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/*=========================================================================
Program: Visualization Toolkit
Module: vtkTetra.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.
=========================================================================*/
// .NAME vtkTetra - a 3D cell that represents a tetrahedron
// .SECTION Description
// vtkTetra is a concrete implementation of vtkCell to represent a 3D
// tetrahedron. vtkTetra uses the standard isoparametric shape functions
// for a linear tetrahedron. The tetrahedron is defined by the four points
// (0-3); where (0,1,2) is the base of the tetrahedron which, using the
// right hand rule, forms a triangle whose normal points in the direction
// of the fourth point.
// .SECTION See Also
// vtkConvexPointSet vtkHexahedron vtkPyramid vtkVoxel vtkWedge
#ifndef __vtkTetra_h
#define __vtkTetra_h
#include "vtkCell3D.h"
class vtkLine;
class vtkTriangle;
class vtkUnstructuredGrid;
class vtkIncrementalPointLocator;
class VTK_FILTERING_EXPORT vtkTetra : public vtkCell3D
{
public:
static vtkTetra *New();
vtkTypeMacro(vtkTetra,vtkCell3D);
void PrintSelf(ostream& os, vtkIndent indent);
// Description:
// See vtkCell3D API for description of these methods.
virtual void GetEdgePoints(int edgeId, int* &pts);
virtual void GetFacePoints(int faceId, int* &pts);
// Description:
// See the vtkCell API for descriptions of these methods.
int GetCellType() {return VTK_TETRA;}
int GetNumberOfEdges() {return 6;}
int GetNumberOfFaces() {return 4;}
vtkCell *GetEdge(int edgeId);
vtkCell *GetFace(int faceId);
void Contour(double value, vtkDataArray *cellScalars,
vtkIncrementalPointLocator *locator, vtkCellArray *verts,
vtkCellArray *lines, vtkCellArray *polys,
vtkPointData *inPd, vtkPointData *outPd,
vtkCellData *inCd, vtkIdType cellId, vtkCellData *outCd);
void Clip(double value, vtkDataArray *cellScalars,
vtkIncrementalPointLocator *locator, vtkCellArray *connectivity,
vtkPointData *inPd, vtkPointData *outPd,
vtkCellData *inCd, vtkIdType cellId, vtkCellData *outCd,
int insideOut);
int EvaluatePosition(double x[3], double* closestPoint,
int& subId, double pcoords[3],
double& dist2, double *weights);
void EvaluateLocation(int& subId, double pcoords[3], double x[3],
double *weights);
int IntersectWithLine(double p1[3], double p2[3], double tol, double& t,
double x[3], double pcoords[3], int& subId);
int Triangulate(int index, vtkIdList *ptIds, vtkPoints *pts);
void Derivatives(int subId, double pcoords[3], double *values,
int dim, double *derivs);
virtual double *GetParametricCoords();
// Description:
// Returns the set of points that are on the boundary of the tetrahedron that
// are closest parametrically to the point specified. This may include faces,
// edges, or vertices.
int CellBoundary(int subId, double pcoords[3], vtkIdList *pts);
// Description:
// Return the center of the tetrahedron in parametric coordinates.
int GetParametricCenter(double pcoords[3]);
// Description:
// Return the distance of the parametric coordinate provided to the
// cell. If inside the cell, a distance of zero is returned.
double GetParametricDistance(double pcoords[3]);
// Description:
// Compute the center of the tetrahedron,
static void TetraCenter(double p1[3], double p2[3], double p3[3], double p4[3],
double center[3]);
// Description:
// Compute the circumcenter (center[3]) and radius squared (method
// return value) of a tetrahedron defined by the four points x1, x2,
// x3, and x4.
static double Circumsphere(double p1[3], double p2[3], double p3[3],
double p4[3], double center[3]);
// Description:
// Compute the center (center[3]) and radius (method return value) of
// a sphere that just fits inside the faces of a tetrahedron defined
// by the four points x1, x2, x3, and x4.
static double Insphere(double p1[3], double p2[3], double p3[3],
double p4[3], double center[3]);
// Description:
// Given a 3D point x[3], 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
// tetrahedron, there are four barycentric coordinates (because there are
// four vertices), and the sum of the coordinates must equal 1. If a
// point x is inside a simplex, then all four coordinates will be strictly
// positive. If three coordinates are zero (so the fourth =1), then the
// point x is on a vertex. If two coordinates are zero, the point x is on an
// edge (and so on). In this method, you must specify the vertex coordinates
// x1->x4. Returns 0 if tetrahedron is degenerate.
static int BarycentricCoords(double x[3], double x1[3], double x2[3],
double x3[3], double x4[3], double bcoords[4]);
// Description:
// Compute the volume of a tetrahedron defined by the four points
// p1, p2, p3, and p4.
static double ComputeVolume(double p1[3], double p2[3], double p3[3],
double p4[3]);
// Description:
// Given parametric coordinates compute inverse Jacobian transformation
// matrix. Returns 9 elements of 3x3 inverse Jacobian plus interpolation
// function derivatives. Returns 0 if no inverse exists.
int JacobianInverse(double **inverse, double derivs[12]);
// Description:
// @deprecated Replaced by vtkTetra::InterpolateFunctions as of VTK 5.2
static void InterpolationFunctions(double pcoords[3], double weights[4]);
// Description:
// @deprecated Replaced by vtkTetra::InterpolateDerivs as of VTK 5.2
static void InterpolationDerivs(double pcoords[3], double derivs[12]);
// Description:
// Compute the interpolation functions/derivatives
// (aka shape functions/derivatives)
virtual void InterpolateFunctions(double pcoords[3], double weights[4])
{
vtkTetra::InterpolationFunctions(pcoords,weights);
}
virtual void InterpolateDerivs(double pcoords[3], double derivs[12])
{
vtkTetra::InterpolationDerivs(pcoords,derivs);
}
// Description:
// Return the ids of the vertices defining edge/face (`edgeId`/`faceId').
// Ids are related to the cell, not to the dataset.
static int *GetEdgeArray(int edgeId);
static int *GetFaceArray(int faceId);
protected:
vtkTetra();
~vtkTetra();
vtkLine *Line;
vtkTriangle *Triangle;
private:
vtkTetra(const vtkTetra&); // Not implemented.
void operator=(const vtkTetra&); // Not implemented.
};
inline int vtkTetra::GetParametricCenter(double pcoords[3])
{
pcoords[0] = pcoords[1] = pcoords[2] = 0.25;
return 0;
}
#endif