/*========================================================================= Program: Visualization Toolkit Module: vtkTriangle.h Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen All rights reserved. See Copyright.txt or http://www.kitware.com/Copyright.htm for details. This software is distributed WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the above copyright notice for more information. =========================================================================*/ /** * @class vtkTriangle * @brief a cell that represents a triangle * * vtkTriangle is a concrete implementation of vtkCell to represent a triangle * located in 3-space. */ #ifndef vtkTriangle_h #define vtkTriangle_h #include "vtkCell.h" #include "vtkCommonDataModelModule.h" // For export macro #include "vtkMath.h" // Needed for inline methods class vtkLine; class vtkQuadric; class vtkIncrementalPointLocator; class VTKCOMMONDATAMODEL_EXPORT vtkTriangle : public vtkCell { public: static vtkTriangle* New(); vtkTypeMacro(vtkTriangle, vtkCell); void PrintSelf(ostream& os, vtkIndent indent) override; /** * Get the edge specified by edgeId (range 0 to 2) and return that edge's * coordinates. */ vtkCell* GetEdge(int edgeId) override; //@{ /** * See the vtkCell API for descriptions of these methods. */ int GetCellType() override { return VTK_TRIANGLE; } int GetCellDimension() override { return 2; } int GetNumberOfEdges() override { return 3; } int GetNumberOfFaces() override { return 0; } vtkCell* GetFace(int) override { return nullptr; } int CellBoundary(int subId, const double pcoords[3], vtkIdList* pts) override; 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; int EvaluatePosition(const double x[3], double closestPoint[3], int& subId, double pcoords[3], double& dist2, double weights[]) override; void EvaluateLocation(int& subId, const double pcoords[3], double x[3], double* weights) override; int Triangulate(int index, vtkIdList* ptIds, vtkPoints* pts) override; void Derivatives( int subId, const double pcoords[3], const double* values, int dim, double* derivs) override; double* GetParametricCoords() override; //@} /** * A convenience function to compute the area of a vtkTriangle. */ double ComputeArea(); /** * Clip this triangle using scalar value provided. Like contouring, except * that it cuts the triangle to produce other triangles. */ void Clip(double value, vtkDataArray* cellScalars, vtkIncrementalPointLocator* locator, vtkCellArray* polys, vtkPointData* inPd, vtkPointData* outPd, vtkCellData* inCd, vtkIdType cellId, vtkCellData* outCd, int insideOut) override; static void InterpolationFunctions(const double pcoords[3], double sf[3]); static void InterpolationDerivs(const double pcoords[3], double derivs[6]); //@{ /** * Compute the interpolation functions/derivatives * (aka shape functions/derivatives) */ void InterpolateFunctions(const double pcoords[3], double sf[3]) override { vtkTriangle::InterpolationFunctions(pcoords, sf); } void InterpolateDerivs(const double pcoords[3], double derivs[6]) override { vtkTriangle::InterpolationDerivs(pcoords, derivs); } //@} /** * Return the ids of the vertices defining edge (`edgeId`). * Ids are related to the cell, not to the dataset. * * @note The return type changed. It used to be int*, it is now const vtkIdType*. * This is so ids are unified between vtkCell and vtkPoints, and so vtkCell ids * can be used as inputs in algorithms such as vtkPolygon::ComputeNormal. */ const vtkIdType* GetEdgeArray(vtkIdType edgeId); /** * Plane intersection plus in/out test on triangle. The in/out test is * performed using tol as the tolerance. */ int IntersectWithLine(const double p1[3], const double p2[3], double tol, double& t, double x[3], double pcoords[3], int& subId) override; /** * Return the center of the triangle in parametric coordinates. */ int GetParametricCenter(double pcoords[3]) override; /** * Return the distance of the parametric coordinate provided to the * cell. If inside the cell, a distance of zero is returned. */ double GetParametricDistance(const double pcoords[3]) override; /** * Compute the center of the triangle. */ static void TriangleCenter( const double p1[3], const double p2[3], const double p3[3], double center[3]); /** * Compute the area of a triangle in 3D. * See also vtkTriangle::ComputeArea() */ static double TriangleArea(const double p1[3], const double p2[3], const double p3[3]); /** * Compute the circumcenter (center[3]) and radius squared (method * return value) of a triangle defined by the three points x1, x2, * and x3. (Note that the coordinates are 2D. 3D points can be used * but the z-component will be ignored.) */ static double Circumcircle( const double p1[2], const double p2[2], const double p3[2], double center[2]); /** * Given a 2D point x[2], determine the barycentric coordinates of the point. * Barycentric coordinates are a natural coordinate system for simplices that * express a position as a linear combination of the vertices. For a * triangle, there are three barycentric coordinates (because there are * three vertices), and the sum of the coordinates must equal 1. If a * point x is inside a simplex, then all three coordinates will be strictly * positive. If two coordinates are zero (so the third =1), then the * point x is on a vertex. If one coordinates are zero, the point x is on an * edge. In this method, you must specify the vertex coordinates x1->x3. * Returns 0 if triangle is degenerate. */ static int BarycentricCoords(const double x[2], const double x1[2], const double x2[2], const double x3[2], double bcoords[3]); /** * Project triangle defined in 3D to 2D coordinates. Returns 0 if * degenerate triangle; non-zero value otherwise. Input points are x1->x3; * output 2D points are v1->v3. */ static int ProjectTo2D(const double x1[3], const double x2[3], const double x3[3], double v1[2], double v2[2], double v3[2]); /** * Compute the triangle normal from a points list, and a list of point ids * that index into the points list. */ static void ComputeNormal(vtkPoints* p, int numPts, const vtkIdType* pts, double n[3]); /** * Compute the triangle normal from three points. */ static void ComputeNormal( const double v1[3], const double v2[3], const double v3[3], double n[3]); /** * Compute the (unnormalized) triangle normal direction from three points. */ static void ComputeNormalDirection( const double v1[3], const double v2[3], const double v3[3], double n[3]); // Description: // Determine whether or not triangle (p1,q1,r1) intersects triangle // (p2,q2,r2). This method is adapted from Olivier Devillers, Philippe Guigue. // Faster Triangle-Triangle Intersection Tests. RR-4488, IN-RIA. 2002. // . 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]); // Description: // Given a point x, determine whether it is inside (within the // tolerance squared, tol2) the triangle defined by the three // coordinate values p1, p2, p3. Method is via comparing dot products. // (Note: in current implementation the tolerance only works in the // neighborhood of the three vertices of the triangle. static int PointInTriangle(const double x[3], const double x1[3], const double x2[3], const double x3[3], const double tol2); //@{ /** * Calculate the error quadric for this triangle. Return the * quadric as a 4x4 matrix or a vtkQuadric. (from Peter * Lindstrom's Siggraph 2000 paper, "Out-of-Core Simplification of * Large Polygonal Models") */ static void ComputeQuadric( const double x1[3], const double x2[3], const double x3[3], double quadric[4][4]); static void ComputeQuadric( const double x1[3], const double x2[3], const double x3[3], vtkQuadric* quadric); //@} /** * Get the centroid of the triangle. * pointIds can be nullptr if ids are {0, 1, 2} */ static bool ComputeCentroid(vtkPoints* points, const vtkIdType* pointIds, double centroid[3]); protected: vtkTriangle(); ~vtkTriangle() override; vtkLine* Line; private: vtkTriangle(const vtkTriangle&) = delete; void operator=(const vtkTriangle&) = delete; }; //---------------------------------------------------------------------------- inline int vtkTriangle::GetParametricCenter(double pcoords[3]) { pcoords[0] = pcoords[1] = 1. / 3; pcoords[2] = 0.0; return 0; } //---------------------------------------------------------------------------- inline void vtkTriangle::ComputeNormalDirection( const double v1[3], const double v2[3], const double v3[3], double n[3]) { double ax, ay, az, bx, by, bz; // order is important!!! maintain consistency with triangle vertex order ax = v3[0] - v2[0]; ay = v3[1] - v2[1]; az = v3[2] - v2[2]; bx = v1[0] - v2[0]; by = v1[1] - v2[1]; bz = v1[2] - v2[2]; n[0] = (ay * bz - az * by); n[1] = (az * bx - ax * bz); n[2] = (ax * by - ay * bx); } //---------------------------------------------------------------------------- inline void vtkTriangle::ComputeNormal( const double v1[3], const double v2[3], const double v3[3], double n[3]) { double length; vtkTriangle::ComputeNormalDirection(v1, v2, v3, n); if ((length = sqrt((n[0] * n[0] + n[1] * n[1] + n[2] * n[2]))) != 0.0) { n[0] /= length; n[1] /= length; n[2] /= length; } } //---------------------------------------------------------------------------- inline void vtkTriangle::TriangleCenter( const double p1[3], const double p2[3], const double p3[3], double center[3]) { center[0] = (p1[0] + p2[0] + p3[0]) / 3.0; center[1] = (p1[1] + p2[1] + p3[1]) / 3.0; center[2] = (p1[2] + p2[2] + p3[2]) / 3.0; } //---------------------------------------------------------------------------- inline double vtkTriangle::TriangleArea(const double p1[3], const double p2[3], const double p3[3]) { double n[3]; vtkTriangle::ComputeNormalDirection(p1, p2, p3, n); return 0.5 * vtkMath::Norm(n); } #endif