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/*=========================================================================
Program: Visualization Toolkit
Module: vtkQuadraticPyramid.cxx
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.
=========================================================================*/
#include "vtkQuadraticPyramid.h"
#include "vtkObjectFactory.h"
#include "vtkCellData.h"
#include "vtkDoubleArray.h"
#include "vtkTetra.h"
#include "vtkPyramid.h"
#include "vtkMath.h"
#include "vtkPointData.h"
#include "vtkQuadraticEdge.h"
#include "vtkQuadraticQuad.h"
#include "vtkQuadraticTriangle.h"
#include "vtkPoints.h"
vtkStandardNewMacro(vtkQuadraticPyramid);
//----------------------------------------------------------------------------
// Construct the pyramid with 13 points + 1 extra point for internal
// computation.
//
vtkQuadraticPyramid::vtkQuadraticPyramid()
{
// At creation time the cell looks like it has 14 points (during interpolation)
// We initially allocate for 14.
this->Points->SetNumberOfPoints(14);
this->PointIds->SetNumberOfIds(14);
for (int i = 0; i < 14; i++)
{
this->Points->SetPoint(i, 0.0, 0.0, 0.0);
this->PointIds->SetId(i,0);
}
this->Points->SetNumberOfPoints(13);
this->PointIds->SetNumberOfIds(13);
this->Edge = vtkQuadraticEdge::New();
this->Face = vtkQuadraticQuad::New();
this->TriangleFace = vtkQuadraticTriangle::New();
this->Tetra = vtkTetra::New();
this->Pyramid = vtkPyramid::New();
this->PointData = vtkPointData::New();
this->CellData = vtkCellData::New();
this->CellScalars = vtkDoubleArray::New();
this->CellScalars->SetNumberOfTuples(14);
this->Scalars = vtkDoubleArray::New();
this->Scalars->SetNumberOfTuples(5); //num of vertices
}
//----------------------------------------------------------------------------
vtkQuadraticPyramid::~vtkQuadraticPyramid()
{
this->Edge->Delete();
this->Face->Delete();
this->TriangleFace->Delete();
this->Tetra->Delete();
this->Pyramid->Delete();
this->PointData->Delete();
this->CellData->Delete();
this->Scalars->Delete();
this->CellScalars->Delete();
}
//----------------------------------------------------------------------------
static int LinearPyramids[10][5] = { {0,5,13,8,9},
{5,1,6,13,10},
{8,13,7,3,12},
{13,6,2,7,11},
{9,10,11,12,4},
{9,12,11,10,13},
{5,10,9,13,0},
{6,11,10,13,0},
{7,12,11,13,0},
{8,9,12,13,0} };
static int PyramidFaces[5][8] = { {0,3,2,1,8,7,6,5},
{0,1,4,5,10,9,0,0},
{1,2,4,6,11,10,0,0},
{2,3,4,7,12,11,0,0},
{3,0,4,8,9,12,0,0}};
static int PyramidEdges[8][3] = { {0,1,5}, {1,2,6}, {2,3,7},
{3,0,8},{0,4,9},{1,4,10},
{2,4,11}, {3,4,12} };
static double MidPoints[1][3] = { {0.5,0.5,0.0} };
//----------------------------------------------------------------------------
int *vtkQuadraticPyramid::GetEdgeArray(int edgeId)
{
return PyramidEdges[edgeId];
}
//----------------------------------------------------------------------------
int *vtkQuadraticPyramid::GetFaceArray(int faceId)
{
return PyramidFaces[faceId];
}
//----------------------------------------------------------------------------
vtkCell *vtkQuadraticPyramid::GetEdge(int edgeId)
{
edgeId = (edgeId < 0 ? 0 : (edgeId > 7 ? 7 : edgeId ));
for (int i=0; i<3; i++)
{
this->Edge->PointIds->SetId(i,this->PointIds->GetId(PyramidEdges[edgeId][i]));
this->Edge->Points->SetPoint(i,this->Points->GetPoint(PyramidEdges[edgeId][i]));
}
return this->Edge;
}
//----------------------------------------------------------------------------
vtkCell *vtkQuadraticPyramid::GetFace(int faceId)
{
faceId = (faceId < 0 ? 0 : (faceId > 4 ? 4 : faceId ));
// load point id's and coordinates
// be carefull with the first one:
if(faceId > 0)
{
for (int i=0; i<6; i++)
{
this->TriangleFace->PointIds->SetId(i,this->PointIds->GetId(PyramidFaces[faceId][i]));
this->TriangleFace->Points->SetPoint(i,this->Points->GetPoint(PyramidFaces[faceId][i]));
}
return this->TriangleFace;
}
else
{
for (int i=0; i<8; i++)
{
this->Face->PointIds->SetId(i,this->PointIds->GetId(PyramidFaces[faceId][i]));
this->Face->Points->SetPoint(i,this->Points->GetPoint(PyramidFaces[faceId][i]));
}
return this->Face;
}
}
//----------------------------------------------------------------------------
static const double VTK_DIVERGED = 1.e6;
static const int VTK_PYRAMID_MAX_ITERATION=10;
static const double VTK_PYRAMID_CONVERGED=1.e-03;
int vtkQuadraticPyramid::EvaluatePosition(double* x,
double* closestPoint,
int& subId, double pcoords[3],
double& dist2, double *weights)
{
int iteration, converged;
double params[3];
double fcol[3], rcol[3], scol[3], tcol[3];
int i, j;
double d, pt[3];
double derivs[3*13];
// set initial position for Newton's method
subId = 0;
pcoords[0] = pcoords[1] = pcoords[2] = params[0] = params[1] = params[2]=0.5;
// enter iteration loop
for (iteration=converged=0;
!converged && (iteration < VTK_PYRAMID_MAX_ITERATION); iteration++)
{
// calculate element interpolation functions and derivatives
this->InterpolationFunctions(pcoords, weights);
this->InterpolationDerivs(pcoords, derivs);
// calculate newton functions
for (i=0; i<3; i++)
{
fcol[i] = rcol[i] = scol[i] = tcol[i] = 0.0;
}
for (i=0; i<13; i++)
{
this->Points->GetPoint(i, pt);
for (j=0; j<3; j++)
{
fcol[j] += pt[j] * weights[i];
rcol[j] += pt[j] * derivs[i];
scol[j] += pt[j] * derivs[i+13];
tcol[j] += pt[j] * derivs[i+26];
}
}
for (i=0; i<3; i++)
{
fcol[i] -= x[i];
}
// compute determinants and generate improvements
d=vtkMath::Determinant3x3(rcol,scol,tcol);
if ( fabs(d) < 1.e-20)
{
return -1;
}
pcoords[0] = params[0] - 0.5*vtkMath::Determinant3x3 (fcol,scol,tcol) / d;
pcoords[1] = params[1] - 0.5*vtkMath::Determinant3x3 (rcol,fcol,tcol) / d;
pcoords[2] = params[2] - 0.5*vtkMath::Determinant3x3 (rcol,scol,fcol) / d;
// check for convergence
if ( ((fabs(pcoords[0]-params[0])) < VTK_PYRAMID_CONVERGED) &&
((fabs(pcoords[1]-params[1])) < VTK_PYRAMID_CONVERGED) &&
((fabs(pcoords[2]-params[2])) < VTK_PYRAMID_CONVERGED) )
{
converged = 1;
}
// Test for bad divergence (S.Hirschberg 11.12.2001)
else if ((fabs(pcoords[0]) > VTK_DIVERGED) ||
(fabs(pcoords[1]) > VTK_DIVERGED) ||
(fabs(pcoords[2]) > VTK_DIVERGED))
{
return -1;
}
// if not converged, repeat
else
{
params[0] = pcoords[0];
params[1] = pcoords[1];
params[2] = pcoords[2];
}
}
// if not converged, set the parametric coordinates to arbitrary values
// outside of element
if ( !converged )
{
return -1;
}
this->InterpolationFunctions(pcoords, weights);
if ( pcoords[0] >= -0.001 && pcoords[0] <= 1.001 &&
pcoords[1] >= -0.001 && pcoords[1] <= 1.001 &&
pcoords[2] >= -0.001 && pcoords[2] <= 1.001 )
{
if (closestPoint)
{
closestPoint[0] = x[0]; closestPoint[1] = x[1]; closestPoint[2] = x[2];
dist2 = 0.0; //inside pyramid
}
return 1;
}
else
{
double pc[3], w[13];
if (closestPoint)
{
for (i=0; i<3; i++) //only approximate, not really true for warped hexa
{
if (pcoords[i] < 0.0)
{
pc[i] = 0.0;
}
else if (pcoords[i] > 1.0)
{
pc[i] = 1.0;
}
else
{
pc[i] = pcoords[i];
}
}
this->EvaluateLocation(subId, pc, closestPoint,
static_cast<double *>(w));
dist2 = vtkMath::Distance2BetweenPoints(closestPoint,x);
}
return 0;
}
}
//----------------------------------------------------------------------------
void vtkQuadraticPyramid::EvaluateLocation(int& vtkNotUsed(subId),
double pcoords[3],
double x[3], double *weights)
{
int i, j;
double pt[3];
this->InterpolationFunctions(pcoords, weights);
x[0] = x[1] = x[2] = 0.0;
for (i=0; i<13; i++)
{
this->Points->GetPoint(i, pt);
for (j=0; j<3; j++)
{
x[j] += pt[j] * weights[i];
}
}
}
//----------------------------------------------------------------------------
int vtkQuadraticPyramid::CellBoundary(int subId, double pcoords[3],
vtkIdList *pts)
{
return this->Pyramid->CellBoundary(subId, pcoords, pts);
}
//----------------------------------------------------------------------------
void vtkQuadraticPyramid::Subdivide(vtkPointData *inPd, vtkCellData *inCd,
vtkIdType cellId, vtkDataArray *cellScalars)
{
int numMidPts, i, j;
double weights[13];
double x[3];
double s;
//Copy point and cell attribute data, first make sure it's empty:
this->PointData->Initialize();
this->CellData->Initialize();
// Make sure to copy ALL arrays. These field data have to be
// identical to the input field data. Otherwise, CopyData
// that occurs later may not work because the output field
// data was initialized (CopyAllocate) with the input field
// data.
this->PointData->CopyAllOn();
this->CellData->CopyAllOn();
this->PointData->CopyAllocate(inPd,14);
this->CellData->CopyAllocate(inCd,6);
for (i=0; i<13; i++)
{
this->PointData->CopyData(inPd,this->PointIds->GetId(i),i);
this->CellScalars->SetValue( i, cellScalars->GetTuple1(i));
}
for (i=0; i<6; i++)
{
this->CellData->CopyData(inCd,cellId,i);
}
//Interpolate new values
double p[3];
for ( numMidPts=0; numMidPts < 1; numMidPts++ )
{
this->InterpolationFunctions(MidPoints[numMidPts], weights);
x[0] = x[1] = x[2] = 0.0;
s = 0.0;
for (i=0; i<13; i++)
{
this->Points->GetPoint(i, p);
for (j=0; j<3; j++)
{
x[j] += p[j] * weights[i];
}
s += cellScalars->GetTuple1(i) * weights[i];
}
this->Points->SetPoint(13+numMidPts,x);
this->CellScalars->SetValue(13+numMidPts,s);
this->PointData->InterpolatePoint(inPd, 13+numMidPts,
this->PointIds, weights);
}
}
//----------------------------------------------------------------------------
void vtkQuadraticPyramid::Contour(double value,
vtkDataArray* cellScalars,
vtkIncrementalPointLocator* locator,
vtkCellArray *verts,
vtkCellArray* lines,
vtkCellArray* polys,
vtkPointData* inPd,
vtkPointData* outPd,
vtkCellData* inCd,
vtkIdType cellId,
vtkCellData* outCd)
{
int i;
//subdivide into 6 linear pyramids
this->Subdivide(inPd,inCd,cellId,cellScalars);
//contour each linear pyramid separately
this->Scalars->SetNumberOfTuples(5); //num of vertices
for (i=0; i<6; i++) //for each pyramid
{
for (int j=0; j<5; j++) //for each point of pyramid
{
this->Pyramid->Points->SetPoint(j,this->Points->GetPoint(LinearPyramids[i][j]));
this->Pyramid->PointIds->SetId(j,LinearPyramids[i][j]);
this->Scalars->SetValue(j,this->CellScalars->GetValue(LinearPyramids[i][j]));
}
this->Pyramid->Contour(value,this->Scalars,locator,verts,lines,polys,
this->PointData,outPd,this->CellData,cellId,outCd);
}
//contour each linear tetra separately
this->Scalars->SetNumberOfTuples(4); //num of vertices
for (i=6; i<10; i++) //for each tetra
{
for (int j=0; j<4; j++) //for each point of tetra
{
this->Tetra->Points->SetPoint(j,this->Points->GetPoint(LinearPyramids[i][j]));
this->Tetra->PointIds->SetId(j,LinearPyramids[i][j]);
this->Scalars->SetTuple(j,this->CellScalars->GetTuple(LinearPyramids[i][j]));
}
this->Tetra->Contour(value,this->Scalars,locator,verts,lines,polys,
this->PointData,outPd,this->CellData,cellId,outCd);
}
}
//----------------------------------------------------------------------------
// Line-hex intersection. Intersection has to occur within [0,1] parametric
// coordinates and with specified tolerance.
//
int vtkQuadraticPyramid::IntersectWithLine(double* p1, double* p2,
double tol, double& t,
double* x, double* pcoords, int& subId)
{
int intersection=0;
double tTemp;
double pc[3], xTemp[3];
int faceNum;
int inter;
t = VTK_DOUBLE_MAX;
for (faceNum=0; faceNum<5; faceNum++)
{
// We have 8 nodes on rect face
// and 6 on triangle faces
if(faceNum > 0)
{
for (int i=0; i<6; i++)
{
this->TriangleFace->PointIds->SetId(i,
this->PointIds->GetId(PyramidFaces[faceNum][i]));
}
inter = this->TriangleFace->IntersectWithLine(p1, p2, tol, tTemp,
xTemp, pc, subId);
}
else
{
for (int i=0; i<8; i++)
{
this->Face->Points->SetPoint(i,
this->Points->GetPoint(PyramidFaces[faceNum][i]));
}
inter = this->Face->IntersectWithLine(p1, p2, tol, tTemp,
xTemp, pc, subId);
}
if ( inter )
{
intersection = 1;
if ( tTemp < t )
{
t = tTemp;
x[0] = xTemp[0]; x[1] = xTemp[1]; x[2] = xTemp[2];
switch (faceNum)
{
case 0:
pcoords[0] = 0.0; pcoords[1] = pc[1]; pcoords[2] = pc[0];
break;
case 1:
pcoords[0] = 1.0; pcoords[1] = pc[0]; pcoords[2] = pc[1];
break;
case 2:
pcoords[0] = pc[0]; pcoords[1] = 0.0; pcoords[2] = pc[1];
break;
case 3:
pcoords[0] = pc[1]; pcoords[1] = 1.0; pcoords[2] = pc[0];
break;
case 4:
pcoords[0] = pc[1]; pcoords[1] = pc[0]; pcoords[2] = 0.0;
break;
case 5:
pcoords[0] = pc[0]; pcoords[1] = pc[1]; pcoords[2] = 1.0;
break;
}
}
}
}
return intersection;
}
//----------------------------------------------------------------------------
int vtkQuadraticPyramid::Triangulate(int vtkNotUsed(index), vtkIdList *ptIds,
vtkPoints *pts)
{
int i;
int ii;
pts->Reset();
ptIds->Reset();
for (i=0; i < 6; i++)
{
for ( int j=0; j < 5; j++)
{
ptIds->InsertId(5*i+j,this->PointIds->GetId(LinearPyramids[i][j]));
pts->InsertPoint(5*i+j,this->Points->GetPoint(LinearPyramids[i][j]));
}
}
for (ii=0, i=6 ; i < 10; i++, ii++)
{
for ( int j=0; j < 4; j++)
{
ptIds->InsertId(4*ii+j+30,this->PointIds->GetId(LinearPyramids[i][j]));
pts->InsertPoint(4*ii+j+30,this->Points->GetPoint(LinearPyramids[i][j]));
}
}
return 1;
}
//----------------------------------------------------------------------------
// Given parametric coordinates compute inverse Jacobian transformation
// matrix. Returns 9 elements of 3x3 inverse Jacobian plus interpolation
// function derivatives.
//
void vtkQuadraticPyramid::JacobianInverse(double pcoords[3], double **inverse,
double derivs[39])
{
int i, j;
double *m[3], m0[3], m1[3], m2[3];
double x[3];
// compute interpolation function derivatives
this->InterpolationDerivs(pcoords, derivs);
// create Jacobian matrix
m[0] = m0; m[1] = m1; m[2] = m2;
for (i=0; i < 3; i++) //initialize matrix
{
m0[i] = m1[i] = m2[i] = 0.0;
}
for ( j=0; j < 13; j++ )
{
this->Points->GetPoint(j, x);
for ( i=0; i < 3; i++ )
{
m0[i] += x[i] * derivs[j];
m1[i] += x[i] * derivs[13 + j];
m2[i] += x[i] * derivs[26 + j];
}
}
// now find the inverse
if ( vtkMath::InvertMatrix(m,inverse,3) == 0 )
{
vtkErrorMacro(<<"Jacobian inverse not found");
return;
}
}
//----------------------------------------------------------------------------
void vtkQuadraticPyramid::Derivatives(int vtkNotUsed(subId),
double pcoords[3], double *values,
int dim, double *derivs)
{
double *jI[3], j0[3], j1[3], j2[3];
double functionDerivs[3*13], sum[3];
int i, j, k;
// compute inverse Jacobian and interpolation function derivatives
jI[0] = j0; jI[1] = j1; jI[2] = j2;
this->JacobianInverse(pcoords, jI, functionDerivs);
// now compute derivates of values provided
for (k=0; k < dim; k++) //loop over values per vertex
{
sum[0] = sum[1] = sum[2] = 0.0;
for ( i=0; i < 13; i++) //loop over interp. function derivatives
{
sum[0] += functionDerivs[i] * values[dim*i + k];
sum[1] += functionDerivs[13 + i] * values[dim*i + k];
sum[2] += functionDerivs[26 + i] * values[dim*i + k];
}
for (j=0; j < 3; j++) //loop over derivative directions
{
derivs[3*k + j] = sum[0]*jI[j][0] + sum[1]*jI[j][1] + sum[2]*jI[j][2];
}
}
}
//----------------------------------------------------------------------------
// Clip this quadratic pyramid using scalar value provided. Like contouring,
// except that it cuts the pyramid to produce tetrahedra.
//
void vtkQuadraticPyramid::Clip(double value, vtkDataArray* cellScalars,
vtkIncrementalPointLocator* locator, vtkCellArray* tets,
vtkPointData* inPd, vtkPointData* outPd,
vtkCellData* inCd, vtkIdType cellId,
vtkCellData* outCd, int insideOut)
{
int i;
// create six linear pyramid + 4 tetra
this->Subdivide(inPd,inCd,cellId,cellScalars);
//contour each linear pyramid separately
this->Scalars->SetNumberOfTuples(5); //num of vertices
for (i=0; i<6; i++) //for each subdivided pyramid
{
for (int j=0; j<5; j++) //for each of the five vertices of the pyramid
{
this->Pyramid->Points->SetPoint(j,this->Points->GetPoint(LinearPyramids[i][j]));
this->Pyramid->PointIds->SetId(j,LinearPyramids[i][j]);
this->Scalars->SetValue(j,this->CellScalars->GetValue(LinearPyramids[i][j]));
}
this->Pyramid->Clip(value,this->Scalars,locator,tets,this->PointData,outPd,
this->CellData,cellId,outCd,insideOut);
}
this->Scalars->SetNumberOfTuples(4); //num of vertices
for (i=6; i<10; i++) //for each subdivided tetra
{
for (int j=0; j<4; j++) //for each of the four vertices of the tetra
{
this->Tetra->Points->SetPoint(j,this->Points->GetPoint(LinearPyramids[i][j]));
this->Tetra->PointIds->SetId(j,LinearPyramids[i][j]);
this->Scalars->SetValue(j,this->CellScalars->GetValue(LinearPyramids[i][j]));
}
this->Tetra->Clip(value,this->Scalars,locator,tets,this->PointData,outPd,
this->CellData,cellId,outCd,insideOut);
}
}
//----------------------------------------------------------------------------
// Compute interpolation functions for the fifteen nodes.
//
void vtkQuadraticPyramid::InterpolationFunctions(double pcoords[3],
double weights[13])
{
// VTK needs parametric coordinates to be between (0,1). Isoparametric
// shape functions are formulated between (-1,1). Here we do a
// coordinate system conversion from (0,1) to (-1,1).
const double r = 2*pcoords[0] - 1;
const double s = 2*pcoords[1] - 1;
const double t = 2*pcoords[2] - 1;
const double rm = 1.0 - r;
const double rp = 1.0 + r;
const double sm = 1.0 - s;
const double sp = 1.0 + s;
const double tm = 1.0 - t;
const double tp = 1.0 + t;
const double r2 = 1.0 - r*r;
const double s2 = 1.0 - s*s;
const double t2 = 1.0 - t*t;
// corners
weights[0] = 0.125 * rm * sm * tm * (-r - s - t - 2.0);
weights[1] = 0.125 * rp * sm * tm * ( r - s - t - 2.0);
weights[2] = 0.125 * rp * sp * tm * ( r + s - t - 2.0);
weights[3] = 0.125 * rm * sp * tm * (-r + s - t - 2.0);
weights[4] = 0.5 * t * tp;
// midsides of rectangles
weights[5] = 0.25 * r2 * sm * tm;
weights[6] = 0.25 * s2 * rp * tm;
weights[7] = 0.25 * r2 * sp * tm;
weights[8] = 0.25 * s2 * rm * tm;
// midsides of triangles
weights[9] = 0.25 * ( 1 - r ) * (1 - s ) * t2;
weights[10] = 0.25 * ( 1 + r ) * (1 - s ) * t2;
weights[11] = 0.25 * ( 1 + r ) * (1 + s ) * t2;
weights[12] = 0.25 * ( 1 - r ) * (1 + s ) * t2;
}
//----------------------------------------------------------------------------
// Derivatives in parametric space.
//
void vtkQuadraticPyramid::InterpolationDerivs(double pcoords[3],
double derivs[39])
{
//VTK needs parametric coordinates to be between (0,1). Isoparametric
//shape functions are formulated between (-1,1). Here we do a
//coordinate system conversion from (0,1) to (-1,1).
double r = 2*pcoords[0] - 1;
double s = 2*pcoords[1] - 1;
double t = 2*pcoords[2] - 1;
double rm = 1.0 - r;
double rp = 1.0 + r;
double sm = 1.0 - s;
double sp = 1.0 + s;
double tm = 1.0 - t;
//double tp = 1.0 + t;
double r2 = 1.0 - r*r;
double t2 = 1.0 - t*t;
//r-derivatives
// corners
derivs[0] = -0.125*(sm*tm - 2.0*r*sm*tm - s*sm*tm - t*sm*tm - 2.0*sm*tm);
derivs[1] = 0.125*(sm*tm + 2.0*r*sm*tm - s*sm*tm - t*sm*tm - 2.0*sm*tm);
derivs[2] = 0.125*(sp*tm + 2.0*r*sp*tm + s*sp*tm - t*sp*tm - 2.0*sp*tm);
derivs[3] = -0.125*(sp*tm - 2.0*r*sp*tm + s*sp*tm - t*sp*tm - 2.0*sp*tm);
derivs[4] = 0.0;
// midsides of rectangles
derivs[5] = -0.5*r*sm*tm;
derivs[6] = 0.25*(tm - s*s*tm);
derivs[7] = -0.5*r*sp*tm;
derivs[8] = -0.25*(tm - s*s*tm);
// midsides of triangles
derivs[9] = -0.25 * (1 - s ) * (1 - t*t );
derivs[10] = 0.25 * (1 - s ) * (1 - t*t );
derivs[11] = 0.25 * (1 + s ) * (1 - t*t );
derivs[12] = -0.25 * (1 + s ) * (1 - t*t );
//s-derivatives
// corners
derivs[13] = -0.125*(rm*tm - 2.0*s*rm*tm - r*rm*tm - t*rm*tm - 2.0*rm*tm);
derivs[14] = -0.125*(rp*tm - 2.0*s*rp*tm + r*rp*tm - t*rp*tm - 2.0*rp*tm);
derivs[15] = 0.125*(rp*tm + 2.0*s*rp*tm + r*rp*tm - t*rp*tm - 2.0*rp*tm);
derivs[16] = 0.125*(rm*tm + 2.0*s*rm*tm - r*rm*tm - t*rm*tm - 2.0*rm*tm);
derivs[17] = 0.0;
// midsides of rectangles
derivs[18] = -0.25 * tm * r2;
derivs[19] = -0.5 * tm * s * rp;
derivs[20] = 0.25 * tm * r2;
derivs[21] = -0.5 * tm * s * rm;
// midsides of triangles
derivs[22] = -0.25 * rm * t2;
derivs[23] = -0.25 * rp * t2;
derivs[24] = 0.25 * rp * t2;
derivs[25] = 0.25 * rm * t2;
//t-derivatives
// corners
derivs[26] = -0.125*(rm*sm - 2.0*t*rm*sm - r*rm*sm - s*rm*sm - 2.0*rm*sm);
derivs[27] = -0.125*(rp*sm - 2.0*t*rp*sm + r*rp*sm - s*rp*sm - 2.0*rp*sm);
derivs[28] = -0.125*(rp*sp - 2.0*t*rp*sp + r*rp*sp + s*rp*sp - 2.0*rp*sp);
derivs[29] = -0.125*(rm*sp - 2.0*t*rm*sp - r*rm*sp + s*rm*sp - 2.0*rm*sp);
derivs[30] = 0.5 + t;
// midsides of rectangles
derivs[31] = -0.25*(sm - r*r*sm);
derivs[32] = -0.25*(rp - s*s*rp);
derivs[33] = -0.25*(sp - r*r*sp);
derivs[34] = -0.25*(rm - s*s*rm);
// midsides of triangles
derivs[35] = -0.5 * ( 1 - r ) * (1 - s ) * t;
derivs[36] = -0.5 * ( 1 + r ) * (1 - s ) * t;
derivs[37] = -0.5 * ( 1 + r ) * (1 + s ) * t;
derivs[38] = -0.5 * ( 1 - r ) * (1 + s ) * t;
// we compute derivatives in in [-1; 1] but we need them in [ 0; 1]
for(int i = 0; i < 39; i++)
derivs[i] *= 2;
}
static double vtkQPyramidCellPCoords[39] = {0.0,0.0,0.0, 1.0,0.0,0.0, 1.0,1.0,0.0,
0.0,1.0,0.0, 0.0,0.0,1.0, 0.5,0.0,0.0,
1.0,0.5,0.0, 0.5,1.0,0.0, 0.0,0.5,0.0,
0.0,0.0,0.5, 1.0,0.0,0.5,
1.0,1.0,0.5, 0.0,1.0,0.5 };
//----------------------------------------------------------------------------
double *vtkQuadraticPyramid::GetParametricCoords()
{
return vtkQPyramidCellPCoords;
}
//----------------------------------------------------------------------------
void vtkQuadraticPyramid::PrintSelf(ostream& os, vtkIndent indent)
{
this->Superclass::PrintSelf(os,indent);
os << indent << "Edge:\n";
this->Edge->PrintSelf(os,indent.GetNextIndent());
os << indent << "TriangleFace:\n";
this->TriangleFace->PrintSelf(os,indent.GetNextIndent());
os << indent << "Face:\n";
this->Face->PrintSelf(os,indent.GetNextIndent());
os << indent << "Tetra:\n";
this->Tetra->PrintSelf(os,indent.GetNextIndent());
os << indent << "Pyramid:\n";
this->Pyramid->PrintSelf(os,indent.GetNextIndent());
os << indent << "PointData:\n";
this->PointData->PrintSelf(os,indent.GetNextIndent());
os << indent << "CellData:\n";
this->CellData->PrintSelf(os,indent.GetNextIndent());
os << indent << "Scalars:\n";
this->Scalars->PrintSelf(os,indent.GetNextIndent());
}
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