VTK: Common/DataModel/vtkTriangle.h Source File

| VTK 9.3.1

vtkTriangle.h
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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;
34 class vtkIncrementalPointLocator;
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;
66 void Derivatives(
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 {
93 vtkTriangle::InterpolationFunctions(pcoords, sf);
94 }
95 void InterpolateDerivs(const double pcoords[3], double derivs[6]) override
96 {
97 vtkTriangle::InterpolationDerivs(pcoords, derivs);
98 }
100
108 const vtkIdType* GetEdgeArray(vtkIdType edgeId);
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:
229 vtkTriangle();
230 ~vtkTriangle() override;
231
232 vtkLine* Line;
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 //----------------------------------------------------------------------------
248 inline void vtkTriangle::ComputeNormalDirection(
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 //----------------------------------------------------------------------------
265 inline void vtkTriangle::ComputeNormal(
266 const double v1[3], const double v2[3], const double v3[3], double n[3])
267 {
268 vtkTriangle::ComputeNormalDirection(v1, v2, v3, n);
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 //----------------------------------------------------------------------------
280 inline void vtkTriangle::TriangleCenter(
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];
292 vtkTriangle::ComputeNormalDirection(p1, p2, p3, n);
293
294 return 0.5 * vtkMath::Norm(n);
295 }
296
297 VTK_ABI_NAMESPACE_END
298 #endif
vtkCellArray
object to represent cell connectivity
Definition: vtkCellArray.h:185
vtkCellData
represent and manipulate cell attribute data
Definition: vtkCellData.h:40
vtkCell
abstract class to specify cell behavior
Definition: vtkCell.h:59
vtkCell::GetParametricCenter
virtual int GetParametricCenter(double pcoords[3])
Return center of the cell in parametric coordinates.
vtkDataArray
abstract superclass for arrays of numeric data
Definition: vtkDataArray.h:54
vtkIdList
list of point or cell ids
Definition: vtkIdList.h:32
vtkIncrementalPointLocator
Abstract class in support of both point location and point insertion.
Definition: vtkIncrementalPointLocator.h:41
vtkIndent
a simple class to control print indentation
Definition: vtkIndent.h:38
vtkLine
cell represents a 1D line
Definition: vtkLine.h:32
vtkMath::Norm
static float Norm(const float *x, int n)
Compute the norm of n-vector.
vtkPointData
represent and manipulate point attribute data
Definition: vtkPointData.h:39
vtkPoints
represent and manipulate 3D points
Definition: vtkPoints.h:38
vtkQuadric
evaluate implicit quadric function
Definition: vtkQuadric.h:32
vtkTriangle
a cell that represents a triangle
Definition: vtkTriangle.h:37
vtkTriangle::vtkTriangle
vtkTriangle()
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:248
vtkTriangle::GetFace
vtkCell * GetFace(int) override
See the vtkCell API for descriptions of these methods.
Definition: vtkTriangle.h:57
vtkTriangle::EvaluateLocation
void EvaluateLocation(int &subId, const double pcoords[3], double x[3], double *weights) override
See the vtkCell API for descriptions of these methods.
vtkTriangle::GetEdgeArray
const vtkIdType * GetEdgeArray(vtkIdType edgeId)
Return the ids of the vertices defining edge (edgeId).
vtkTriangle::TrianglesIntersect
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])
vtkTriangle::ComputeQuadric
static void ComputeQuadric(const double x1[3], const double x2[3], const double x3[3], vtkQuadric *quadric)
Calculate the error quadric for this triangle.
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...
vtkTriangle::EvaluatePosition
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.
vtkTriangle::GetParametricCenter
int GetParametricCenter(double pcoords[3]) override
Return the center of the triangle in parametric coordinates.
Definition: vtkTriangle.h:240
vtkTriangle::GetEdge
vtkCell * GetEdge(int edgeId) override
Get the edge specified by edgeId (range 0 to 2) and return that edge's coordinates.
vtkTriangle::PointInTriangle
static int PointInTriangle(const double x[3], const double x1[3], const double x2[3], const double x3[3], double tol2)
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
See the vtkCell API for descriptions of these methods.
vtkTriangle::GetNumberOfFaces
int GetNumberOfFaces() override
See the vtkCell API for descriptions of these methods.
Definition: vtkTriangle.h:56
vtkTriangle::Clip
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.
vtkTriangle::CellBoundary
int CellBoundary(int subId, const double pcoords[3], vtkIdList *pts) override
See the vtkCell API for descriptions of these methods.
vtkTriangle::Line
vtkLine * Line
Definition: vtkTriangle.h:232
vtkTriangle::InterpolateFunctions
void InterpolateFunctions(const double pcoords[3], double sf[3]) override
Compute the interpolation functions/derivatives (aka shape functions/derivatives)
Definition: vtkTriangle.h:91
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::ProjectTo2D
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.
vtkTriangle::ComputeCentroid
static bool ComputeCentroid(vtkPoints *points, const vtkIdType *pointIds, double centroid[3])
Get the centroid of the triangle.
vtkTriangle::New
static vtkTriangle * New()
vtkTriangle::GetParametricDistance
double GetParametricDistance(const double pcoords[3]) override
Return the distance of the parametric coordinate provided to the cell.
vtkTriangle::~vtkTriangle
~vtkTriangle() override
vtkTriangle::IntersectWithLine
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.
vtkTriangle::Triangulate
int Triangulate(int index, vtkIdList *ptIds, vtkPoints *pts) override
See the vtkCell API for descriptions of these methods.
vtkTriangle::InterpolateDerivs
void InterpolateDerivs(const double pcoords[3], double derivs[6]) override
Compute the interpolation functions/derivatives (aka shape functions/derivatives)
Definition: vtkTriangle.h:95
vtkTriangle::PrintSelf
void PrintSelf(ostream &os, vtkIndent indent) override
Methods invoked by print to print information about the object including superclasses.
vtkTriangle::Circumcircle
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...
vtkTriangle::InterpolationDerivs
static void InterpolationDerivs(const double pcoords[3], double derivs[6])
vtkTriangle::ComputeQuadric
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.
vtkTriangle::GetCellDimension
int GetCellDimension() override
See the vtkCell API for descriptions of these methods.
Definition: vtkTriangle.h:54
vtkTriangle::GetParametricCoords
double * GetParametricCoords() override
See the vtkCell API for descriptions of these methods.
vtkTriangle::ComputeArea
double ComputeArea()
A convenience function to compute the area of a vtkTriangle.
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
vtkTriangle::BarycentricCoords
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.
vtkTriangle::GetNumberOfEdges
int GetNumberOfEdges() override
See the vtkCell API for descriptions of these methods.
Definition: vtkTriangle.h:55
vtkTriangle::Derivatives
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.
vtkTriangle::InterpolationFunctions
static void InterpolationFunctions(const double pcoords[3], double sf[3])
vtkTriangle::GetCellType
int GetCellType() override
See the vtkCell API for descriptions of these methods.
Definition: vtkTriangle.h:53
vtkX3D::points
@ points
Definition: vtkX3D.h:446
vtkX3D::length
@ length
Definition: vtkX3D.h:393
vtkX3D::value
@ value
Definition: vtkX3D.h:220
vtkX3D::center
@ center
Definition: vtkX3D.h:230
vtkX3D::index
@ index
Definition: vtkX3D.h:246
VTK_TRIANGLE
@ VTK_TRIANGLE
Definition: vtkCellType.h:51
vtkCell.h
vtkMath.h
vtkIdType
int vtkIdType
Definition: vtkType.h:315