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298 lines
10 KiB
C++
298 lines
10 KiB
C++
/*=========================================================================
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Program: Visualization Toolkit
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Module: vtkTriangle.h
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Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen
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All rights reserved.
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See Copyright.txt or http://www.kitware.com/Copyright.htm for details.
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This software is distributed WITHOUT ANY WARRANTY; without even
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the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
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PURPOSE. See the above copyright notice for more information.
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=========================================================================*/
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/**
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* @class vtkTriangle
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* @brief a cell that represents a triangle
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*
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* vtkTriangle is a concrete implementation of vtkCell to represent a triangle
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* located in 3-space.
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*/
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#ifndef vtkTriangle_h
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#define vtkTriangle_h
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#include "vtkCell.h"
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#include "vtkCommonDataModelModule.h" // For export macro
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#include "vtkMath.h" // Needed for inline methods
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class vtkLine;
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class vtkQuadric;
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class vtkIncrementalPointLocator;
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class VTKCOMMONDATAMODEL_EXPORT vtkTriangle : public vtkCell
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{
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public:
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static vtkTriangle* New();
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vtkTypeMacro(vtkTriangle, vtkCell);
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void PrintSelf(ostream& os, vtkIndent indent) override;
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/**
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* Get the edge specified by edgeId (range 0 to 2) and return that edge's
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* coordinates.
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*/
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vtkCell* GetEdge(int edgeId) override;
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//@{
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/**
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* See the vtkCell API for descriptions of these methods.
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*/
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int GetCellType() override { return VTK_TRIANGLE; }
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int GetCellDimension() override { return 2; }
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int GetNumberOfEdges() override { return 3; }
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int GetNumberOfFaces() override { return 0; }
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vtkCell* GetFace(int) override { return nullptr; }
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int CellBoundary(int subId, const double pcoords[3], vtkIdList* pts) override;
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void Contour(double value, vtkDataArray* cellScalars, vtkIncrementalPointLocator* locator,
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vtkCellArray* verts, vtkCellArray* lines, vtkCellArray* polys, vtkPointData* inPd,
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vtkPointData* outPd, vtkCellData* inCd, vtkIdType cellId, vtkCellData* outCd) override;
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int EvaluatePosition(const double x[3], double closestPoint[3], int& subId, double pcoords[3],
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double& dist2, double weights[]) override;
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void EvaluateLocation(int& subId, const double pcoords[3], double x[3], double* weights) override;
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int Triangulate(int index, vtkIdList* ptIds, vtkPoints* pts) override;
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void Derivatives(
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int subId, const double pcoords[3], const double* values, int dim, double* derivs) override;
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double* GetParametricCoords() override;
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//@}
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/**
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* A convenience function to compute the area of a vtkTriangle.
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*/
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double ComputeArea();
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/**
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* Clip this triangle using scalar value provided. Like contouring, except
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* that it cuts the triangle to produce other triangles.
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*/
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void Clip(double value, vtkDataArray* cellScalars, vtkIncrementalPointLocator* locator,
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vtkCellArray* polys, vtkPointData* inPd, vtkPointData* outPd, vtkCellData* inCd,
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vtkIdType cellId, vtkCellData* outCd, int insideOut) override;
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static void InterpolationFunctions(const double pcoords[3], double sf[3]);
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static void InterpolationDerivs(const double pcoords[3], double derivs[6]);
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//@{
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/**
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* Compute the interpolation functions/derivatives
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* (aka shape functions/derivatives)
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*/
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void InterpolateFunctions(const double pcoords[3], double sf[3]) override
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{
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vtkTriangle::InterpolationFunctions(pcoords, sf);
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}
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void InterpolateDerivs(const double pcoords[3], double derivs[6]) override
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{
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vtkTriangle::InterpolationDerivs(pcoords, derivs);
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}
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//@}
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/**
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* Return the ids of the vertices defining edge (`edgeId`).
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* Ids are related to the cell, not to the dataset.
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*
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* @note The return type changed. It used to be int*, it is now const vtkIdType*.
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* This is so ids are unified between vtkCell and vtkPoints, and so vtkCell ids
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* can be used as inputs in algorithms such as vtkPolygon::ComputeNormal.
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*/
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const vtkIdType* GetEdgeArray(vtkIdType edgeId);
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/**
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* Plane intersection plus in/out test on triangle. The in/out test is
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* performed using tol as the tolerance.
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*/
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int IntersectWithLine(const double p1[3], const double p2[3], double tol, double& t, double x[3],
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double pcoords[3], int& subId) override;
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/**
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* Return the center of the triangle in parametric coordinates.
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*/
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int GetParametricCenter(double pcoords[3]) override;
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/**
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* Return the distance of the parametric coordinate provided to the
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* cell. If inside the cell, a distance of zero is returned.
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*/
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double GetParametricDistance(const double pcoords[3]) override;
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/**
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* Compute the center of the triangle.
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*/
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static void TriangleCenter(
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const double p1[3], const double p2[3], const double p3[3], double center[3]);
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/**
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* Compute the area of a triangle in 3D.
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* See also vtkTriangle::ComputeArea()
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*/
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static double TriangleArea(const double p1[3], const double p2[3], const double p3[3]);
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/**
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* Compute the circumcenter (center[3]) and radius squared (method
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* return value) of a triangle defined by the three points x1, x2,
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* and x3. (Note that the coordinates are 2D. 3D points can be used
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* but the z-component will be ignored.)
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*/
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static double Circumcircle(
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const double p1[2], const double p2[2], const double p3[2], double center[2]);
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/**
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* Given a 2D point x[2], determine the barycentric coordinates of the point.
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* Barycentric coordinates are a natural coordinate system for simplices that
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* express a position as a linear combination of the vertices. For a
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* triangle, there are three barycentric coordinates (because there are
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* three vertices), and the sum of the coordinates must equal 1. If a
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* point x is inside a simplex, then all three coordinates will be strictly
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* positive. If two coordinates are zero (so the third =1), then the
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* point x is on a vertex. If one coordinates are zero, the point x is on an
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* edge. In this method, you must specify the vertex coordinates x1->x3.
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* Returns 0 if triangle is degenerate.
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*/
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static int BarycentricCoords(const double x[2], const double x1[2], const double x2[2],
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const double x3[2], double bcoords[3]);
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/**
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* Project triangle defined in 3D to 2D coordinates. Returns 0 if
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* degenerate triangle; non-zero value otherwise. Input points are x1->x3;
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* output 2D points are v1->v3.
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*/
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static int ProjectTo2D(const double x1[3], const double x2[3], const double x3[3], double v1[2],
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double v2[2], double v3[2]);
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/**
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* Compute the triangle normal from a points list, and a list of point ids
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* that index into the points list.
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*/
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static void ComputeNormal(vtkPoints* p, int numPts, const vtkIdType* pts, double n[3]);
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/**
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* Compute the triangle normal from three points.
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*/
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static void ComputeNormal(
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const double v1[3], const double v2[3], const double v3[3], double n[3]);
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/**
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* Compute the (unnormalized) triangle normal direction from three points.
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*/
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static void ComputeNormalDirection(
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const double v1[3], const double v2[3], const double v3[3], double n[3]);
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// Description:
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// Determine whether or not triangle (p1,q1,r1) intersects triangle
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// (p2,q2,r2). This method is adapted from Olivier Devillers, Philippe Guigue.
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// Faster Triangle-Triangle Intersection Tests. RR-4488, IN-RIA. 2002.
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// <inria-00072100>.
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static int TrianglesIntersect(const double p1[3], const double q1[3], const double r1[3],
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const double p2[3], const double q2[3], const double r2[3]);
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// Description:
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// Given a point x, determine whether it is inside (within the
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// tolerance squared, tol2) the triangle defined by the three
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// coordinate values p1, p2, p3. Method is via comparing dot products.
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// (Note: in current implementation the tolerance only works in the
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// neighborhood of the three vertices of the triangle.
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static int PointInTriangle(const double x[3], const double x1[3], const double x2[3],
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const double x3[3], const double tol2);
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//@{
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/**
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* Calculate the error quadric for this triangle. Return the
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* quadric as a 4x4 matrix or a vtkQuadric. (from Peter
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* Lindstrom's Siggraph 2000 paper, "Out-of-Core Simplification of
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* Large Polygonal Models")
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*/
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static void ComputeQuadric(
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const double x1[3], const double x2[3], const double x3[3], double quadric[4][4]);
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static void ComputeQuadric(
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const double x1[3], const double x2[3], const double x3[3], vtkQuadric* quadric);
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//@}
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/**
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* Get the centroid of the triangle.
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* pointIds can be nullptr if ids are {0, 1, 2}
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*/
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static bool ComputeCentroid(vtkPoints* points, const vtkIdType* pointIds, double centroid[3]);
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protected:
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vtkTriangle();
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~vtkTriangle() override;
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vtkLine* Line;
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private:
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vtkTriangle(const vtkTriangle&) = delete;
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void operator=(const vtkTriangle&) = delete;
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};
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//----------------------------------------------------------------------------
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inline int vtkTriangle::GetParametricCenter(double pcoords[3])
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{
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pcoords[0] = pcoords[1] = 1. / 3;
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pcoords[2] = 0.0;
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return 0;
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}
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//----------------------------------------------------------------------------
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inline void vtkTriangle::ComputeNormalDirection(
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const double v1[3], const double v2[3], const double v3[3], double n[3])
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{
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double ax, ay, az, bx, by, bz;
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// order is important!!! maintain consistency with triangle vertex order
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ax = v3[0] - v2[0];
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ay = v3[1] - v2[1];
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az = v3[2] - v2[2];
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bx = v1[0] - v2[0];
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by = v1[1] - v2[1];
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bz = v1[2] - v2[2];
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n[0] = (ay * bz - az * by);
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n[1] = (az * bx - ax * bz);
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n[2] = (ax * by - ay * bx);
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}
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//----------------------------------------------------------------------------
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inline void vtkTriangle::ComputeNormal(
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const double v1[3], const double v2[3], const double v3[3], double n[3])
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{
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double length;
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vtkTriangle::ComputeNormalDirection(v1, v2, v3, n);
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if ((length = sqrt((n[0] * n[0] + n[1] * n[1] + n[2] * n[2]))) != 0.0)
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{
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n[0] /= length;
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n[1] /= length;
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n[2] /= length;
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}
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}
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//----------------------------------------------------------------------------
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inline void vtkTriangle::TriangleCenter(
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const double p1[3], const double p2[3], const double p3[3], double center[3])
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{
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center[0] = (p1[0] + p2[0] + p3[0]) / 3.0;
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center[1] = (p1[1] + p2[1] + p3[1]) / 3.0;
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center[2] = (p1[2] + p2[2] + p3[2]) / 3.0;
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}
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//----------------------------------------------------------------------------
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inline double vtkTriangle::TriangleArea(const double p1[3], const double p2[3], const double p3[3])
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{
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double n[3];
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vtkTriangle::ComputeNormalDirection(p1, p2, p3, n);
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return 0.5 * vtkMath::Norm(n);
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}
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#endif
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