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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 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 vtkQuadraticPyramid
* @brief cell represents a parabolic, 13-node isoparametric pyramid
*
* 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 lie
* on the edges defined by (0,1), (1,2), (2,3), (3,0), (0,4), (1,4), (2,4),
* (3,4), respectively. The parametric location of vertex #4 is [0, 0, 1].
*
* @sa
* vtkQuadraticEdge vtkQuadraticTriangle vtkQuadraticTetra
* vtkQuadraticHexahedron vtkQuadraticQuad vtkQuadraticWedge
*
* @par 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 "vtkCommonDataModelModule.h" // For export macro
#include "vtkNonLinearCell.h"
class vtkQuadraticEdge;
class vtkQuadraticQuad;
class vtkQuadraticTriangle;
class vtkTetra;
class vtkPyramid;
class vtkDoubleArray;
class VTKCOMMONDATAMODEL_EXPORT vtkQuadraticPyramid : public vtkNonLinearCell
{
public:
static vtkQuadraticPyramid* New();
vtkTypeMacro(vtkQuadraticPyramid, vtkNonLinearCell);
void PrintSelf(ostream& os, vtkIndent indent) override;
//@{
/**
* Implement the vtkCell API. See the vtkCell API for descriptions
* of these methods.
*/
int GetCellType() override { return VTK_QUADRATIC_PYRAMID; }
int GetCellDimension() override { return 3; }
int GetNumberOfEdges() override { return 8; }
int GetNumberOfFaces() override { return 5; }
vtkCell* GetEdge(int edgeId) override;
vtkCell* GetFace(int faceId) override;
//@}
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;
/**
* 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) override;
/**
* Line-edge intersection. Intersection has to occur within [0,1] parametric
* coordinates and with specified 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 quadratic pyramid in parametric coordinates.
*/
int GetParametricCenter(double pcoords[3]) override;
static void InterpolationFunctions(const double pcoords[3], double weights[13]);
static void InterpolationDerivs(const double pcoords[3], double derivs[39]);
//@{
/**
* Compute the interpolation functions/derivatives
* (aka shape functions/derivatives)
*/
void InterpolateFunctions(const double pcoords[3], double weights[13]) override
{
vtkQuadraticPyramid::InterpolationFunctions(pcoords, weights);
}
void InterpolateDerivs(const double pcoords[3], double derivs[39]) override
{
vtkQuadraticPyramid::InterpolationDerivs(pcoords, derivs);
}
//@}
//@{
/**
* Return the ids of the vertices defining edge/face (`edgeId`/`faceId').
* 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.
*/
static const vtkIdType* GetEdgeArray(vtkIdType edgeId);
static const vtkIdType* GetFaceArray(vtkIdType faceId);
//@}
/**
* Given parametric coordinates compute inverse Jacobian transformation
* matrix. Returns 9 elements of 3x3 inverse Jacobian plus interpolation
* function derivatives.
*/
void JacobianInverse(const double pcoords[3], double** inverse, double derivs[39]);
protected:
vtkQuadraticPyramid();
~vtkQuadraticPyramid() override;
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
//@{
/**
* This method adds in a point at the center of the quadrilateral face
* and then interpolates values to that point. In order to do this it
* also resizes certain member variable arrays. For safety should call
* ResizeArrays() after the results of Subdivide() are not needed anymore.
**/
void Subdivide(
vtkPointData* inPd, vtkCellData* inCd, vtkIdType cellId, vtkDataArray* cellScalars);
//@}
//@{
/**
* Resize the superclasses' member arrays to newSize where newSize should either be
* 13 or 14. Call with 13 to reset the reallocation done in the Subdivide()
* method or call with 14 to add one extra tuple for the generated point in
* Subdivice. For efficiency it only resizes the superclasses' arrays.
**/
void ResizeArrays(vtkIdType newSize);
//@}
private:
vtkQuadraticPyramid(const vtkQuadraticPyramid&) = delete;
void operator=(const vtkQuadraticPyramid&) = delete;
};
//----------------------------------------------------------------------------
// Return the center of the quadratic pyramid in parametric coordinates.
//
inline int vtkQuadraticPyramid::GetParametricCenter(double pcoords[3])
{
pcoords[0] = pcoords[1] = 6.0 / 13.0;
pcoords[2] = 3.0 / 13.0;
return 0;
}
#endif
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