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/*=========================================================================
Program: Visualization Toolkit
Module: vtkQuadraticHexahedron.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 "vtkQuadraticHexahedron.h"
#include "vtkObjectFactory.h"
#include "vtkCellData.h"
#include "vtkDoubleArray.h"
#include "vtkHexahedron.h"
#include "vtkMath.h"
#include "vtkPointData.h"
#include "vtkQuadraticEdge.h"
#include "vtkQuadraticQuad.h"
#include "vtkPoints.h"
vtkStandardNewMacro(vtkQuadraticHexahedron);
//----------------------------------------------------------------------------
// Construct the hex with 20 points + 7 extra points for internal
// computation.
vtkQuadraticHexahedron::vtkQuadraticHexahedron()
{
// At times the cell looks like it has 27 points (during interpolation)
// We initially allocate for 27.
this->Points->SetNumberOfPoints(27);
this->PointIds->SetNumberOfIds(27);
for (int i = 0; i < 27; i++)
{
this->Points->SetPoint(i, 0.0, 0.0, 0.0);
this->PointIds->SetId(i,0);
}
this->Points->SetNumberOfPoints(20);
this->PointIds->SetNumberOfIds(20);
this->Edge = vtkQuadraticEdge::New();
this->Face = vtkQuadraticQuad::New();
this->Hex = vtkHexahedron::New();
this->PointData = vtkPointData::New();
this->CellData = vtkCellData::New();
this->CellScalars = vtkDoubleArray::New();
this->CellScalars->SetNumberOfTuples(27);
this->Scalars = vtkDoubleArray::New();
this->Scalars->SetNumberOfTuples(8);
}
//----------------------------------------------------------------------------
vtkQuadraticHexahedron::~vtkQuadraticHexahedron()
{
this->Edge->Delete();
this->Face->Delete();
this->Hex->Delete();
this->PointData->Delete();
this->CellData->Delete();
this->Scalars->Delete();
this->CellScalars->Delete();
}
static int LinearHexs[8][8] = {
{ 0, 8, 24, 11, 16, 22, 26, 20},
{ 8, 1, 9, 24, 22, 17, 21, 26},
{11, 24, 10, 3, 20, 26, 23, 19},
{24, 9, 2, 10, 26, 21, 18, 23},
{16, 22, 26, 20, 4, 12, 25, 15},
{22, 17, 21, 26, 12, 5, 13, 25},
{20, 26, 23, 19, 15, 25, 14, 7},
{26, 21, 18, 23, 25, 13, 6, 14} };
static int HexFaces[6][8] = {
{0, 4, 7, 3, 16, 15, 19, 11},
{1, 2, 6, 5, 9, 18, 13, 17},
{0, 1, 5, 4, 8, 17, 12, 16},
{3, 7, 6, 2, 19, 14, 18, 10},
{0, 3, 2, 1, 11, 10, 9, 8},
{4, 5, 6, 7, 12, 13, 14, 15} };
static int HexEdges[12][3] = {
{0, 1, 8}, {1, 2, 9}, {3, 2, 10}, {0, 3, 11},
{4, 5, 12}, {5, 6, 13}, {7, 6, 14}, {4, 7, 15},
{0, 4, 16}, {1, 5, 17}, {3, 7, 19}, {2, 6, 18}
};
static double MidPoints[7][3] = { {0.0,0.5,0.5}, // 20
{1.0,0.5,0.5}, // 21
{0.5,0.0,0.5}, // 22
{0.5,1.0,0.5}, // 23
{0.5,0.5,0.0}, // 24
{0.5,0.5,1.0}, // 25
{0.5,0.5,0.5} }; // 26
//----------------------------------------------------------------------------
int *vtkQuadraticHexahedron::GetEdgeArray(int edgeId)
{
return HexEdges[edgeId];
}
//----------------------------------------------------------------------------
int *vtkQuadraticHexahedron::GetFaceArray(int faceId)
{
return HexFaces[faceId];
}
//----------------------------------------------------------------------------
vtkCell *vtkQuadraticHexahedron::GetEdge(int edgeId)
{
edgeId = (edgeId < 0 ? 0 : (edgeId > 11 ? 11 : edgeId ));
for (int i=0; i<3; i++)
{
this->Edge->PointIds->SetId(i,this->PointIds->GetId(HexEdges[edgeId][i]));
this->Edge->Points->SetPoint(i,this->Points->GetPoint(HexEdges[edgeId][i]));
}
return this->Edge;
}
//----------------------------------------------------------------------------
vtkCell *vtkQuadraticHexahedron::GetFace(int faceId)
{
faceId = (faceId < 0 ? 0 : (faceId > 5 ? 5 : faceId ));
for (int i=0; i<8; i++)
{
this->Face->PointIds->SetId(i,this->PointIds->GetId(HexFaces[faceId][i]));
this->Face->Points->SetPoint(i,this->Points->GetPoint(HexFaces[faceId][i]));
}
return this->Face;
}
//----------------------------------------------------------------------------
void vtkQuadraticHexahedron::Subdivide(vtkPointData *inPd, vtkCellData *inCd,
vtkIdType cellId, vtkDataArray *cellScalars)
{
int numMidPts, i, j;
double weights[20];
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,27);
this->CellData->CopyAllocate(inCd,8);
for (i=0; i<20; i++)
{
this->PointData->CopyData(inPd,this->PointIds->GetId(i),i);
this->CellScalars->SetValue( i, cellScalars->GetTuple1(i));
}
for (i=0; i<8; i++)
{
this->CellData->CopyData(inCd,cellId,i);
}
//Interpolate new values
double p[3];
for ( numMidPts=0; numMidPts < 7; numMidPts++ )
{
this->InterpolationFunctions(MidPoints[numMidPts], weights);
x[0] = x[1] = x[2] = 0.0;
s = 0.0;
for (i=0; i<20; 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(20+numMidPts,x);
this->CellScalars->SetValue(20+numMidPts,s);
this->PointData->InterpolatePoint(inPd, 20+numMidPts,
this->PointIds, weights);
}
}
//----------------------------------------------------------------------------
static const double VTK_DIVERGED = 1.e6;
static const int VTK_HEX_MAX_ITERATION=10;
static const double VTK_HEX_CONVERGED=1.e-03;
int vtkQuadraticHexahedron::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[60];
// 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_HEX_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<20; 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+20];
tcol[j] += pt[j] * derivs[i+40];
}
}
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_HEX_CONVERGED) &&
((fabs(pcoords[1]-params[1])) < VTK_HEX_CONVERGED) &&
((fabs(pcoords[2]-params[2])) < VTK_HEX_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 hexahedron
}
return 1;
}
else
{
double pc[3], w[20];
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 vtkQuadraticHexahedron::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<20; i++)
{
this->Points->GetPoint(i, pt);
for (j=0; j<3; j++)
{
x[j] += pt[j] * weights[i];
}
}
}
//----------------------------------------------------------------------------
int vtkQuadraticHexahedron::CellBoundary( int subId,
double pcoords[3],
vtkIdList *pts )
{
for ( int i = 0; i < 8; ++ i ) // For each of the eight vertices of the hex
{
this->Hex->PointIds->SetId( i, this->PointIds->GetId( i ) );
}
return this->Hex->CellBoundary( subId, pcoords, pts );
}
//----------------------------------------------------------------------------
void vtkQuadraticHexahedron::Contour(double value,
vtkDataArray* cellScalars,
vtkIncrementalPointLocator* locator,
vtkCellArray *verts,
vtkCellArray* lines,
vtkCellArray* polys,
vtkPointData* inPd,
vtkPointData* outPd,
vtkCellData* inCd,
vtkIdType cellId,
vtkCellData* outCd)
{
//subdivide into 8 linear hexs
this->Subdivide(inPd,inCd,cellId, cellScalars);
//contour each linear quad separately
for (int i=0; i<8; i++) // For each subdivided hexahedron
{
for (int j=0; j<8; j++) // For each of the eight vertices of the hexhedron
{
this->Hex->Points->SetPoint(j,this->Points->GetPoint(LinearHexs[i][j]));
this->Hex->PointIds->SetId(j,LinearHexs[i][j]);
this->Scalars->SetValue(j,this->CellScalars->GetValue(LinearHexs[i][j]));
}
this->Hex->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 vtkQuadraticHexahedron::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;
t = VTK_DOUBLE_MAX;
for (faceNum=0; faceNum<6; faceNum++)
{
for (int i=0; i<8; i++)
{
this->Face->Points->SetPoint(i,
this->Points->GetPoint(HexFaces[faceNum][i]));
}
if ( this->Face->IntersectWithLine(p1, p2, tol, tTemp,
xTemp, pc, subId) )
{
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 vtkQuadraticHexahedron::Triangulate(int vtkNotUsed(index),
vtkIdList *ptIds, vtkPoints *pts)
{
pts->Reset();
ptIds->Reset();
ptIds->InsertId(0,this->PointIds->GetId(0));
pts->InsertPoint(0,this->Points->GetPoint(0));
ptIds->InsertId(1,this->PointIds->GetId(1));
pts->InsertPoint(1,this->Points->GetPoint(1));
return 1;
}
//----------------------------------------------------------------------------
// Given parametric coordinates compute inverse Jacobian transformation
// matrix. Returns 9 elements of 3x3 inverse Jacobian plus interpolation
// function derivatives.
void vtkQuadraticHexahedron::JacobianInverse(double pcoords[3],
double **inverse,
double derivs[60])
{
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 < 20; j++ )
{
this->Points->GetPoint(j, x);
for ( i=0; i < 3; i++ )
{
m0[i] += x[i] * derivs[j];
m1[i] += x[i] * derivs[20 + j];
m2[i] += x[i] * derivs[40 + j];
}
}
// now find the inverse
if ( vtkMath::InvertMatrix(m,inverse,3) == 0 )
{
vtkErrorMacro(<<"Jacobian inverse not found");
return;
}
}
//----------------------------------------------------------------------------
void vtkQuadraticHexahedron::Derivatives(int vtkNotUsed(subId),
double pcoords[3], double *values,
int dim, double *derivs)
{
double *jI[3], j0[3], j1[3], j2[3];
double functionDerivs[60], 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 < 20; i++) //loop over interp. function derivatives
{
sum[0] += functionDerivs[i] * values[dim*i + k];
sum[1] += functionDerivs[20 + i] * values[dim*i + k];
sum[2] += functionDerivs[40 + 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 hex using scalar value provided. Like contouring,
// except that it cuts the hex to produce tetrahedra.
void vtkQuadraticHexahedron::Clip(double value,
vtkDataArray* cellScalars,
vtkIncrementalPointLocator* locator, vtkCellArray* tets,
vtkPointData* inPd, vtkPointData* outPd,
vtkCellData* inCd, vtkIdType cellId,
vtkCellData* outCd, int insideOut)
{
//create eight linear hexes
this->Subdivide(inPd,inCd,cellId,cellScalars);
//contour each linear hex separately
for (int i=0; i<8; i++) // For each subdivided hexahedron
{
for (int j=0; j<8; j++) // For each of the eight vertices of the hexhedron
{
this->Hex->Points->SetPoint(j,this->Points->GetPoint(LinearHexs[i][j]));
this->Hex->PointIds->SetId(j,LinearHexs[i][j]);
this->Scalars->SetValue(j,this->CellScalars->GetValue(LinearHexs[i][j]));
}
this->Hex->Clip(value,this->Scalars,locator,tets,this->PointData,outPd,
this->CellData,cellId,outCd,insideOut);
}
}
//----------------------------------------------------------------------------
// Compute interpolation functions for the twenty nodes.
void vtkQuadraticHexahedron::InterpolationFunctions(double pcoords[3],
double weights[20])
{
//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 = 2.0*(pcoords[0]-0.5);
double s = 2.0*(pcoords[1]-0.5);
double t = 2.0*(pcoords[2]-0.5);
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 s2 = 1.0 - s*s;
double t2 = 1.0 - t*t;
//The eight corner points
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] = 0.125 * rm * sm * tp * (-r - s + t - 2.0);
weights[5] = 0.125 * rp * sm * tp * ( r - s + t - 2.0);
weights[6] = 0.125 * rp * sp * tp * ( r + s + t - 2.0);
weights[7] = 0.125 * rm * sp * tp * (-r + s + t - 2.0);
//The mid-edge nodes
weights[8] = 0.25 * r2 * sm * tm;
weights[9] = 0.25 * s2 * rp * tm;
weights[10] = 0.25 * r2 * sp * tm;
weights[11] = 0.25 * s2 * rm * tm;
weights[12] = 0.25 * r2 * sm * tp;
weights[13] = 0.25 * s2 * rp * tp;
weights[14] = 0.25 * r2 * sp * tp;
weights[15] = 0.25 * s2 * rm * tp;
weights[16] = 0.25 * t2 * rm * sm;
weights[17] = 0.25 * t2 * rp * sm;
weights[18] = 0.25 * t2 * rp * sp;
weights[19] = 0.25 * t2 * rm * sp;
}
//----------------------------------------------------------------------------
// Derivatives in parametric space.
void vtkQuadraticHexahedron::InterpolationDerivs(double pcoords[3],
double derivs[60])
{
//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 = 2.0*(pcoords[0]-0.5);
double s = 2.0*(pcoords[1]-0.5);
double t = 2.0*(pcoords[2]-0.5);
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;
//r-derivatives
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] = -0.125*(sm*tp - 2.0*r*sm*tp - s*sm*tp + t*sm*tp - 2.0*sm*tp);
derivs[5] = 0.125*(sm*tp + 2.0*r*sm*tp - s*sm*tp + t*sm*tp - 2.0*sm*tp);
derivs[6] = 0.125*(sp*tp + 2.0*r*sp*tp + s*sp*tp + t*sp*tp - 2.0*sp*tp);
derivs[7] = -0.125*(sp*tp - 2.0*r*sp*tp + s*sp*tp + t*sp*tp - 2.0*sp*tp);
derivs[8] = -0.5*r*sm*tm;
derivs[9] = 0.25*(tm - s*s*tm);
derivs[10] = -0.5*r*sp*tm;
derivs[11] = -0.25*(tm - s*s*tm);
derivs[12] = -0.5*r*sm*tp;
derivs[13] = 0.25*(tp - s*s*tp);
derivs[14] = -0.5*r*sp*tp;
derivs[15] = -0.25*(tp - s*s*tp);
derivs[16] = -0.25*(sm - t*t*sm);
derivs[17] = 0.25*(sm - t*t*sm);
derivs[18] = 0.25*(sp - t*t*sp);
derivs[19] = -0.25*(sp - t*t*sp);
//s-derivatives
derivs[20] = -0.125*(rm*tm - 2.0*s*rm*tm - r*rm*tm - t*rm*tm - 2.0*rm*tm);
derivs[21] = -0.125*(rp*tm - 2.0*s*rp*tm + r*rp*tm - t*rp*tm - 2.0*rp*tm);
derivs[22] = 0.125*(rp*tm + 2.0*s*rp*tm + r*rp*tm - t*rp*tm - 2.0*rp*tm);
derivs[23] = 0.125*(rm*tm + 2.0*s*rm*tm - r*rm*tm - t*rm*tm - 2.0*rm*tm);
derivs[24] = -0.125*(rm*tp - 2.0*s*rm*tp - r*rm*tp + t*rm*tp - 2.0*rm*tp);
derivs[25] = -0.125*(rp*tp - 2.0*s*rp*tp + r*rp*tp + t*rp*tp - 2.0*rp*tp);
derivs[26] = 0.125*(rp*tp + 2.0*s*rp*tp + r*rp*tp + t*rp*tp - 2.0*rp*tp);
derivs[27] = 0.125*(rm*tp + 2.0*s*rm*tp - r*rm*tp + t*rm*tp - 2.0*rm*tp);
derivs[28] = -0.25*(tm - r*r*tm);
derivs[29] = -0.5*s*rp*tm;
derivs[30] = 0.25*(tm - r*r*tm);
derivs[31] = -0.5*s*rm*tm;
derivs[32] = -0.25*(tp - r*r*tp);
derivs[33] = -0.5*s*rp*tp;
derivs[34] = 0.25*(tp - r*r*tp);
derivs[35] = -0.5*s*rm*tp;
derivs[36] = -0.25*(rm - t*t*rm);
derivs[37] = -0.25*(rp - t*t*rp);
derivs[38] = 0.25*(rp - t*t*rp);
derivs[39] = 0.25*(rm - t*t*rm);
//t-derivatives
derivs[40] = -0.125*(rm*sm - 2.0*t*rm*sm - r*rm*sm - s*rm*sm - 2.0*rm*sm);
derivs[41] = -0.125*(rp*sm - 2.0*t*rp*sm + r*rp*sm - s*rp*sm - 2.0*rp*sm);
derivs[42] = -0.125*(rp*sp - 2.0*t*rp*sp + r*rp*sp + s*rp*sp - 2.0*rp*sp);
derivs[43] = -0.125*(rm*sp - 2.0*t*rm*sp - r*rm*sp + s*rm*sp - 2.0*rm*sp);
derivs[44] = 0.125*(rm*sm + 2.0*t*rm*sm - r*rm*sm - s*rm*sm - 2.0*rm*sm);
derivs[45] = 0.125*(rp*sm + 2.0*t*rp*sm + r*rp*sm - s*rp*sm - 2.0*rp*sm);
derivs[46] = 0.125*(rp*sp + 2.0*t*rp*sp + r*rp*sp + s*rp*sp - 2.0*rp*sp);
derivs[47] = 0.125*(rm*sp + 2.0*t*rm*sp - r*rm*sp + s*rm*sp - 2.0*rm*sp);
derivs[48] = -0.25*(sm - r*r*sm);
derivs[49] = -0.25*(rp - s*s*rp);
derivs[50] = -0.25*(sp - r*r*sp);
derivs[51] = -0.25*(rm - s*s*rm);
derivs[52] = 0.25*(sm - r*r*sm);
derivs[53] = 0.25*(rp - s*s*rp);
derivs[54] = 0.25*(sp - r*r*sp);
derivs[55] = 0.25*(rm - s*s*rm);
derivs[56] = -0.5*t*rm*sm;
derivs[57] = -0.5*t*rp*sm;
derivs[58] = -0.5*t*rp*sp;
derivs[59] = -0.5*t*rm*sp;
// we compute derivatives in in [-1; 1] but we need them in [ 0; 1]
for(int i = 0; i < 60; i++)
derivs[i] *= 2;
}
//----------------------------------------------------------------------------
static double vtkQHexCellPCoords[60] = {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, 1.0,0.0,1.0,
1.0,1.0,1.0, 0.0,1.0,1.0, 0.5,0.0,0.0,
1.0,0.5,0.0, 0.5,1.0,0.0, 0.0,0.5,0.0,
0.5,0.0,1.0, 1.0,0.5,1.0, 0.5,1.0,1.0,
0.0,0.5,1.0, 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 *vtkQuadraticHexahedron::GetParametricCoords()
{
return vtkQHexCellPCoords;
}
//----------------------------------------------------------------------------
void vtkQuadraticHexahedron::PrintSelf(ostream& os, vtkIndent indent)
{
this->Superclass::PrintSelf(os,indent);
os << indent << "Edge:\n";
this->Edge->PrintSelf(os,indent.GetNextIndent());
os << indent << "Face:\n";
this->Face->PrintSelf(os,indent.GetNextIndent());
os << indent << "Hex:\n";
this->Hex->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());
}