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Program: Visualization Toolkit
Module: vtkQuadraticPyramid.h
Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen
All rights reserved.
See Copyright.txt or for details.
This software is distributed WITHOUT ANY WARRANTY; without even
PURPOSE. See the above copyright notice for more information.
// .NAME vtkQuadraticPyramid - cell represents a parabolic, 13-node isoparametric pyramid
// .SECTION Description
// vtkQuadraticPyramid is a concrete implementation of vtkNonLinearCell to
// represent a three-dimensional, 13-node isoparametric parabolic
// pyramid. The interpolation is the standard finite element, quadratic
// isoparametric shape function. The cell includes a mid-edge node. The
// ordering of the thirteen points defining the cell is point ids (0-4,5-12)
// where point ids 0-4 are the five corner vertices of the pyramid; followed
// by eight midedge nodes (5-12). Note that these midedge nodes correspond lie
// on the edges defined by (0,1), (1,2), (2,3), (3,0), (0,4), (1,4), (2,4),
// (3,4).
// .SECTION See Also
// vtkQuadraticEdge vtkQuadraticTriangle vtkQuadraticTetra
// vtkQuadraticHexahedron vtkQuadraticQuad vtkQuadraticWedge
// .SECTION Thanks
// The shape functions and derivatives could be implemented thanks to
// the report Pyramid Solid Elements Linear and Quadratic Iso-P Models
// From Center For Aerospace Structures
#ifndef __vtkQuadraticPyramid_h
#define __vtkQuadraticPyramid_h
#include "vtkNonLinearCell.h"
class vtkQuadraticEdge;
class vtkQuadraticQuad;
class vtkQuadraticTriangle;
class vtkTetra;
class vtkPyramid;
class vtkDoubleArray;
class VTK_FILTERING_EXPORT vtkQuadraticPyramid : public vtkNonLinearCell
static vtkQuadraticPyramid *New();
void PrintSelf(ostream& os, vtkIndent indent);
// Description:
// Implement the vtkCell API. See the vtkCell API for descriptions
// of these methods.
int GetCellType() {return VTK_QUADRATIC_PYRAMID;};
int GetCellDimension() {return 3;}
int GetNumberOfEdges() {return 8;}
int GetNumberOfFaces() {return 5;}
vtkCell *GetEdge(int edgeId);
vtkCell *GetFace(int faceId);
int CellBoundary(int subId, double pcoords[3], vtkIdList *pts);
void Contour(double value, vtkDataArray *cellScalars,
vtkIncrementalPointLocator *locator, vtkCellArray *verts,
vtkCellArray *lines, vtkCellArray *polys,
vtkPointData *inPd, vtkPointData *outPd,
vtkCellData *inCd, vtkIdType cellId, vtkCellData *outCd);
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 Triangulate(int index, vtkIdList *ptIds, vtkPoints *pts);
void Derivatives(int subId, double pcoords[3], double *values,
int dim, double *derivs);
virtual double *GetParametricCoords();
// Description:
// Clip this quadratic triangle using scalar value provided. Like
// contouring, except that it cuts the triangle to produce linear
// triangles.
void Clip(double value, vtkDataArray *cellScalars,
vtkIncrementalPointLocator *locator, vtkCellArray *tets,
vtkPointData *inPd, vtkPointData *outPd,
vtkCellData *inCd, vtkIdType cellId, vtkCellData *outCd,
int insideOut);
// Description:
// Line-edge intersection. Intersection has to occur within [0,1] parametric
// coordinates and with specified tolerance.
int IntersectWithLine(double p1[3], double p2[3], double tol, double& t,
double x[3], double pcoords[3], int& subId);
// Description:
// Return the center of the quadratic pyramid in parametric coordinates.
int GetParametricCenter(double pcoords[3]);
// Description:
// @deprecated Replaced by vtkQuadraticPyramid::InterpolateFunctions as of VTK 5.2
static void InterpolationFunctions(double pcoords[3], double weights[13]);
// Description:
// @deprecated Replaced by vtkQuadraticPyramid::InterpolateDerivs as of VTK 5.2
static void InterpolationDerivs(double pcoords[3], double derivs[39]);
// Description:
// Compute the interpolation functions/derivatives
// (aka shape functions/derivatives)
virtual void InterpolateFunctions(double pcoords[3], double weights[13])
virtual void InterpolateDerivs(double pcoords[3], double derivs[39])
// 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);
// Description:
// Given parametric coordinates compute inverse Jacobian transformation
// matrix. Returns 9 elements of 3x3 inverse Jacobian plus interpolation
// function derivatives.
void JacobianInverse(double pcoords[3], double **inverse, double derivs[39]);
vtkQuadraticEdge *Edge;
vtkQuadraticTriangle *TriangleFace;
vtkQuadraticQuad *Face;
vtkTetra *Tetra;
vtkPyramid *Pyramid;
vtkPointData *PointData;
vtkCellData *CellData;
vtkDoubleArray *CellScalars;
vtkDoubleArray *Scalars; //used to avoid New/Delete in contouring/clipping
void Subdivide(vtkPointData *inPd, vtkCellData *inCd, vtkIdType cellId,
vtkDataArray *cellScalars);
vtkQuadraticPyramid(const vtkQuadraticPyramid&); // Not implemented.
void operator=(const vtkQuadraticPyramid&); // Not implemented.
// Return the center of the quadratic pyramid in parametric coordinates.
inline int vtkQuadraticPyramid::GetParametricCenter(double pcoords[3])
pcoords[0] = pcoords[1] = 6./13;
pcoords[2] = 3./13;
return 0;