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842 lines
27 KiB
C++
842 lines
27 KiB
C++
/*=========================================================================
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Program: Visualization Toolkit
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Module: vtkQuadraticPyramid.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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#include "vtkQuadraticPyramid.h"
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#include "vtkObjectFactory.h"
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#include "vtkCellData.h"
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#include "vtkDoubleArray.h"
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#include "vtkTetra.h"
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#include "vtkPyramid.h"
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#include "vtkMath.h"
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#include "vtkPointData.h"
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#include "vtkQuadraticEdge.h"
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#include "vtkQuadraticQuad.h"
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#include "vtkQuadraticTriangle.h"
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#include "vtkPoints.h"
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vtkStandardNewMacro(vtkQuadraticPyramid);
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//----------------------------------------------------------------------------
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// Construct the pyramid with 13 points + 1 extra point for internal
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// computation.
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//
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vtkQuadraticPyramid::vtkQuadraticPyramid()
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{
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// At creation time the cell looks like it has 14 points (during interpolation)
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// We initially allocate for 14.
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this->Points->SetNumberOfPoints(14);
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this->PointIds->SetNumberOfIds(14);
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for (int i = 0; i < 14; 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(13);
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this->PointIds->SetNumberOfIds(13);
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this->Edge = vtkQuadraticEdge::New();
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this->Face = vtkQuadraticQuad::New();
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this->TriangleFace = vtkQuadraticTriangle::New();
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this->Tetra = vtkTetra::New();
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this->Pyramid = vtkPyramid::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(14);
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this->Scalars = vtkDoubleArray::New();
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this->Scalars->SetNumberOfTuples(5); //num of vertices
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}
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//----------------------------------------------------------------------------
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vtkQuadraticPyramid::~vtkQuadraticPyramid()
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{
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this->Edge->Delete();
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this->Face->Delete();
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this->TriangleFace->Delete();
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this->Tetra->Delete();
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this->Pyramid->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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//----------------------------------------------------------------------------
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static int LinearPyramids[10][5] = { {0,5,13,8,9},
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{5,1,6,13,10},
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{8,13,7,3,12},
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{13,6,2,7,11},
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{9,10,11,12,4},
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{9,12,11,10,13},
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{5,10,9,13,0},
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{6,11,10,13,0},
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{7,12,11,13,0},
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{8,9,12,13,0} };
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static int PyramidFaces[5][8] = { {0,3,2,1,8,7,6,5},
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{0,1,4,5,10,9,0,0},
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{1,2,4,6,11,10,0,0},
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{2,3,4,7,12,11,0,0},
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{3,0,4,8,9,12,0,0}};
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static int PyramidEdges[8][3] = { {0,1,5}, {1,2,6}, {2,3,7},
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{3,0,8},{0,4,9},{1,4,10},
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{2,4,11}, {3,4,12} };
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static double MidPoints[1][3] = { {0.5,0.5,0.0} };
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//----------------------------------------------------------------------------
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int *vtkQuadraticPyramid::GetEdgeArray(int edgeId)
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{
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return PyramidEdges[edgeId];
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}
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//----------------------------------------------------------------------------
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int *vtkQuadraticPyramid::GetFaceArray(int faceId)
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{
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return PyramidFaces[faceId];
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}
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//----------------------------------------------------------------------------
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vtkCell *vtkQuadraticPyramid::GetEdge(int edgeId)
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{
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edgeId = (edgeId < 0 ? 0 : (edgeId > 7 ? 7 : 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(PyramidEdges[edgeId][i]));
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this->Edge->Points->SetPoint(i,this->Points->GetPoint(PyramidEdges[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 *vtkQuadraticPyramid::GetFace(int faceId)
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{
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faceId = (faceId < 0 ? 0 : (faceId > 4 ? 4 : faceId ));
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// load point id's and coordinates
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// be careful with the first one:
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if(faceId > 0)
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{
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for (int i=0; i<6; i++)
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{
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this->TriangleFace->PointIds->SetId(i,this->PointIds->GetId(PyramidFaces[faceId][i]));
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this->TriangleFace->Points->SetPoint(i,this->Points->GetPoint(PyramidFaces[faceId][i]));
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}
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return this->TriangleFace;
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}
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else
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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->PointIds->SetId(i,this->PointIds->GetId(PyramidFaces[faceId][i]));
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this->Face->Points->SetPoint(i,this->Points->GetPoint(PyramidFaces[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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//----------------------------------------------------------------------------
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static const double VTK_DIVERGED = 1.e6;
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static const int VTK_PYRAMID_MAX_ITERATION=10;
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static const double VTK_PYRAMID_CONVERGED=1.e-03;
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int vtkQuadraticPyramid::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 i, j;
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subId = 0;
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// There are problems searching for the apex point so we check if
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// we are there first before doing the full parametric inversion.
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vtkPoints* points = this->GetPoints();
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double apexPoint[3];
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points->GetPoint(4, apexPoint);
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dist2 = vtkMath::Distance2BetweenPoints(apexPoint, x);
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double baseMidpoint[3];
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points->GetPoint(0, baseMidpoint);
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for(i=1;i<4;i++)
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{
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double tmp[3];
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points->GetPoint(i, tmp);
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for(j=0;j<3;j++)
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{
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baseMidpoint[j] += tmp[j];
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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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baseMidpoint[i] /= 4.;
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}
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double length2 = vtkMath::Distance2BetweenPoints(apexPoint, baseMidpoint);
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// we use .001 as the relative tolerance here since that is the same
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// that is used for the interior cell check below but we need to
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// square it here because we're looking at dist2^2.
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if(dist2 == 0. || ( length2 != 0. && dist2/length2 < 1.e-6) )
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{
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pcoords[0] = pcoords[1] = 0;
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pcoords[2] = 1;
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this->InterpolationFunctions(pcoords, weights);
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if(closestPoint)
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{
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memcpy(closestPoint, x, 3*sizeof(double));
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dist2 = 0.;
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}
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return 1;
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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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double d, pt[3];
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double derivs[3*13];
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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_PYRAMID_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<13; 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+13];
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tcol[j] += pt[j] * derivs[i+26];
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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_PYRAMID_CONVERGED) &&
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((fabs(pcoords[1]-params[1])) < VTK_PYRAMID_CONVERGED) &&
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((fabs(pcoords[2]-params[2])) < VTK_PYRAMID_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 pyramid
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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[13];
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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 vtkQuadraticPyramid::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<13; 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 vtkQuadraticPyramid::CellBoundary(int subId, double pcoords[3],
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vtkIdList *pts)
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{
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return this->Pyramid->CellBoundary(subId, pcoords, pts);
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}
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//----------------------------------------------------------------------------
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void vtkQuadraticPyramid::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[13];
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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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// Make sure to copy ALL arrays. These field data have to be
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// identical to the input field data. Otherwise, CopyData
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// that occurs later may not work because the output field
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// data was initialized (CopyAllocate) with the input field
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// data.
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this->PointData->CopyAllOn();
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this->CellData->CopyAllOn();
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this->PointData->CopyAllocate(inPd,14);
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this->CellData->CopyAllocate(inCd,6);
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for (i=0; i<13; 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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for (i=0; i<6; i++)
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{
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this->CellData->CopyData(inCd,cellId,i);
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}
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//Interpolate new values
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double p[3];
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this->Points->Resize(14);
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this->CellScalars->Resize(14);
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for ( numMidPts=0; numMidPts < 1; 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<13; 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(13+numMidPts,x);
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this->CellScalars->SetValue(13+numMidPts,s);
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this->PointData->InterpolatePoint(inPd, 13+numMidPts,
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this->PointIds, weights);
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}
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}
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//----------------------------------------------------------------------------
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void vtkQuadraticPyramid::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,
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vtkIdType cellId,
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vtkCellData* outCd)
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{
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int i;
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//subdivide into 6 linear pyramids
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this->Subdivide(inPd,inCd,cellId,cellScalars);
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//contour each linear pyramid separately
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this->Scalars->SetNumberOfTuples(5); //num of vertices
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for (i=0; i<6; i++) //for each pyramid
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{
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for (int j=0; j<5; j++) //for each point of pyramid
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{
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this->Pyramid->Points->SetPoint(j,this->Points->GetPoint(LinearPyramids[i][j]));
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this->Pyramid->PointIds->SetId(j,LinearPyramids[i][j]);
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this->Scalars->SetValue(j,this->CellScalars->GetValue(LinearPyramids[i][j]));
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}
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this->Pyramid->Contour(value,this->Scalars,locator,verts,lines,polys,
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this->PointData,outPd,this->CellData,i,outCd);
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}
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//contour each linear tetra separately
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this->Scalars->SetNumberOfTuples(4); //num of vertices
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for (i=6; i<10; i++) //for each tetra
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{
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for (int j=0; j<4; j++) //for each point of tetra
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{
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this->Tetra->Points->SetPoint(j,this->Points->GetPoint(LinearPyramids[i][j]));
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this->Tetra->PointIds->SetId(j,LinearPyramids[i][j]);
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this->Scalars->SetTuple(j,this->CellScalars->GetTuple(LinearPyramids[i][j]));
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}
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this->Tetra->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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//
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int vtkQuadraticPyramid::IntersectWithLine(double* p1, double* p2,
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double tol, double& t,
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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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int inter;
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t = VTK_DOUBLE_MAX;
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this->TriangleFace->GetPoints()->ShallowCopy(this->GetPoints());
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for (faceNum=0; faceNum<5; faceNum++)
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{
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// We have 8 nodes on rect face
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// and 6 on triangle faces
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if(faceNum > 0)
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{
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for (int i=0; i<6; i++)
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{
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this->TriangleFace->PointIds->SetId(i,
|
|
this->PointIds->GetId(PyramidFaces[faceNum][i]));
|
|
}
|
|
inter = this->TriangleFace->IntersectWithLine(p1, p2, tol, tTemp,
|
|
xTemp, pc, subId);
|
|
}
|
|
else
|
|
{
|
|
// No need to set the PointIds. They are set in the Face constructor
|
|
// Points need to be set to correspond with the contructor's PointIds.
|
|
for (int i=0; i<8; i++)
|
|
{
|
|
this->Face->Points->SetPoint(i,
|
|
this->Points->GetPoint(PyramidFaces[faceNum][i]));
|
|
}
|
|
inter = this->Face->IntersectWithLine(p1, p2, tol, tTemp,
|
|
xTemp, pc, subId);
|
|
}
|
|
if ( inter )
|
|
{
|
|
intersection = 1;
|
|
if ( tTemp < t )
|
|
{
|
|
t = tTemp;
|
|
x[0] = xTemp[0]; x[1] = xTemp[1]; x[2] = xTemp[2];
|
|
switch (faceNum)
|
|
{
|
|
case 0:
|
|
pcoords[0] = 0.0; pcoords[1] = pc[1]; pcoords[2] = pc[0];
|
|
break;
|
|
|
|
case 1:
|
|
pcoords[0] = 1.0; pcoords[1] = pc[0]; pcoords[2] = pc[1];
|
|
break;
|
|
|
|
case 2:
|
|
pcoords[0] = pc[0]; pcoords[1] = 0.0; pcoords[2] = pc[1];
|
|
break;
|
|
|
|
case 3:
|
|
pcoords[0] = pc[1]; pcoords[1] = 1.0; pcoords[2] = pc[0];
|
|
break;
|
|
|
|
case 4:
|
|
pcoords[0] = pc[1]; pcoords[1] = pc[0]; pcoords[2] = 0.0;
|
|
break;
|
|
|
|
case 5:
|
|
pcoords[0] = pc[0]; pcoords[1] = pc[1]; pcoords[2] = 1.0;
|
|
break;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
return intersection;
|
|
}
|
|
|
|
//----------------------------------------------------------------------------
|
|
int vtkQuadraticPyramid::Triangulate(int vtkNotUsed(index), vtkIdList *ptIds,
|
|
vtkPoints *pts)
|
|
{
|
|
int i;
|
|
int ii;
|
|
pts->Reset();
|
|
ptIds->Reset();
|
|
|
|
for (i=0; i < 6; i++)
|
|
{
|
|
for ( int j=0; j < 5; j++)
|
|
{
|
|
ptIds->InsertId(5*i+j,this->PointIds->GetId(LinearPyramids[i][j]));
|
|
pts->InsertPoint(5*i+j,this->Points->GetPoint(LinearPyramids[i][j]));
|
|
}
|
|
}
|
|
|
|
for (ii=0, i=6 ; i < 10; i++, ii++)
|
|
{
|
|
for ( int j=0; j < 4; j++)
|
|
{
|
|
ptIds->InsertId(4*ii+j+30,this->PointIds->GetId(LinearPyramids[i][j]));
|
|
pts->InsertPoint(4*ii+j+30,this->Points->GetPoint(LinearPyramids[i][j]));
|
|
}
|
|
}
|
|
|
|
return 1;
|
|
}
|
|
|
|
//----------------------------------------------------------------------------
|
|
// Given parametric coordinates compute inverse Jacobian transformation
|
|
// matrix. Returns 9 elements of 3x3 inverse Jacobian plus interpolation
|
|
// function derivatives.
|
|
//
|
|
void vtkQuadraticPyramid::JacobianInverse(double pcoords[3], double **inverse,
|
|
double derivs[39])
|
|
{
|
|
int i, j;
|
|
double *m[3], m0[3], m1[3], m2[3];
|
|
double x[3];
|
|
|
|
// compute interpolation function derivatives
|
|
this->InterpolationDerivs(pcoords, derivs);
|
|
|
|
// create Jacobian matrix
|
|
m[0] = m0; m[1] = m1; m[2] = m2;
|
|
for (i=0; i < 3; i++) //initialize matrix
|
|
{
|
|
m0[i] = m1[i] = m2[i] = 0.0;
|
|
}
|
|
|
|
for ( j=0; j < 13; j++ )
|
|
{
|
|
this->Points->GetPoint(j, x);
|
|
for ( i=0; i < 3; i++ )
|
|
{
|
|
m0[i] += x[i] * derivs[j];
|
|
m1[i] += x[i] * derivs[13 + j];
|
|
m2[i] += x[i] * derivs[26 + j];
|
|
}
|
|
}
|
|
|
|
// now find the inverse
|
|
if ( vtkMath::InvertMatrix(m,inverse,3) == 0 )
|
|
{
|
|
vtkErrorMacro(<<"Jacobian inverse not found");
|
|
return;
|
|
}
|
|
}
|
|
|
|
//----------------------------------------------------------------------------
|
|
void vtkQuadraticPyramid::Derivatives(int vtkNotUsed(subId),
|
|
double pcoords[3], double *values,
|
|
int dim, double *derivs)
|
|
{
|
|
double *jI[3], j0[3], j1[3], j2[3];
|
|
double functionDerivs[3*13], sum[3];
|
|
int i, j, k;
|
|
|
|
// compute inverse Jacobian and interpolation function derivatives
|
|
jI[0] = j0; jI[1] = j1; jI[2] = j2;
|
|
this->JacobianInverse(pcoords, jI, functionDerivs);
|
|
|
|
// now compute derivates of values provided
|
|
for (k=0; k < dim; k++) //loop over values per vertex
|
|
{
|
|
sum[0] = sum[1] = sum[2] = 0.0;
|
|
for ( i=0; i < 13; i++) //loop over interp. function derivatives
|
|
{
|
|
sum[0] += functionDerivs[i] * values[dim*i + k];
|
|
sum[1] += functionDerivs[13 + i] * values[dim*i + k];
|
|
sum[2] += functionDerivs[26 + i] * values[dim*i + k];
|
|
}
|
|
for (j=0; j < 3; j++) //loop over derivative directions
|
|
{
|
|
derivs[3*k + j] = sum[0]*jI[j][0] + sum[1]*jI[j][1] + sum[2]*jI[j][2];
|
|
}
|
|
}
|
|
}
|
|
|
|
//----------------------------------------------------------------------------
|
|
// Clip this quadratic pyramid using scalar value provided. Like contouring,
|
|
// except that it cuts the pyramid to produce tetrahedra.
|
|
//
|
|
void vtkQuadraticPyramid::Clip(double value, vtkDataArray* cellScalars,
|
|
vtkIncrementalPointLocator* locator, vtkCellArray* tets,
|
|
vtkPointData* inPd, vtkPointData* outPd,
|
|
vtkCellData* inCd, vtkIdType cellId,
|
|
vtkCellData* outCd, int insideOut)
|
|
{
|
|
int i;
|
|
// create six linear pyramid + 4 tetra
|
|
this->Subdivide(inPd,inCd,cellId,cellScalars);
|
|
|
|
//contour each linear pyramid separately
|
|
this->Scalars->SetNumberOfTuples(5); //num of vertices
|
|
for (i=0; i<6; i++) //for each subdivided pyramid
|
|
{
|
|
for (int j=0; j<5; j++) //for each of the five vertices of the pyramid
|
|
{
|
|
this->Pyramid->Points->SetPoint(j,this->Points->GetPoint(LinearPyramids[i][j]));
|
|
this->Pyramid->PointIds->SetId(j,LinearPyramids[i][j]);
|
|
this->Scalars->SetValue(j,this->CellScalars->GetValue(LinearPyramids[i][j]));
|
|
}
|
|
this->Pyramid->Clip(value,this->Scalars,locator,tets,this->PointData,outPd,
|
|
this->CellData,cellId,outCd,insideOut);
|
|
}
|
|
|
|
this->Scalars->SetNumberOfTuples(4); //num of vertices
|
|
for (i=6; i<10; i++) //for each subdivided tetra
|
|
{
|
|
for (int j=0; j<4; j++) //for each of the four vertices of the tetra
|
|
{
|
|
this->Tetra->Points->SetPoint(j,this->Points->GetPoint(LinearPyramids[i][j]));
|
|
this->Tetra->PointIds->SetId(j,LinearPyramids[i][j]);
|
|
this->Scalars->SetValue(j,this->CellScalars->GetValue(LinearPyramids[i][j]));
|
|
}
|
|
this->Tetra->Clip(value,this->Scalars,locator,tets,this->PointData,outPd,
|
|
this->CellData,cellId,outCd,insideOut);
|
|
}
|
|
}
|
|
|
|
//----------------------------------------------------------------------------
|
|
// Compute interpolation functions for the fifteen nodes.
|
|
//
|
|
void vtkQuadraticPyramid::InterpolationFunctions(double pcoords[3],
|
|
double weights[13])
|
|
{
|
|
// VTK needs parametric coordinates to be between (0,1). Isoparametric
|
|
// shape functions are formulated between (-1,1). Here we do a
|
|
// coordinate system conversion from (0,1) to (-1,1).
|
|
const double r = 2.0*(pcoords[0] - 0.5);
|
|
const double s = 2.0*(pcoords[1] - 0.5);
|
|
const double t = 2.0*(pcoords[2] - 0.5);
|
|
const double r2 = r*r;
|
|
const double s2 = s*s;
|
|
const double t2 = t*t;
|
|
|
|
weights[0] = -(1 - r) * (1 - s) * (1 - t) * (4 + 3*r + 3*s + 2*r*s + 2*t + r*t + s*t + 2*r*s*t) / 16.0;
|
|
weights[1] = -(1 + r) * (1 - s) * (1 - t) * (4 - 3*r + 3*s - 2*r*s + 2*t - r*t + s*t - 2*r*s*t) / 16.0;
|
|
weights[2] = -(1 + r) * (1 + s) * (1 - t) * (4 - 3*r - 3*s + 2*r*s + 2*t - r*t - s*t + 2*r*s*t) / 16.0;
|
|
weights[3] = -(1 - r) * (1 + s) * (1 - t) * (4 + 3*r - 3*s - 2*r*s + 2*t + r*t - s*t - 2*r*s*t) / 16.0;
|
|
|
|
weights[4] = t * (1 + t) / 2.0;
|
|
|
|
weights[5] = (1 - r2) * (1 - s) * (1 - t) * (2 + s + s*t) / 8.0;
|
|
weights[6] = (1 + r) * (1 - s2) * (1 - t) * (2 - r - r*t) / 8.0;
|
|
weights[7] = (1 - r2) * (1 + s) * (1 - t) * (2 - s - s*t) / 8.0;
|
|
weights[8] = (1 - r) * (1 - s2) * (1 - t) * (2 + r + r*t) / 8.0;
|
|
|
|
weights[9] = (1 - r) * (1 - s) * (1 - t2) / 4.0;
|
|
weights[10] = (1 + r) * (1 - s) * (1 - t2) / 4.0;
|
|
weights[11] = (1 + r) * (1 + s) * (1 - t2) / 4.0;
|
|
weights[12] = (1 - r) * (1 + s) * (1 - t2) / 4.0;
|
|
|
|
}
|
|
|
|
//----------------------------------------------------------------------------
|
|
// Derivatives in parametric space.
|
|
//
|
|
void vtkQuadraticPyramid::InterpolationDerivs(double pcoords[3],
|
|
double derivs[39])
|
|
{
|
|
//VTK needs parametric coordinates to be between (0,1). Isoparametric
|
|
//shape functions are formulated between (-1,1). Here we do a
|
|
//coordinate system conversion from (0,1) to (-1,1).
|
|
double r = 2*pcoords[0] - 1;
|
|
double s = 2*pcoords[1] - 1;
|
|
double t = 2*pcoords[2] - 1;
|
|
|
|
double rm = 1.0 - r;
|
|
double rp = 1.0 + r;
|
|
double sm = 1.0 - s;
|
|
double sp = 1.0 + s;
|
|
double tm = 1.0 - t;
|
|
//double tp = 1.0 + t;
|
|
double r2 = 1.0 - r*r;
|
|
double t2 = 1.0 - t*t;
|
|
|
|
//r-derivatives
|
|
// corners
|
|
derivs[0] = -0.125*(sm*tm - 2.0*r*sm*tm - s*sm*tm - t*sm*tm - 2.0*sm*tm);
|
|
derivs[1] = 0.125*(sm*tm + 2.0*r*sm*tm - s*sm*tm - t*sm*tm - 2.0*sm*tm);
|
|
derivs[2] = 0.125*(sp*tm + 2.0*r*sp*tm + s*sp*tm - t*sp*tm - 2.0*sp*tm);
|
|
derivs[3] = -0.125*(sp*tm - 2.0*r*sp*tm + s*sp*tm - t*sp*tm - 2.0*sp*tm);
|
|
derivs[4] = 0.0;
|
|
|
|
// midsides of rectangles
|
|
derivs[5] = -0.5*r*sm*tm;
|
|
derivs[6] = 0.25*(tm - s*s*tm);
|
|
derivs[7] = -0.5*r*sp*tm;
|
|
derivs[8] = -0.25*(tm - s*s*tm);
|
|
|
|
// midsides of triangles
|
|
derivs[9] = -0.25 * (1 - s ) * (1 - t*t );
|
|
derivs[10] = 0.25 * (1 - s ) * (1 - t*t );
|
|
derivs[11] = 0.25 * (1 + s ) * (1 - t*t );
|
|
derivs[12] = -0.25 * (1 + s ) * (1 - t*t );
|
|
|
|
//s-derivatives
|
|
// corners
|
|
derivs[13] = -0.125*(rm*tm - 2.0*s*rm*tm - r*rm*tm - t*rm*tm - 2.0*rm*tm);
|
|
derivs[14] = -0.125*(rp*tm - 2.0*s*rp*tm + r*rp*tm - t*rp*tm - 2.0*rp*tm);
|
|
derivs[15] = 0.125*(rp*tm + 2.0*s*rp*tm + r*rp*tm - t*rp*tm - 2.0*rp*tm);
|
|
derivs[16] = 0.125*(rm*tm + 2.0*s*rm*tm - r*rm*tm - t*rm*tm - 2.0*rm*tm);
|
|
derivs[17] = 0.0;
|
|
|
|
// midsides of rectangles
|
|
derivs[18] = -0.25 * tm * r2;
|
|
derivs[19] = -0.5 * tm * s * rp;
|
|
derivs[20] = 0.25 * tm * r2;
|
|
derivs[21] = -0.5 * tm * s * rm;
|
|
|
|
// midsides of triangles
|
|
derivs[22] = -0.25 * rm * t2;
|
|
derivs[23] = -0.25 * rp * t2;
|
|
derivs[24] = 0.25 * rp * t2;
|
|
derivs[25] = 0.25 * rm * t2;
|
|
|
|
//t-derivatives
|
|
// corners
|
|
derivs[26] = -0.125*(rm*sm - 2.0*t*rm*sm - r*rm*sm - s*rm*sm - 2.0*rm*sm);
|
|
derivs[27] = -0.125*(rp*sm - 2.0*t*rp*sm + r*rp*sm - s*rp*sm - 2.0*rp*sm);
|
|
derivs[28] = -0.125*(rp*sp - 2.0*t*rp*sp + r*rp*sp + s*rp*sp - 2.0*rp*sp);
|
|
derivs[29] = -0.125*(rm*sp - 2.0*t*rm*sp - r*rm*sp + s*rm*sp - 2.0*rm*sp);
|
|
derivs[30] = 0.5 + t;
|
|
|
|
// midsides of rectangles
|
|
derivs[31] = -0.25*(sm - r*r*sm);
|
|
derivs[32] = -0.25*(rp - s*s*rp);
|
|
derivs[33] = -0.25*(sp - r*r*sp);
|
|
derivs[34] = -0.25*(rm - s*s*rm);
|
|
|
|
|
|
// midsides of triangles
|
|
derivs[35] = -0.5 * ( 1 - r ) * (1 - s ) * t;
|
|
derivs[36] = -0.5 * ( 1 + r ) * (1 - s ) * t;
|
|
derivs[37] = -0.5 * ( 1 + r ) * (1 + s ) * t;
|
|
derivs[38] = -0.5 * ( 1 - r ) * (1 + s ) * t;
|
|
|
|
// we compute derivatives in in [-1; 1] but we need them in [ 0; 1]
|
|
for(int i = 0; i < 39; i++)
|
|
derivs[i] *= 2;
|
|
}
|
|
|
|
static double vtkQPyramidCellPCoords[39] = {0.0,0.0,0.0, 1.0,0.0,0.0, 1.0,1.0,0.0,
|
|
0.0,1.0,0.0, 0.0,0.0,1.0, 0.5,0.0,0.0,
|
|
1.0,0.5,0.0, 0.5,1.0,0.0, 0.0,0.5,0.0,
|
|
0.0,0.0,0.5, 1.0,0.0,0.5,
|
|
1.0,1.0,0.5, 0.0,1.0,0.5 };
|
|
|
|
//----------------------------------------------------------------------------
|
|
double *vtkQuadraticPyramid::GetParametricCoords()
|
|
{
|
|
return vtkQPyramidCellPCoords;
|
|
}
|
|
|
|
//----------------------------------------------------------------------------
|
|
void vtkQuadraticPyramid::PrintSelf(ostream& os, vtkIndent indent)
|
|
{
|
|
this->Superclass::PrintSelf(os,indent);
|
|
|
|
os << indent << "Edge:\n";
|
|
this->Edge->PrintSelf(os,indent.GetNextIndent());
|
|
os << indent << "TriangleFace:\n";
|
|
this->TriangleFace->PrintSelf(os,indent.GetNextIndent());
|
|
os << indent << "Face:\n";
|
|
this->Face->PrintSelf(os,indent.GetNextIndent());
|
|
os << indent << "Tetra:\n";
|
|
this->Tetra->PrintSelf(os,indent.GetNextIndent());
|
|
os << indent << "Pyramid:\n";
|
|
this->Pyramid->PrintSelf(os,indent.GetNextIndent());
|
|
os << indent << "PointData:\n";
|
|
this->PointData->PrintSelf(os,indent.GetNextIndent());
|
|
os << indent << "CellData:\n";
|
|
this->CellData->PrintSelf(os,indent.GetNextIndent());
|
|
os << indent << "Scalars:\n";
|
|
this->Scalars->PrintSelf(os,indent.GetNextIndent());
|
|
}
|