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705 lines
24 KiB
705 lines
24 KiB
/*=========================================================================
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Program: Visualization Toolkit
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Module: $RCSfile: vtkQuadraticHexahedron.cxx,v $
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Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen
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All rights reserved.
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See Copyright.txt or http://www.kitware.com/Copyright.htm for details.
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This software is distributed WITHOUT ANY WARRANTY; without even
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the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
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PURPOSE. See the above copyright notice for more information.
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=========================================================================*/
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#include "vtkQuadraticHexahedron.h"
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#include "vtkCellData.h"
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#include "vtkDoubleArray.h"
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#include "vtkHexahedron.h"
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#include "vtkMath.h"
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#include "vtkObjectFactory.h"
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#include "vtkPointData.h"
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#include "vtkPointLocator.h"
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#include "vtkPolyData.h"
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#include "vtkQuadraticEdge.h"
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#include "vtkQuadraticQuad.h"
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vtkCxxRevisionMacro(vtkQuadraticHexahedron, "$Revision: 1.2 $");
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vtkStandardNewMacro(vtkQuadraticHexahedron);
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//----------------------------------------------------------------------------
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// Construct the hex with 20 points + 7 extra points for internal
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// computation.
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vtkQuadraticHexahedron::vtkQuadraticHexahedron()
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{
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// At times the cell looks like it has 27 points (during interpolation)
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// We initially allocate for 27.
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this->Points->SetNumberOfPoints(27);
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this->PointIds->SetNumberOfIds(27);
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for (int i = 0; i < 27; i++)
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{
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this->Points->SetPoint(i, 0.0, 0.0, 0.0);
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this->PointIds->SetId(i,0);
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}
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this->Points->SetNumberOfPoints(20);
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this->PointIds->SetNumberOfIds(20);
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this->Edge = vtkQuadraticEdge::New();
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this->Face = vtkQuadraticQuad::New();
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this->Hex = vtkHexahedron::New();
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this->PointData = vtkPointData::New();
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this->CellData = vtkCellData::New();
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this->CellScalars = vtkDoubleArray::New();
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this->CellScalars->SetNumberOfTuples(27);
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this->Scalars = vtkDoubleArray::New();
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this->Scalars->SetNumberOfTuples(8);
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}
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//----------------------------------------------------------------------------
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vtkQuadraticHexahedron::~vtkQuadraticHexahedron()
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{
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this->Edge->Delete();
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this->Face->Delete();
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this->Hex->Delete();
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this->PointData->Delete();
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this->CellData->Delete();
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this->Scalars->Delete();
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this->CellScalars->Delete();
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}
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static int LinearHexs[8][8] = { {0,8,24,11,16,22,26,20},
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{8,1,9,24,22,17,21,26},
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{11,24,10,3,20,26,23,19},
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{24,9,2,10,26,21,18,23},
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{16,22,26,20,4,12,25,15},
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{22,17,21,26,12,5,13,25},
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{20,26,23,19,15,25,14,7},
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{26,21,18,23,25,13,6,14} };
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static int HexFaces[6][8] = { {0,4,7,3,16,15,19,11},
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{1,2,6,5,9,18,13,17},
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{0,1,5,4,8,17,12,16},
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{3,7,6,2,19,14,18,10},
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{0,3,2,1,11,10,9,8},
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{4,5,6,7,12,13,14,15} };
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static int HexEdges[12][3] = { {0,1,8}, {1,2,9}, {3,2,10}, {0,3,11},
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{4,5,12}, {5,6,13}, {7,6,14}, {4,7,15},
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{0,4,16}, {1,5,17}, {3,7,19}, {2,6,18} };
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static double MidPoints[7][3] = { {0.0,0.5,0.5}, {1.0,0.5,0.5},
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{0.5,0.0,0.5}, {0.5,1.0,0.5},
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{0.5,0.5,0.0}, {0.5,0.5,1.0},
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{0.5,0.5,0.5} };
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//----------------------------------------------------------------------------
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vtkCell *vtkQuadraticHexahedron::GetEdge(int edgeId)
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{
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edgeId = (edgeId < 0 ? 0 : (edgeId > 11 ? 11 : edgeId ));
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for (int i=0; i<3; i++)
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{
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this->Edge->PointIds->SetId(i,this->PointIds->GetId(HexEdges[edgeId][i]));
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this->Edge->Points->SetPoint(i,this->Points->GetPoint(HexEdges[edgeId][i]));
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}
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return this->Edge;
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}
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//----------------------------------------------------------------------------
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vtkCell *vtkQuadraticHexahedron::GetFace(int faceId)
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{
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faceId = (faceId < 0 ? 0 : (faceId > 5 ? 5 : faceId ));
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for (int i=0; i<8; i++)
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{
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this->Face->PointIds->SetId(i,this->PointIds->GetId(HexFaces[faceId][i]));
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this->Face->Points->SetPoint(i,this->Points->GetPoint(HexFaces[faceId][i]));
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}
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return this->Face;
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}
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//----------------------------------------------------------------------------
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void vtkQuadraticHexahedron::Subdivide(vtkPointData *inPd, vtkCellData *inCd,
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vtkIdType cellId, vtkDataArray *cellScalars)
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{
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int numMidPts, i, j;
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double weights[20];
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double x[3];
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double s;
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//Copy point and cell attribute data, first make sure it's empty:
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this->PointData->Initialize();
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this->CellData->Initialize();
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this->PointData->CopyAllocate(inPd,27);
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this->CellData->CopyAllocate(inCd,8);
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for (i=0; i<20; i++)
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{
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this->PointData->CopyData(inPd,this->PointIds->GetId(i),i);
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this->CellScalars->SetValue( i, cellScalars->GetTuple1(i));
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}
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this->CellData->CopyData(inCd,cellId,0);
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//Interpolate new values
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double p[3];
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for ( numMidPts=0; numMidPts < 7; numMidPts++ )
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{
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this->InterpolationFunctions(MidPoints[numMidPts], weights);
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x[0] = x[1] = x[2] = 0.0;
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s = 0.0;
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for (i=0; i<20; i++)
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{
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this->Points->GetPoint(i, p);
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for (j=0; j<3; j++)
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{
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x[j] += p[j] * weights[i];
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}
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s += cellScalars->GetTuple1(i) * weights[i];
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}
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this->Points->SetPoint(20+numMidPts,x);
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this->CellScalars->SetValue(20+numMidPts,s);
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this->PointData->InterpolatePoint(inPd, 20+numMidPts,
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this->PointIds, weights);
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}
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}
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//----------------------------------------------------------------------------
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static const double VTK_DIVERGED = 1.e6;
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static const int VTK_HEX_MAX_ITERATION=10;
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static const double VTK_HEX_CONVERGED=1.e-03;
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int vtkQuadraticHexahedron::EvaluatePosition(double* x,
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double* closestPoint,
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int& subId, double pcoords[3],
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double& dist2, double *weights)
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{
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int iteration, converged;
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double params[3];
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double fcol[3], rcol[3], scol[3], tcol[3];
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int i, j;
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double d, pt[3];
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double derivs[60];
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// set initial position for Newton's method
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subId = 0;
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pcoords[0] = pcoords[1] = pcoords[2] = params[0] = params[1] = params[2]=0.5;
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// enter iteration loop
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for (iteration=converged=0;
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!converged && (iteration < VTK_HEX_MAX_ITERATION); iteration++)
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{
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// calculate element interpolation functions and derivatives
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this->InterpolationFunctions(pcoords, weights);
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this->InterpolationDerivs(pcoords, derivs);
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// calculate newton functions
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for (i=0; i<3; i++)
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{
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fcol[i] = rcol[i] = scol[i] = tcol[i] = 0.0;
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}
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for (i=0; i<20; i++)
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{
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this->Points->GetPoint(i, pt);
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for (j=0; j<3; j++)
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{
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fcol[j] += pt[j] * weights[i];
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rcol[j] += pt[j] * derivs[i];
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scol[j] += pt[j] * derivs[i+20];
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tcol[j] += pt[j] * derivs[i+40];
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}
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}
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for (i=0; i<3; i++)
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{
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fcol[i] -= x[i];
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}
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// compute determinants and generate improvements
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d=vtkMath::Determinant3x3(rcol,scol,tcol);
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if ( fabs(d) < 1.e-20)
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{
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return -1;
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}
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pcoords[0] = params[0] - 0.5*vtkMath::Determinant3x3 (fcol,scol,tcol) / d;
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pcoords[1] = params[1] - 0.5*vtkMath::Determinant3x3 (rcol,fcol,tcol) / d;
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pcoords[2] = params[2] - 0.5*vtkMath::Determinant3x3 (rcol,scol,fcol) / d;
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// check for convergence
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if ( ((fabs(pcoords[0]-params[0])) < VTK_HEX_CONVERGED) &&
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((fabs(pcoords[1]-params[1])) < VTK_HEX_CONVERGED) &&
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((fabs(pcoords[2]-params[2])) < VTK_HEX_CONVERGED) )
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{
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converged = 1;
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}
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// Test for bad divergence (S.Hirschberg 11.12.2001)
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else if ((fabs(pcoords[0]) > VTK_DIVERGED) ||
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(fabs(pcoords[1]) > VTK_DIVERGED) ||
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(fabs(pcoords[2]) > VTK_DIVERGED))
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{
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return -1;
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}
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// if not converged, repeat
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else
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{
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params[0] = pcoords[0];
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params[1] = pcoords[1];
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params[2] = pcoords[2];
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}
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}
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// if not converged, set the parametric coordinates to arbitrary values
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// outside of element
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if ( !converged )
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{
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return -1;
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}
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this->InterpolationFunctions(pcoords, weights);
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if ( pcoords[0] >= -0.001 && pcoords[0] <= 1.001 &&
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pcoords[1] >= -0.001 && pcoords[1] <= 1.001 &&
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pcoords[2] >= -0.001 && pcoords[2] <= 1.001 )
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{
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if (closestPoint)
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{
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closestPoint[0] = x[0]; closestPoint[1] = x[1]; closestPoint[2] = x[2];
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dist2 = 0.0; //inside hexahedron
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}
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return 1;
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}
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else
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{
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double pc[3], w[20];
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if (closestPoint)
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{
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for (i=0; i<3; i++) //only approximate, not really true for warped hexa
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{
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if (pcoords[i] < 0.0)
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{
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pc[i] = 0.0;
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}
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else if (pcoords[i] > 1.0)
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{
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pc[i] = 1.0;
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}
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else
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{
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pc[i] = pcoords[i];
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}
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}
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this->EvaluateLocation(subId, pc, closestPoint, (double *)w);
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dist2 = vtkMath::Distance2BetweenPoints(closestPoint,x);
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}
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return 0;
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}
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}
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//----------------------------------------------------------------------------
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void vtkQuadraticHexahedron::EvaluateLocation(int& vtkNotUsed(subId),
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double pcoords[3],
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double x[3], double *weights)
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{
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int i, j;
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double pt[3];
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this->InterpolationFunctions(pcoords, weights);
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x[0] = x[1] = x[2] = 0.0;
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for (i=0; i<20; i++)
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{
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this->Points->GetPoint(i, pt);
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for (j=0; j<3; j++)
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{
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x[j] += pt[j] * weights[i];
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}
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}
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}
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//----------------------------------------------------------------------------
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int vtkQuadraticHexahedron::CellBoundary(int subId, double pcoords[3],
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vtkIdList *pts)
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{
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return this->Hex->CellBoundary(subId, pcoords, pts);
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}
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//----------------------------------------------------------------------------
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void vtkQuadraticHexahedron::Contour(double value,
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vtkDataArray* cellScalars,
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vtkPointLocator* locator,
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vtkCellArray *verts,
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vtkCellArray* lines,
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vtkCellArray* polys,
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vtkPointData* inPd,
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vtkPointData* outPd,
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vtkCellData* inCd,
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vtkIdType cellId,
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vtkCellData* outCd)
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{
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//subdivide into 8 linear hexs
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this->Subdivide(inPd,inCd,cellId, cellScalars);
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//contour each linear quad separately
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for (int i=0; i<8; i++) // For each subdivided hexahedron
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{
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for (int j=0; j<8; j++) // For each of the eight vertices of the hexhedron
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{
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this->Hex->Points->SetPoint(j,this->Points->GetPoint(LinearHexs[i][j]));
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this->Hex->PointIds->SetId(j,LinearHexs[i][j]);
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this->Scalars->SetValue(j,this->CellScalars->GetValue(LinearHexs[i][j]));
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}
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this->Hex->Contour(value,this->Scalars,locator,verts,lines,polys,
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this->PointData,outPd,this->CellData,cellId,outCd);
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}
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}
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//----------------------------------------------------------------------------
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// Line-hex intersection. Intersection has to occur within [0,1] parametric
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// coordinates and with specified tolerance.
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int vtkQuadraticHexahedron::IntersectWithLine(double* p1, double* p2,
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double tol, double& t,
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double* x, double* pcoords,
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int& subId)
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{
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int intersection=0;
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double tTemp;
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double pc[3], xTemp[3];
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int faceNum;
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t = VTK_DOUBLE_MAX;
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for (faceNum=0; faceNum<6; faceNum++)
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{
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for (int i=0; i<8; i++)
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{
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this->Face->Points->SetPoint(i,
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this->Points->GetPoint(HexFaces[faceNum][i]));
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}
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if ( this->Face->IntersectWithLine(p1, p2, tol, tTemp,
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xTemp, pc, subId) )
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{
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intersection = 1;
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if ( tTemp < t )
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{
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t = tTemp;
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x[0] = xTemp[0]; x[1] = xTemp[1]; x[2] = xTemp[2];
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switch (faceNum)
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{
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case 0:
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pcoords[0] = 0.0; pcoords[1] = pc[1]; pcoords[2] = pc[0];
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break;
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case 1:
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pcoords[0] = 1.0; pcoords[1] = pc[0]; pcoords[2] = pc[1];
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break;
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case 2:
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pcoords[0] = pc[0]; pcoords[1] = 0.0; pcoords[2] = pc[1];
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break;
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case 3:
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pcoords[0] = pc[1]; pcoords[1] = 1.0; pcoords[2] = pc[0];
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break;
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case 4:
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pcoords[0] = pc[1]; pcoords[1] = pc[0]; pcoords[2] = 0.0;
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break;
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case 5:
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pcoords[0] = pc[0]; pcoords[1] = pc[1]; pcoords[2] = 1.0;
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break;
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}
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}
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}
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}
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return intersection;
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}
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//----------------------------------------------------------------------------
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int vtkQuadraticHexahedron::Triangulate(int vtkNotUsed(index),
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vtkIdList *ptIds, vtkPoints *pts)
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{
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pts->Reset();
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ptIds->Reset();
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ptIds->InsertId(0,this->PointIds->GetId(0));
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pts->InsertPoint(0,this->Points->GetPoint(0));
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ptIds->InsertId(1,this->PointIds->GetId(1));
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pts->InsertPoint(1,this->Points->GetPoint(1));
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return 1;
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}
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//----------------------------------------------------------------------------
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// Given parametric coordinates compute inverse Jacobian transformation
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// matrix. Returns 9 elements of 3x3 inverse Jacobian plus interpolation
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// function derivatives.
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void vtkQuadraticHexahedron::JacobianInverse(double pcoords[3],
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double **inverse,
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double derivs[60])
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{
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int i, j;
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double *m[3], m0[3], m1[3], m2[3];
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double x[3];
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// compute interpolation function derivatives
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this->InterpolationDerivs(pcoords, derivs);
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// create Jacobian matrix
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m[0] = m0; m[1] = m1; m[2] = m2;
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for (i=0; i < 3; i++) //initialize matrix
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{
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m0[i] = m1[i] = m2[i] = 0.0;
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}
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for ( j=0; j < 20; j++ )
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{
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this->Points->GetPoint(j, x);
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for ( i=0; i < 3; i++ )
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{
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m0[i] += x[i] * derivs[j];
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m1[i] += x[i] * derivs[20 + j];
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m2[i] += x[i] * derivs[40 + j];
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}
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}
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// now find the inverse
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if ( vtkMath::InvertMatrix(m,inverse,3) == 0 )
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{
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vtkErrorMacro(<<"Jacobian inverse not found");
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return;
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}
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}
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//----------------------------------------------------------------------------
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void vtkQuadraticHexahedron::Derivatives(int vtkNotUsed(subId),
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double pcoords[3], double *values,
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int dim, double *derivs)
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{
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|
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,
|
|
vtkPointLocator* 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;
|
|
}
|
|
|
|
//----------------------------------------------------------------------------
|
|
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());
|
|
}
|
|
|