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755 lines
22 KiB
C++
755 lines
22 KiB
C++
/*=========================================================================
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Program: Visualization Toolkit
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Module: vtkTriQuadraticHexahedron.cxx
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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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//Thanks to Soeren Gebbert who developed this class and
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//integrated it into VTK 5.0.
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#include "vtkTriQuadraticHexahedron.h"
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#include "vtkObjectFactory.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 "vtkQuadraticEdge.h"
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#include "vtkBiQuadraticQuad.h"
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#include "vtkPoints.h"
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vtkStandardNewMacro (vtkTriQuadraticHexahedron);
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//----------------------------------------------------------------------------
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// Construct the triquadhex with 27 nodes
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vtkTriQuadraticHexahedron::vtkTriQuadraticHexahedron ()
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{
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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->Edge = vtkQuadraticEdge::New ();
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this->Face = vtkBiQuadraticQuad::New ();
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this->Hex = vtkHexahedron::New ();
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this->Scalars = vtkDoubleArray::New ();
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this->Scalars->SetNumberOfTuples (8); // vertices of a linear hexahedron
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}
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//----------------------------------------------------------------------------
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vtkTriQuadraticHexahedron::~vtkTriQuadraticHexahedron ()
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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->Scalars->Delete ();
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}
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//----------------------------------------------------------------------------
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static int LinearHexs[8][8] = {
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{ 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][9] = {
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{0, 4, 7, 3, 16, 15, 19, 11, 20},
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{1, 2, 6, 5, 9, 18, 13, 17, 21},
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{0, 1, 5, 4, 8, 17, 12, 16, 22},
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{3, 7, 6, 2, 19, 14, 18, 10, 23},
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{0, 3, 2, 1, 11, 10, 9, 8, 24},
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{4, 5, 6, 7, 12, 13, 14, 15, 25} };
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static int HexEdges[12][3] = {
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{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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};
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//----------------------------------------------------------------------------
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int *vtkTriQuadraticHexahedron::GetEdgeArray(int edgeId)
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{
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return HexEdges[edgeId];
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}
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//----------------------------------------------------------------------------
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int *vtkTriQuadraticHexahedron::GetFaceArray(int faceId)
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{
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return HexFaces[faceId];
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}
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//----------------------------------------------------------------------------
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vtkCell * vtkTriQuadraticHexahedron::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 * vtkTriQuadraticHexahedron::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 < 9; 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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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 vtkTriQuadraticHexahedron::EvaluatePosition (double *x,
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double *closestPoint,
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int &subId, double pcoords[3], 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 = 0.0;
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double pt[3];
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double derivs[81];
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double hexweights[8];
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// set initial position for Newton's method
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pcoords[0] = pcoords[1] = pcoords[2] = params[0] = params[1] = params[2] = 0.5;
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subId = 0;
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// Use a tri-linear hexahederon to get good starting values
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vtkHexahedron *hex = vtkHexahedron::New();
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for(i = 0; i < 8; i++)
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hex->GetPoints()->SetPoint(i, this->Points->GetPoint(i));
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hex->EvaluatePosition(x, closestPoint, subId, pcoords, dist2, hexweights);
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hex->Delete();
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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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// enter iteration loop
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for (iteration = converged = 0; !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 < 27; 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 + 27];
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tcol[j] += pt[j] * derivs[i + 54];
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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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vtkDebugMacro (<<"Determinant incorrect, iteration " << iteration);
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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) || (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 && 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];
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closestPoint[1] = x[1];
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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[27];
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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,
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static_cast<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 vtkTriQuadraticHexahedron::EvaluateLocation (int &vtkNotUsed (subId),
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double pcoords[3], 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 < 27; 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
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vtkTriQuadraticHexahedron::CellBoundary (int subId, double pcoords[3], 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 vtkTriQuadraticHexahedron::Contour (double value,
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vtkDataArray * cellScalars,
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vtkIncrementalPointLocator * 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, vtkIdType cellId, vtkCellData * outCd)
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{
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//contour each linear hex separately
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for (int i = 0; i < 8; i++)
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{
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for (int j = 0; j < 8; j++)
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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, this->PointIds->GetId(LinearHexs[i][j]));
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this->Scalars->SetValue (j, cellScalars->GetTuple1 (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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inPd, outPd, inCd, cellId, outCd);
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}
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}
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//----------------------------------------------------------------------------
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// Clip this triquadratic hex using scalar value provided. Like contouring,
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// except that it cuts the hex to produce tetrahedra.
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void vtkTriQuadraticHexahedron::Clip (double value,
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vtkDataArray * cellScalars,
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vtkIncrementalPointLocator * locator,
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vtkCellArray * tets,
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vtkPointData * inPd,
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vtkPointData * outPd,
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vtkCellData * inCd, vtkIdType cellId,
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vtkCellData * outCd, int insideOut)
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{
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//clip each linear hex separately
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for (int i = 0; i < 8; i++)
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{
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for (int j = 0; j < 8; j++)
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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, this->PointIds->GetId(LinearHexs[i][j]));
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this->Scalars->SetValue (j, cellScalars->GetTuple1 (LinearHexs[i][j]));
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}
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this->Hex->Clip (value, this->Scalars, locator, tets, inPd, outPd, inCd, cellId, outCd, insideOut);
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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 vtkTriQuadraticHexahedron::IntersectWithLine (double *p1, double *p2,
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double tol, double &t, double *x, double *pcoords, 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 < 9; i++)
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{
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this->Face->PointIds->SetId(i,this->PointIds->GetId(HexFaces[faceNum][i]));
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this->Face->Points->SetPoint (i, this->Points->GetPoint (HexFaces[faceNum][i]));
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}
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if (this->Face->IntersectWithLine (p1, p2, tol, tTemp, 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];
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x[1] = xTemp[1];
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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;
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pcoords[1] = pc[1];
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pcoords[2] = pc[0];
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break;
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case 1:
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pcoords[0] = 1.0;
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pcoords[1] = pc[0];
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pcoords[2] = pc[1];
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break;
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case 2:
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pcoords[0] = pc[0];
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pcoords[1] = 0.0;
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pcoords[2] = pc[1];
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break;
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case 3:
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pcoords[0] = pc[1];
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pcoords[1] = 1.0;
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pcoords[2] = pc[0];
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break;
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case 4:
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pcoords[0] = pc[1];
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pcoords[1] = pc[0];
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pcoords[2] = 0.0;
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break;
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case 5:
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pcoords[0] = pc[0];
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pcoords[1] = pc[1];
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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 vtkTriQuadraticHexahedron::Triangulate (int vtkNotUsed (index), 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
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vtkTriQuadraticHexahedron::JacobianInverse (double pcoords[3], double **inverse, double derivs[81])
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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;
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m[1] = m1;
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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 < 27; 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[27 + j];
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m2[i] += x[i] * derivs[54 + 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 vtkTriQuadraticHexahedron::Derivatives (int vtkNotUsed (subId),
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double pcoords[3], double *values, int dim, double *derivs)
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{
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double *jI[3], j0[3], j1[3], j2[3];
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double functionDerivs[81], sum[3];
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int i, j, k;
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// compute inverse Jacobian and interpolation function derivatives
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jI[0] = j0;
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jI[1] = j1;
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jI[2] = j2;
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this->JacobianInverse (pcoords, jI, functionDerivs);
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// 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 < 27; i++) //loop over interp. function derivatives
|
|
{
|
|
sum[0] += functionDerivs[i] * values[dim * i + k];
|
|
sum[1] += functionDerivs[27 + i] * values[dim * i + k];
|
|
sum[2] += functionDerivs[54 + 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];
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
|
|
//----------------------------------------------------------------------------
|
|
// Compute interpolation functions for the 27 nodes.
|
|
void vtkTriQuadraticHexahedron::InterpolationFunctions (double pcoords[3], double weights[27])
|
|
{
|
|
//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 g1r = -0.5 * r * (1 - r);
|
|
double g1s = -0.5 * s * (1 - s);
|
|
double g1t = -0.5 * t * (1 - t);
|
|
|
|
double g2r = (1 + r)*(1 - r);
|
|
double g2s = (1 + s)*(1 - s);
|
|
double g2t = (1 + t)*(1 - t);
|
|
|
|
double g3r = 0.5 * r * (1 + r);
|
|
double g3s = 0.5 * s * (1 + s);
|
|
double g3t = 0.5 * t * (1 + t);
|
|
|
|
|
|
//The eight corner points
|
|
weights[0] = g1r * g1s * g1t;
|
|
weights[1] = g3r * g1s * g1t;
|
|
weights[2] = g3r * g3s * g1t;
|
|
weights[3] = g1r * g3s * g1t;
|
|
weights[4] = g1r * g1s * g3t;
|
|
weights[5] = g3r * g1s * g3t;
|
|
weights[6] = g3r * g3s * g3t;
|
|
weights[7] = g1r * g3s * g3t;
|
|
|
|
//The mid-edge nodes
|
|
weights[8] = g2r * g1s * g1t;
|
|
weights[9] = g3r * g2s * g1t;
|
|
weights[10] = g2r * g3s * g1t;
|
|
weights[11] = g1r * g2s * g1t;
|
|
weights[12] = g2r * g1s * g3t;
|
|
weights[13] = g3r * g2s * g3t;
|
|
weights[14] = g2r * g3s * g3t;
|
|
weights[15] = g1r * g2s * g3t;
|
|
weights[16] = g1r * g1s * g2t;
|
|
weights[17] = g3r * g1s * g2t;
|
|
weights[18] = g3r * g3s * g2t;
|
|
weights[19] = g1r * g3s * g2t;
|
|
|
|
//face center nodes
|
|
weights[22] = g2r * g1s * g2t;
|
|
weights[21] = g3r * g2s * g2t;
|
|
weights[23] = g2r * g3s * g2t;
|
|
weights[20] = g1r * g2s * g2t;
|
|
weights[24] = g2r * g2s * g1t;
|
|
weights[25] = g2r * g2s * g3t;
|
|
|
|
//Cell center node
|
|
weights[26] = g2r * g2s * g2t;
|
|
}
|
|
|
|
//----------------------------------------------------------------------------
|
|
// Derivatives in parametric space.
|
|
void vtkTriQuadraticHexahedron::InterpolationDerivs (double pcoords[3],
|
|
double derivs[81])
|
|
{
|
|
//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 g1r = -0.5 * r * (1 - r);
|
|
double g1s = -0.5 * s * (1 - s);
|
|
double g1t = -0.5 * t * (1 - t);
|
|
|
|
double g2r = (1 + r)*(1 - r);
|
|
double g2s = (1 + s)*(1 - s);
|
|
double g2t = (1 + t)*(1 - t);
|
|
|
|
double g3r = 0.5 * r * (1 + r);
|
|
double g3s = 0.5 * s * (1 + s);
|
|
double g3t = 0.5 * t * (1 + t);
|
|
|
|
double g1r_r = r - 0.5;
|
|
double g1s_s = s - 0.5;
|
|
double g1t_t = t - 0.5;
|
|
|
|
double g2r_r = -2*r;
|
|
double g2s_s = -2*s;
|
|
double g2t_t = -2*t;
|
|
|
|
double g3r_r = r + 0.5;
|
|
double g3s_s = s + 0.5;
|
|
double g3t_t = t + 0.5;
|
|
|
|
|
|
//r-derivatives
|
|
derivs[0] = g1r_r * g1s * g1t;
|
|
derivs[1] = g3r_r * g1s * g1t;
|
|
derivs[2] = g3r_r * g3s * g1t;
|
|
derivs[3] = g1r_r * g3s * g1t;
|
|
derivs[4] = g1r_r * g1s * g3t;
|
|
derivs[5] = g3r_r * g1s * g3t;
|
|
derivs[6] = g3r_r * g3s * g3t;
|
|
derivs[7] = g1r_r * g3s * g3t;
|
|
derivs[8] = g2r_r * g1s * g1t;
|
|
derivs[9] = g3r_r * g2s * g1t;
|
|
derivs[10]= g2r_r * g3s * g1t;
|
|
derivs[11]= g1r_r * g2s * g1t;
|
|
derivs[12]= g2r_r * g1s * g3t;
|
|
derivs[13]= g3r_r * g2s * g3t;
|
|
derivs[14]= g2r_r * g3s * g3t;
|
|
derivs[15]= g1r_r * g2s * g3t;
|
|
derivs[16]= g1r_r * g1s * g2t;
|
|
derivs[17]= g3r_r * g1s * g2t;
|
|
derivs[18]= g3r_r * g3s * g2t;
|
|
derivs[19]= g1r_r * g3s * g2t;
|
|
derivs[20]= g1r_r * g2s * g2t;
|
|
derivs[21]= g3r_r * g2s * g2t;
|
|
derivs[22]= g2r_r * g1s * g2t;
|
|
derivs[23]= g2r_r * g3s * g2t;
|
|
derivs[24]= g2r_r * g2s * g1t;
|
|
derivs[25]= g2r_r * g2s * g3t;
|
|
derivs[26]= g2r_r * g2s * g2t;
|
|
|
|
//s-derivatives
|
|
derivs[27] = g1r * g1s_s * g1t;
|
|
derivs[28] = g3r * g1s_s * g1t;
|
|
derivs[29] = g3r * g3s_s * g1t;
|
|
derivs[30] = g1r * g3s_s * g1t;
|
|
derivs[31] = g1r * g1s_s * g3t;
|
|
derivs[32] = g3r * g1s_s * g3t;
|
|
derivs[33] = g3r * g3s_s * g3t;
|
|
derivs[34] = g1r * g3s_s * g3t;
|
|
derivs[35] = g2r * g1s_s * g1t;
|
|
derivs[36] = g3r * g2s_s * g1t;
|
|
derivs[37] = g2r * g3s_s * g1t;
|
|
derivs[38] = g1r * g2s_s * g1t;
|
|
derivs[39] = g2r * g1s_s * g3t;
|
|
derivs[40] = g3r * g2s_s * g3t;
|
|
derivs[41] = g2r * g3s_s * g3t;
|
|
derivs[42] = g1r * g2s_s * g3t;
|
|
derivs[43] = g1r * g1s_s * g2t;
|
|
derivs[44] = g3r * g1s_s * g2t;
|
|
derivs[45] = g3r * g3s_s * g2t;
|
|
derivs[46] = g1r * g3s_s * g2t;
|
|
derivs[47] = g1r * g2s_s * g2t;
|
|
derivs[48] = g3r * g2s_s * g2t;
|
|
derivs[49] = g2r * g1s_s * g2t;
|
|
derivs[50] = g2r * g3s_s * g2t;
|
|
derivs[51] = g2r * g2s_s * g1t;
|
|
derivs[52] = g2r * g2s_s * g3t;
|
|
derivs[53] = g2r * g2s_s * g2t;
|
|
|
|
//t-derivatives
|
|
derivs[54] = g1r * g1s * g1t_t;
|
|
derivs[55] = g3r * g1s * g1t_t;
|
|
derivs[56] = g3r * g3s * g1t_t;
|
|
derivs[57] = g1r * g3s * g1t_t;
|
|
derivs[58] = g1r * g1s * g3t_t;
|
|
derivs[59] = g3r * g1s * g3t_t;
|
|
derivs[60] = g3r * g3s * g3t_t;
|
|
derivs[61] = g1r * g3s * g3t_t;
|
|
derivs[62] = g2r * g1s * g1t_t;
|
|
derivs[63] = g3r * g2s * g1t_t;
|
|
derivs[64] = g2r * g3s * g1t_t;
|
|
derivs[65] = g1r * g2s * g1t_t;
|
|
derivs[66] = g2r * g1s * g3t_t;
|
|
derivs[67] = g3r * g2s * g3t_t;
|
|
derivs[68] = g2r * g3s * g3t_t;
|
|
derivs[69] = g1r * g2s * g3t_t;
|
|
derivs[70] = g1r * g1s * g2t_t;
|
|
derivs[71] = g3r * g1s * g2t_t;
|
|
derivs[72] = g3r * g3s * g2t_t;
|
|
derivs[73] = g1r * g3s * g2t_t;
|
|
derivs[74] = g1r * g2s * g2t_t;
|
|
derivs[75] = g3r * g2s * g2t_t;
|
|
derivs[76] = g2r * g1s * g2t_t;
|
|
derivs[77] = g2r * g3s * g2t_t;
|
|
derivs[78] = g2r * g2s * g1t_t;
|
|
derivs[79] = g2r * g2s * g3t_t;
|
|
derivs[80] = g2r * g2s * g2t_t;
|
|
|
|
// we compute derivatives in in [-1; 1] but we need them in [ 0; 1]
|
|
for(int i = 0; i < 81; i++)
|
|
derivs[i] *= 2;
|
|
|
|
}
|
|
|
|
//----------------------------------------------------------------------------
|
|
static double vtkQHexCellPCoords[81] = {
|
|
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
|
|
0.5, 0.5, 0.0, // 24
|
|
0.5, 0.5, 1.0, // 25
|
|
0.5, 0.5, 0.5 // 26
|
|
};
|
|
|
|
double *vtkTriQuadraticHexahedron::GetParametricCoords ()
|
|
{
|
|
return vtkQHexCellPCoords;
|
|
}
|
|
|
|
//----------------------------------------------------------------------------
|
|
void vtkTriQuadraticHexahedron::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 << "Scalars:\n";
|
|
this->Scalars->PrintSelf (os, indent.GetNextIndent ());
|
|
}
|