You cannot select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
787 lines
28 KiB
C++
787 lines
28 KiB
C++
/*=========================================================================
|
|
|
|
Program: Visualization Toolkit
|
|
Module: vtkBiQuadraticQuadraticHexahedron.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.
|
|
|
|
=========================================================================*/
|
|
|
|
//Thanks to Soeren Gebbert who developed this class and
|
|
//integrated it into VTK 5.0.
|
|
|
|
#include "vtkBiQuadraticQuadraticHexahedron.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 "vtkBiQuadraticQuad.h"
|
|
#include "vtkPoints.h"
|
|
#include <cassert>
|
|
|
|
vtkStandardNewMacro(vtkBiQuadraticQuadraticHexahedron);
|
|
|
|
//----------------------------------------------------------------------------
|
|
// Construct the hex with 24 points + 3 extra points for internal
|
|
// computation.
|
|
vtkBiQuadraticQuadraticHexahedron::vtkBiQuadraticQuadraticHexahedron()
|
|
{
|
|
// 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(24);
|
|
this->PointIds->SetNumberOfIds(24);
|
|
|
|
this->Edge = vtkQuadraticEdge::New();
|
|
this->Face = vtkQuadraticQuad::New();
|
|
this->BiQuadFace = vtkBiQuadraticQuad::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); // vertices of a linear hexahedron
|
|
|
|
}
|
|
|
|
//----------------------------------------------------------------------------
|
|
vtkBiQuadraticQuadraticHexahedron::~vtkBiQuadraticQuadraticHexahedron()
|
|
{
|
|
this->Edge->Delete();
|
|
this->Face->Delete();
|
|
this->BiQuadFace->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][9] = {
|
|
{0,4,7,3,16,15,19,11, 20},//BiQuadQuad
|
|
{1,2,6,5,9,18,13,17,21},//BiQuadQuad
|
|
{0,1,5,4,8,17,12,16,22}, //BiQuadQuad
|
|
{3,7,6,2,19,14,18,10,23},//BiQuadQuad
|
|
{0,3,2,1,11,10,9,8, 0},//QuadQuad
|
|
{4,5,6,7,12,13,14,15, 0} };//QuadQuad
|
|
|
|
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[3][3] = { {0.5,0.5,0.0}, {0.5,0.5,1.0}, {0.5,0.5,0.5} };
|
|
|
|
//----------------------------------------------------------------------------
|
|
int *vtkBiQuadraticQuadraticHexahedron::GetEdgeArray(int edgeId)
|
|
{
|
|
return HexEdges[edgeId];
|
|
}
|
|
//----------------------------------------------------------------------------
|
|
int *vtkBiQuadraticQuadraticHexahedron::GetFaceArray(int faceId)
|
|
{
|
|
return HexFaces[faceId];
|
|
}
|
|
|
|
|
|
//----------------------------------------------------------------------------
|
|
vtkCell *vtkBiQuadraticQuadraticHexahedron::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 *vtkBiQuadraticQuadraticHexahedron::GetFace(int faceId)
|
|
{
|
|
faceId = (faceId < 0 ? 0 : (faceId > 5 ? 5 : faceId ));
|
|
|
|
//4 BiQuaduadaticQuads
|
|
if(faceId < 4)
|
|
{
|
|
for (int i=0; i<9; i++)
|
|
{
|
|
this->BiQuadFace->PointIds->SetId(i,this->PointIds->GetId(HexFaces[faceId][i]));
|
|
this->BiQuadFace->Points->SetPoint(i,this->Points->GetPoint(HexFaces[faceId][i]));
|
|
}
|
|
return this->BiQuadFace;
|
|
}
|
|
else
|
|
{ //2 QuadraticQuads
|
|
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 vtkBiQuadraticQuadraticHexahedron::Subdivide(vtkPointData *inPd, vtkCellData *inCd,
|
|
vtkIdType cellId, vtkDataArray *cellScalars)
|
|
{
|
|
int numMidPts, i, j;
|
|
double weights[24];
|
|
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<24; i++)
|
|
{
|
|
this->PointData->CopyData(inPd,this->PointIds->GetId(i),i);
|
|
this->CellScalars->SetValue( i, cellScalars->GetTuple1(i));
|
|
}
|
|
this->CellData->CopyData(inCd,cellId,0);
|
|
|
|
//Interpolate new values
|
|
double p[3];
|
|
this->Points->Resize(27);
|
|
this->CellScalars->Resize(27);
|
|
for ( numMidPts=0; numMidPts < 3; numMidPts++ )
|
|
{
|
|
this->InterpolationFunctions(MidPoints[numMidPts], weights);
|
|
|
|
x[0] = x[1] = x[2] = 0.0;
|
|
s = 0.0;
|
|
for (i=0; i<24; 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(24+numMidPts,x);
|
|
this->CellScalars->SetValue(24+numMidPts,s);
|
|
this->PointData->InterpolatePoint(inPd, 24+numMidPts, this->PointIds, weights);
|
|
}
|
|
}
|
|
|
|
//----------------------------------------------------------------------------
|
|
static const double VTK_DIVERGED = 1.e6;
|
|
static const int VTK_HEX_MAX_ITERATION=20;
|
|
static const double VTK_HEX_CONVERGED=1.e-03;
|
|
|
|
int vtkBiQuadraticQuadraticHexahedron::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[72];
|
|
double hexweights[8];
|
|
|
|
// set initial position for Newton's method
|
|
pcoords[0] = pcoords[1] = pcoords[2] = params[0] = params[1] = params[2]=0.0;
|
|
subId = 0;
|
|
|
|
// Use a tri-linear hexahederon to get good starting values
|
|
vtkHexahedron *hex = vtkHexahedron::New();
|
|
for(i = 0; i < 8; i++)
|
|
hex->GetPoints()->SetPoint(i, this->Points->GetPoint(i));
|
|
|
|
hex->EvaluatePosition(x, closestPoint, subId, pcoords, dist2, hexweights);
|
|
hex->Delete();
|
|
|
|
params[0] = pcoords[0];
|
|
params[1] = pcoords[1];
|
|
params[2] = pcoords[2];
|
|
|
|
// 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<24; 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+24];
|
|
tcol[j] += pt[j] * derivs[i+48];
|
|
}
|
|
}
|
|
|
|
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)
|
|
{
|
|
vtkDebugMacro (<<"Determinant incorrect, iteration " << iteration);
|
|
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[24];
|
|
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 vtkBiQuadraticQuadraticHexahedron::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<24; i++)
|
|
{
|
|
this->Points->GetPoint(i, pt);
|
|
for (j=0; j<3; j++)
|
|
{
|
|
x[j] += pt[j] * weights[i];
|
|
}
|
|
}
|
|
}
|
|
|
|
//----------------------------------------------------------------------------
|
|
int vtkBiQuadraticQuadraticHexahedron::CellBoundary(int subId, double pcoords[3],
|
|
vtkIdList *pts)
|
|
{
|
|
return this->Hex->CellBoundary(subId, pcoords, pts);
|
|
}
|
|
|
|
//----------------------------------------------------------------------------
|
|
void vtkBiQuadraticQuadraticHexahedron::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,i,outCd);
|
|
}
|
|
}
|
|
|
|
//----------------------------------------------------------------------------
|
|
// Line-hex intersection. Intersection has to occur within [0,1] parametric
|
|
// coordinates and with specified tolerance.
|
|
int vtkBiQuadraticQuadraticHexahedron::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];
|
|
|
|
t = VTK_DOUBLE_MAX;
|
|
for (int faceNum=0; faceNum<6; faceNum++)
|
|
{
|
|
int status = 0;
|
|
//4 BiQuaduadaticQuads
|
|
if(faceNum < 4)
|
|
{
|
|
for (int i=0; i<9; i++)
|
|
{
|
|
this->BiQuadFace->PointIds->SetId(i,
|
|
this->PointIds->GetId(HexFaces[faceNum][i]));
|
|
this->BiQuadFace->Points->SetPoint(i,
|
|
this->Points->GetPoint(HexFaces[faceNum][i]));
|
|
}
|
|
status = this->BiQuadFace->IntersectWithLine(p1, p2, tol, tTemp, xTemp, pc, subId);
|
|
|
|
}
|
|
else
|
|
{ //2 QuadraticQuads
|
|
for (int i=0; i<8; i++)
|
|
{
|
|
this->Face->PointIds->SetId(i,this->PointIds->GetId(HexFaces[faceNum][i]));
|
|
this->Face->Points->SetPoint(i,this->Points->GetPoint(HexFaces[faceNum][i]));
|
|
}
|
|
status = this->Face->IntersectWithLine(p1, p2, tol, tTemp, xTemp, pc, subId);
|
|
}
|
|
|
|
if (status)
|
|
{
|
|
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;
|
|
default:
|
|
assert("check: impossible case." && 0); // reaching this line is a bug.
|
|
break;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
return intersection;
|
|
}
|
|
|
|
//----------------------------------------------------------------------------
|
|
int vtkBiQuadraticQuadraticHexahedron::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 vtkBiQuadraticQuadraticHexahedron::JacobianInverse(double pcoords[3],
|
|
double **inverse,
|
|
double derivs[72])
|
|
{
|
|
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 < 24; j++ )
|
|
{
|
|
this->Points->GetPoint(j, x);
|
|
for ( i=0; i < 3; i++ )
|
|
{
|
|
m0[i] += x[i] * derivs[j];
|
|
m1[i] += x[i] * derivs[24 + j];
|
|
m2[i] += x[i] * derivs[48 + j];
|
|
}
|
|
}
|
|
|
|
// now find the inverse
|
|
if ( vtkMath::InvertMatrix(m,inverse,3) == 0 )
|
|
{
|
|
return;
|
|
}
|
|
}
|
|
|
|
//----------------------------------------------------------------------------
|
|
void vtkBiQuadraticQuadraticHexahedron::Derivatives(int vtkNotUsed(subId),
|
|
double pcoords[3], double *values,
|
|
int dim, double *derivs)
|
|
{
|
|
double *jI[3], j0[3], j1[3], j2[3];
|
|
double functionDerivs[72], 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 < 24; i++) //loop over interp. function derivatives
|
|
{
|
|
sum[0] += functionDerivs[i] * values[dim*i + k];
|
|
sum[1] += functionDerivs[24 + i] * values[dim*i + k];
|
|
sum[2] += functionDerivs[48 + 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 vtkBiQuadraticQuadraticHexahedron::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 four nodes.
|
|
void vtkBiQuadraticQuadraticHexahedron::InterpolationFunctions(double pcoords[3],
|
|
double weights[24])
|
|
{
|
|
//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 x = 2.0*(pcoords[0]-0.5);
|
|
double y = 2.0*(pcoords[1]-0.5);
|
|
double z = 2.0*(pcoords[2]-0.5);
|
|
|
|
//The eight corner points
|
|
weights[0] = ( 0.25*(x*(1-x))*(y*(1-y)) - 0.25*(1+x)*(1-x)*(1+y)*(1-y))*(-0.5*z*(1-z));
|
|
weights[1] = (-0.25*(x*(1+x))*(y*(1-y)) - 0.25*(1+x)*(1-x)*(1+y)*(1-y))*(-0.5*z*(1-z));
|
|
weights[2] = ( 0.25*(x*(1+x))*(y*(1+y)) - 0.25*(1+x)*(1-x)*(1+y)*(1-y))*(-0.5*z*(1-z));
|
|
weights[3] = (-0.25*(x*(1-x))*(y*(1+y)) - 0.25*(1+x)*(1-x)*(1+y)*(1-y))*(-0.5*z*(1-z));
|
|
weights[4] = ( 0.25*(x*(1-x))*(y*(1-y)) - 0.25*(1+x)*(1-x)*(1+y)*(1-y))*( 0.5*z*(1+z));
|
|
weights[5] = (-0.25*(x*(1+x))*(y*(1-y)) - 0.25*(1+x)*(1-x)*(1+y)*(1-y))*( 0.5*z*(1+z));
|
|
weights[6] = ( 0.25*(x*(1+x))*(y*(1+y)) - 0.25*(1+x)*(1-x)*(1+y)*(1-y))*( 0.5*z*(1+z));
|
|
weights[7] = (-0.25*(x*(1-x))*(y*(1+y)) - 0.25*(1+x)*(1-x)*(1+y)*(1-y))*( 0.5*z*(1+z));
|
|
|
|
//The mid-edge nodes
|
|
weights[8] = 0.5*((1+x)*(1-x))*(1-y) *(-0.5*z*(1-z));
|
|
weights[9] = 0.5*((1+y)*(1-y))*(1+x) *(-0.5*z*(1-z));
|
|
weights[10] = 0.5*((1+x)*(1-x))*(1+y) *(-0.5*z*(1-z));
|
|
weights[11] = 0.5*((1+y)*(1-y))*(1-x) *(-0.5*z*(1-z));
|
|
weights[12] = 0.5*((1+x)*(1-x))*(1-y) *( 0.5*z*(1+z));
|
|
weights[13] = 0.5*((1+y)*(1-y))*(1+x) *( 0.5*z*(1+z));
|
|
weights[14] = 0.5*((1+x)*(1-x))*(1+y) *( 0.5*z*(1+z));
|
|
weights[15] = 0.5*((1+y)*(1-y))*(1-x) *( 0.5*z*(1+z));
|
|
weights[16] =( 0.25*(x*(1-x))*(y*(1-y)) - 0.25*(1+x)*(1-x)*(1+y)*(1-y)) *((1+z)*(1-z));
|
|
weights[17] =(-0.25*(x*(1+x))*(y*(1-y)) - 0.25*(1+x)*(1-x)*(1+y)*(1-y)) *((1+z)*(1-z));
|
|
weights[18] =( 0.25*(x*(1+x))*(y*(1+y)) - 0.25*(1+x)*(1-x)*(1+y)*(1-y)) *((1+z)*(1-z));
|
|
weights[19] =(-0.25*(x*(1-x))*(y*(1+y)) - 0.25*(1+x)*(1-x)*(1+y)*(1-y)) *((1+z)*(1-z));
|
|
|
|
//Face center Nodes in xz and yz direction
|
|
weights[20] = 0.5*((1+y)*(1-y))*(1-x) *((1+z)*(1-z));
|
|
weights[21] = 0.5*((1+y)*(1-y))*(1+x) *((1+z)*(1-z));
|
|
weights[22] = 0.5*((1+x)*(1-x))*(1-y) *((1+z)*(1-z));
|
|
weights[23] = 0.5*((1+x)*(1-x))*(1+y) *((1+z)*(1-z));
|
|
}
|
|
|
|
|
|
//----------------------------------------------------------------------------
|
|
// Derivatives in parametric space.
|
|
void vtkBiQuadraticQuadraticHexahedron::InterpolationDerivs(double pcoords[3],
|
|
double derivs[72])
|
|
{
|
|
//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 x = 2.0*(pcoords[0]-0.5);
|
|
double y = 2.0*(pcoords[1]-0.5);
|
|
double z = 2.0*(pcoords[2]-0.5);
|
|
|
|
// x direction
|
|
derivs[0] =-((y*y+(2*x-1)*y-2*x)*z*z+(-y*y+(1-2*x)*y+2*x)*z)/8;
|
|
derivs[1] =((y*y+(-2*x-1)*y+2*x)*z*z+(-y*y+(2*x+1)*y-2*x)*z)/8;
|
|
derivs[2] =((y*y+(2*x+1)*y+2*x)*z*z+(-y*y+(-2*x-1)*y-2*x)*z)/8;
|
|
derivs[3] =-((y*y+(1-2*x)*y-2*x)*z*z+(-y*y+(2*x-1)*y+2*x)*z)/8;
|
|
derivs[4] =-((y*y+(2*x-1)*y-2*x)*z*z+(y*y+(2*x-1)*y-2*x)*z)/8;
|
|
derivs[5] =((y*y+(-2*x-1)*y+2*x)*z*z+(y*y+(-2*x-1)*y+2*x)*z)/8;
|
|
derivs[6] =((y*y+(2*x+1)*y+2*x)*z*z+(y*y+(2*x+1)*y+2*x)*z)/8;
|
|
derivs[7] =-((y*y+(1-2*x)*y-2*x)*z*z+(y*y+(1-2*x)*y-2*x)*z)/8;
|
|
derivs[8] =((x*y-x)*z*z+(x-x*y)*z)/2;
|
|
derivs[9] =-((y*y-1)*z*z+(1-y*y)*z)/4;
|
|
derivs[10] =-((x*y+x)*z*z+(-x*y-x)*z)/2;
|
|
derivs[11] =((y*y-1)*z*z+(1-y*y)*z)/4;
|
|
derivs[12] =((x*y-x)*z*z+(x*y-x)*z)/2;
|
|
derivs[13] =-((y*y-1)*z*z+(y*y-1)*z)/4;
|
|
derivs[14] =-((x*y+x)*z*z+(x*y+x)*z)/2;
|
|
derivs[15] =((y*y-1)*z*z+(y*y-1)*z)/4;
|
|
derivs[16] =((y*y+(2*x-1)*y-2*x)*z*z-y*y+(1-2*x)*y+2*x)/4;
|
|
derivs[17] =-((y*y+(-2*x-1)*y+2*x)*z*z-y*y+(2*x+1)*y-2*x)/4;
|
|
derivs[18] =-((y*y+(2*x+1)*y+2*x)*z*z-y*y+(-2*x-1)*y-2*x)/4;
|
|
derivs[19] =((y*y+(1-2*x)*y-2*x)*z*z-y*y+(2*x-1)*y+2*x)/4;
|
|
derivs[20] =-((y*y-1)*z*z-y*y+1)/2;
|
|
derivs[21] =((y*y-1)*z*z-y*y+1)/2;
|
|
derivs[22] =(x-x*y)*z*z+x*y-x;
|
|
derivs[23] =(x*y+x)*z*z-x*y-x;
|
|
// y direction
|
|
derivs[24] =-(((2*x-2)*y+x*x-x)*z*z+((2-2*x)*y-x*x+x)*z)/8;
|
|
derivs[25] =(((2*x+2)*y-x*x-x)*z*z+((-2*x-2)*y+x*x+x)*z)/8;
|
|
derivs[26] =(((2*x+2)*y+x*x+x)*z*z+((-2*x-2)*y-x*x-x)*z)/8;
|
|
derivs[27] =-(((2*x-2)*y-x*x+x)*z*z+((2-2*x)*y+x*x-x)*z)/8;
|
|
derivs[28] =-(((2*x-2)*y+x*x-x)*z*z+((2*x-2)*y+x*x-x)*z)/8;
|
|
derivs[29] =(((2*x+2)*y-x*x-x)*z*z+((2*x+2)*y-x*x-x)*z)/8;
|
|
derivs[30] =(((2*x+2)*y+x*x+x)*z*z+((2*x+2)*y+x*x+x)*z)/8;
|
|
derivs[31] =-(((2*x-2)*y-x*x+x)*z*z+((2*x-2)*y-x*x+x)*z)/8;
|
|
derivs[32] =((x*x-1)*z*z+(1-x*x)*z)/4;
|
|
derivs[33] =-((x+1)*y*z*z+(-x-1)*y*z)/2;
|
|
derivs[34] =-((x*x-1)*z*z+(1-x*x)*z)/4;
|
|
derivs[35] =((x-1)*y*z*z+(1-x)*y*z)/2;
|
|
derivs[36] =((x*x-1)*z*z+(x*x-1)*z)/4;
|
|
derivs[37] =-((x+1)*y*z*z+(x+1)*y*z)/2;
|
|
derivs[38] =-((x*x-1)*z*z+(x*x-1)*z)/4;
|
|
derivs[39] =((x-1)*y*z*z+(x-1)*y*z)/2;
|
|
derivs[40] =(((2*x-2)*y+x*x-x)*z*z+(2-2*x)*y-x*x+x)/4;
|
|
derivs[41] =-(((2*x+2)*y-x*x-x)*z*z+(-2*x-2)*y+x*x+x)/4;
|
|
derivs[42] =-(((2*x+2)*y+x*x+x)*z*z+(-2*x-2)*y-x*x-x)/4;
|
|
derivs[43] =(((2*x-2)*y-x*x+x)*z*z+(2-2*x)*y+x*x-x)/4;
|
|
derivs[44] =(1-x)*y*z*z+(x-1)*y;
|
|
derivs[45] =(x+1)*y*z*z+(-x-1)*y;
|
|
derivs[46] =-((x*x-1)*z*z-x*x+1)/2;
|
|
derivs[47] =((x*x-1)*z*z-x*x+1)/2;
|
|
// z direction
|
|
derivs[48] =-(((2*x-2)*y*y+(2*x*x-2*x)*y-2*x*x+2)*z+(1-x)*y*y+(x-x*x)*y+x*x-1)/8;
|
|
derivs[49] =(((2*x+2)*y*y+(-2*x*x-2*x)*y+2*x*x-2)*z+(-x-1)*y*y+(x*x+x)*y-x*x+1)/8;
|
|
derivs[50] =(((2*x+2)*y*y+(2*x*x+2*x)*y+2*x*x-2)*z+(-x-1)*y*y+(-x*x-x)*y-x*x+1)/8;
|
|
derivs[51] =-(((2*x-2)*y*y+(2*x-2*x*x)*y-2*x*x+2)*z+(1-x)*y*y+(x*x-x)*y+x*x-1)/8;
|
|
derivs[52] =-(((2*x-2)*y*y+(2*x*x-2*x)*y-2*x*x+2)*z+(x-1)*y*y+(x*x-x)*y-x*x+1)/8;
|
|
derivs[53] =(((2*x+2)*y*y+(-2*x*x-2*x)*y+2*x*x-2)*z+(x+1)*y*y+(-x*x-x)*y+x*x-1)/8;
|
|
derivs[54] =(((2*x+2)*y*y+(2*x*x+2*x)*y+2*x*x-2)*z+(x+1)*y*y+(x*x+x)*y+x*x-1)/8;
|
|
derivs[55] =-(((2*x-2)*y*y+(2*x-2*x*x)*y-2*x*x+2)*z+(x-1)*y*y+(x-x*x)*y-x*x+1)/8;
|
|
derivs[56] =(((2*x*x-2)*y-2*x*x+2)*z+(1-x*x)*y+x*x-1)/4;
|
|
derivs[57] =-(((2*x+2)*y*y-2*x-2)*z+(-x-1)*y*y+x+1)/4;
|
|
derivs[58] =-(((2*x*x-2)*y+2*x*x-2)*z+(1-x*x)*y-x*x+1)/4;
|
|
derivs[59] =(((2*x-2)*y*y-2*x+2)*z+(1-x)*y*y+x-1)/4;
|
|
derivs[60] =(((2*x*x-2)*y-2*x*x+2)*z+(x*x-1)*y-x*x+1)/4;
|
|
derivs[61] =-(((2*x+2)*y*y-2*x-2)*z+(x+1)*y*y-x-1)/4;
|
|
derivs[62] =-(((2*x*x-2)*y+2*x*x-2)*z+(x*x-1)*y+x*x-1)/4;
|
|
derivs[63] =(((2*x-2)*y*y-2*x+2)*z+(x-1)*y*y-x+1)/4;
|
|
derivs[64] =((x-1)*y*y+(x*x-x)*y-x*x+1)*z/2;
|
|
derivs[65] =-((x+1)*y*y+(-x*x-x)*y+x*x-1)*z/2;
|
|
derivs[66] =-((x+1)*y*y+(x*x+x)*y+x*x-1)*z/2;
|
|
derivs[67] =((x-1)*y*y+(x-x*x)*y-x*x+1)*z/2;
|
|
derivs[68] =((1-x)*y*y+x-1)*z;
|
|
derivs[69] =((x+1)*y*y-x-1)*z;
|
|
derivs[70] =((1-x*x)*y+x*x-1)*z;
|
|
derivs[71] =((x*x-1)*y+x*x-1)*z;
|
|
|
|
// we compute derivatives in in [-1; 1] but we need them in [ 0; 1]
|
|
for(int i = 0; i < 72; i++)
|
|
derivs[i] *= 2;
|
|
|
|
}
|
|
|
|
//----------------------------------------------------------------------------
|
|
static double vtkQHexCellPCoords[72] ={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,
|
|
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
|
|
|
|
double *vtkBiQuadraticQuadraticHexahedron::GetParametricCoords()
|
|
{
|
|
return vtkQHexCellPCoords;
|
|
}
|
|
|
|
//----------------------------------------------------------------------------
|
|
void vtkBiQuadraticQuadraticHexahedron::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());
|
|
this->BiQuadFace->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());
|
|
}
|