  static int BarycentricCoords(double x[2], double x1[2], double x2[2],
175  double x3[2], double bcoords[3]);
176 
177 
183  static int ProjectTo2D(double x1[3], double x2[3], double x3[3],
184  double v1[2], double v2[2], double v3[2]);
185 
190  static void ComputeNormal(vtkPoints *p, int numPts, vtkIdType *pts,
191  double n[3]);
192 
196  static void ComputeNormal(double v1[3], double v2[3], double v3[3], double n[3]);
197 
201  static void ComputeNormalDirection(double v1[3], double v2[3], double v3[3],
202  double n[3]);
203 
211  static int PointInTriangle(double x[3], double x1[3],
212  double x2[3], double x3[3],
213  double tol2);
214 
216 
222  static void ComputeQuadric(double x1[3], double x2[3], double x3[3],
223  double quadric[4][4]);
224  static void ComputeQuadric(double x1[3], double x2[3], double x3[3],
225  vtkQuadric *quadric);
227 
228 
229 protected:
231  ~vtkTriangle() VTK_OVERRIDE;
232 
233  vtkLine *Line;
234 
235 private:
236  vtkTriangle(const vtkTriangle&) VTK_DELETE_FUNCTION;
237  void operator=(const vtkTriangle&) VTK_DELETE_FUNCTION;
238 };
239 
240 //----------------------------------------------------------------------------
241 inline int vtkTriangle::GetParametricCenter(double pcoords[3])
242 {
243  pcoords[0] = pcoords[1] = 1./3; pcoords[2] = 0.0;
244  return 0;
245 }
246 
247 //----------------------------------------------------------------------------
248 inline void vtkTriangle::ComputeNormalDirection(double v1[3], double v2[3],
249  double v3[3], double n[3])
250 {
251  double ax, ay, az, bx, by, bz;
252 
253  // order is important!!! maintain consistency with triangle vertex order
254  ax = v3[0] - v2[0]; ay = v3[1] - v2[1]; az = v3[2] - v2[2];
255  bx = v1[0] - v2[0]; by = v1[1] - v2[1]; bz = v1[2] - v2[2];
256 
257  n[0] = (ay * bz - az * by);
258  n[1] = (az * bx - ax * bz);
259  n[2] = (ax * by - ay * bx);
260 }
261 
262 //----------------------------------------------------------------------------
263 inline void vtkTriangle::ComputeNormal(double v1[3], double v2[3],
264  double v3[3], double n[3])
265 {
266  double length;
267 
269 
270  if ( (length = sqrt((n[0]*n[0] + n[1]*n[1] + n[2]*n[2]))) != 0.0 )
271  {
272  n[0] /= length;
273  n[1] /= length;
274  n[2] /= length;
275  }
276 }
277 
278 //----------------------------------------------------------------------------
279 inline void vtkTriangle::TriangleCenter(double p1[3], double p2[3],
280  double p3[3], double center[3])
281 {
282  center[0] = (p1[0]+p2[0]+p3[0]) / 3.0;
283  center[1] = (p1[1]+p2[1]+p3[1]) / 3.0;
284  center[2] = (p1[2]+p2[2]+p3[2]) / 3.0;
285 }
286 
287 //----------------------------------------------------------------------------
288 inline double vtkTriangle::TriangleArea(double p1[3], double p2[3], double p3[3])
289 {
290  double n[3];
292 
293  return 0.5*vtkMath::Norm(n);
294 }
295 
296 #endif
297 
298 
vtkPoints
represent and manipulate 3D points
Definition: vtkPoints.h:40
vtkTriangle::BarycentricCoords
static int BarycentricCoords(double x[2], double x1[2], double x2[2], double x3[2], double bcoords[3])
Given a 2D point x[2], determine the barycentric coordinates of the point.
vtkMath::Norm
static float Norm(const float *x, int n)
Compute the norm of n-vector.
vtkTriangle::GetEdgeArray
int * GetEdgeArray(int edgeId)
Return the ids of the vertices defining edge (edgeId).
vtkMath.h
vtkPointData
represent and manipulate point attribute data
Definition: vtkPointData.h:38
vtkX3D::value
@ value
Definition: vtkX3D.h:220
vtkTriangle::TriangleArea
static double TriangleArea(double p1[3], double p2[3], double p3[3])
Compute the area of a triangle in 3D.
Definition: vtkTriangle.h:288
vtkIdType
int vtkIdType
Definition: vtkType.h:287
vtkTriangle::InterpolationDerivs
static void InterpolationDerivs(double pcoords[3], double derivs[6])
vtkTriangle::EvaluatePosition
int EvaluatePosition(double x[3], double *closestPoint, int &subId, double pcoords[3], double &dist2, double *weights) override
Given a point x[3] return inside(=1), outside(=0) cell, or (-1) computational problem encountered; ev...
vtkTriangle::New
static vtkTriangle * New()
vtkTriangle::ComputeNormal
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...
vtkTriangle::PointInTriangle
static int PointInTriangle(double x[3], double x1[3], double x2[3], double x3[3], double tol2)
Given a point x, determine whether it is inside (within the tolerance squared, tol2) the triangle def...
vtkX3D::length
@ length
Definition: vtkX3D.h:393
vtkTriangle::GetFace
vtkCell * GetFace(int) override
Return the face cell from the faceId of the cell.
Definition: vtkTriangle.h:62
vtkX3D::center
@ center
Definition: vtkX3D.h:230
vtkDataArray
abstract superclass for arrays of numeric data
Definition: vtkDataArray.h:55
vtkTriangle::GetCellType
int GetCellType() override
See the vtkCell API for descriptions of these methods.
Definition: vtkTriangle.h:58
vtkQuadric
evaluate implicit quadric function
Definition: vtkQuadric.h:37
vtkLine
cell represents a 1D line
Definition: vtkLine.h:36
vtkTriangle::ProjectTo2D
static int ProjectTo2D(double x1[3], double x2[3], double x3[3], double v1[2], double v2[2], double v3[2])
Project triangle defined in 3D to 2D coordinates.
vtkCell.h
vtkTriangle::IntersectWithLine
int IntersectWithLine(double p1[3], double p2[3], double tol, double &t, double x[3], double pcoords[3], int &subId) override
Plane intersection plus in/out test on triangle.
vtkTriangle::ComputeNormalDirection
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:248
vtkTriangle::InterpolateDerivs
void InterpolateDerivs(double pcoords[3], double derivs[6]) override
Definition: vtkTriangle.h:112
vtkTriangle::GetNumberOfFaces
int GetNumberOfFaces() override
Return the number of faces in the cell.
Definition: vtkTriangle.h:61
vtkTriangle::ComputeQuadric
static void ComputeQuadric(double x1[3], double x2[3], double x3[3], vtkQuadric *quadric)
vtkTriangle::Circumcircle
static double Circumcircle(double p1[2], double p2[2], double p3[2], double center[2])
Compute the circumcenter (center[3]) and radius squared (method return value) of a triangle defined b...
vtkTriangle::vtkTriangle
vtkTriangle()
vtkTriangle::Derivatives
void Derivatives(int subId, double pcoords[3], double *values, int dim, double *derivs) override
Compute derivatives given cell subId and parametric coordinates.
vtkCell
abstract class to specify cell behavior
Definition: vtkCell.h:60
vtkCellData
represent and manipulate cell attribute data
Definition: vtkCellData.h:39
vtkIndent
a simple class to control print indentation
Definition: vtkIndent.h:40
vtkCellArray
object to represent cell connectivity
Definition: vtkCellArray.h:51
vtkTriangle::Contour
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
Generate contouring primitives.
vtkIncrementalPointLocator
Abstract class in support of both point location and point insertion.
Definition: vtkIncrementalPointLocator.h:52
vtkIdList
list of point or cell ids
Definition: vtkIdList.h:37
vtkTriangle::EvaluateLocation
void EvaluateLocation(int &subId, double pcoords[3], double x[3], double *weights) override
Determine global coordinate (x[3]) from subId and parametric coordinates.
vtkTriangle::PrintSelf
void PrintSelf(ostream &os, vtkIndent indent) override
Methods invoked by print to print information about the object including superclasses.
vtkTriangle::Triangulate
int Triangulate(int index, vtkIdList *ptIds, vtkPoints *pts) override
Generate simplices of proper dimension.
vtkTriangle::InterpolationFunctions
static void InterpolationFunctions(double pcoords[3], double sf[3])
vtkTriangle
a cell that represents a triangle
Definition: vtkTriangle.h:42
vtkTriangle::TriangleCenter
static void TriangleCenter(double p1[3], double p2[3], double p3[3], double center[3])
Compute the center of the triangle.
Definition: vtkTriangle.h:279
vtkTriangle::CellBoundary
int CellBoundary(int subId, double pcoords[3], vtkIdList *pts) override
Given parametric coordinates of a point, return the closest cell boundary, and whether the point is i...
vtkTriangle::ComputeQuadric
static void ComputeQuadric(double x1[3], double x2[3], double x3[3], double quadric[4][4])
Calculate the error quadric for this triangle.
vtkTriangle::GetParametricDistance
double GetParametricDistance(double pcoords[3]) override
Return the distance of the parametric coordinate provided to the cell.
vtkTriangle::~vtkTriangle
~vtkTriangle() override
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:59
vtkTriangle::GetNumberOfEdges
int GetNumberOfEdges() override
Return the number of edges in the cell.
Definition: vtkTriangle.h:60
vtkTriangle::GetParametricCoords
double * GetParametricCoords() override
Return a contiguous array of parametric coordinates of the points defining this cell.
vtkX3D::index
@ index
Definition: vtkX3D.h:246
VTK_TRIANGLE
@ VTK_TRIANGLE
Definition: vtkCellType.h:50
vtkTriangle::GetEdge
vtkCell * GetEdge(int edgeId) override
Get the edge specified by edgeId (range 0 to 2) and return that edge's coordinates.