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699 lines
22 KiB
C++
699 lines
22 KiB
C++
/*=========================================================================
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Program: Visualization Toolkit
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Module: vtkBiQuadraticQuadraticWedge.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 "vtkBiQuadraticQuadraticWedge.h"
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#include "vtkObjectFactory.h"
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#include "vtkDoubleArray.h"
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#include "vtkWedge.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 "vtkQuadraticTriangle.h"
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#include "vtkPoints.h"
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#include <cassert>
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vtkStandardNewMacro (vtkBiQuadraticQuadraticWedge);
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//----------------------------------------------------------------------------
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// Construct the biquadratic quadratic wedge with 18 points
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vtkBiQuadraticQuadraticWedge::vtkBiQuadraticQuadraticWedge ()
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{
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this->Points->SetNumberOfPoints (18);
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this->PointIds->SetNumberOfIds (18);
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for (int i = 0; i < 18; 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->TriangleFace = vtkQuadraticTriangle::New ();
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this->Wedge = vtkWedge::New ();
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this->Scalars = vtkDoubleArray::New ();
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this->Scalars->SetNumberOfTuples (6); //Number of vertices from a linear wedge
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}
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//----------------------------------------------------------------------------
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vtkBiQuadraticQuadraticWedge::~vtkBiQuadraticQuadraticWedge ()
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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->Wedge->Delete ();
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this->Scalars->Delete ();
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}
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//----------------------------------------------------------------------------
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// We are using 8 linear wedge
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static int LinearWedges[8][6] = { {0,6,8,12,15,17},
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{6,7,8,15,16,17},
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{6,1,7,15,13,16},
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{8,7,2,17,16,14},
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{12,15,17,3,9,11},
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{15,16,17,9,10,11},
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{15,13,16,9,4,10},
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{17,16,14,11,10,5} };
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// We use 2 quadratic triangles and 3 quadratic-linear quads
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static int WedgeFaces[5][9] = {
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{0, 1, 2, 6, 7, 8, 0, 0, 0}, // first quad triangle
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{3, 5, 4, 11, 10, 9, 0, 0, 0}, // second quad triangle
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{0, 3, 4, 1, 12, 9, 13, 6, 15}, // 1. biquad quad
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{1, 4, 5, 2, 13, 10, 14, 7, 16}, // 2. biquad quad
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{2, 5, 3, 0, 14, 11, 12, 8, 17} // 3. biquad quad
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};
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// We have 9 quadratic edges
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static int WedgeEdges[9][3] = {
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{0, 1, 6}, {1, 2, 7}, {2, 0, 8},
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{3, 4, 9}, {4, 5, 10}, {5, 3, 11},
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{0, 3, 12}, {1, 4, 13}, {2, 5, 14}
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};
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//----------------------------------------------------------------------------
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int *vtkBiQuadraticQuadraticWedge::GetEdgeArray(int edgeId)
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{
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return WedgeEdges[edgeId];
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}
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//----------------------------------------------------------------------------
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int *vtkBiQuadraticQuadraticWedge::GetFaceArray(int faceId)
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{
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return WedgeFaces[faceId];
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}
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//----------------------------------------------------------------------------
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vtkCell *vtkBiQuadraticQuadraticWedge::GetEdge(int edgeId)
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{
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edgeId = (edgeId < 0 ? 0 : (edgeId > 8 ? 8 : edgeId));
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//We have 9 quadratic edges
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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 (WedgeEdges[edgeId][i]));
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this->Edge->Points->SetPoint (i, this->Points->GetPoint (WedgeEdges[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 *vtkBiQuadraticQuadraticWedge::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 last two:
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if (faceId < 2)
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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 (WedgeFaces[faceId][i]));
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this->TriangleFace->Points->SetPoint (i, this->Points->GetPoint (WedgeFaces[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 < 9; i++)
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{
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this->Face->PointIds->SetId (i, this->PointIds->GetId (WedgeFaces[faceId][i]));
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this->Face->Points->SetPoint (i, this->Points->GetPoint (WedgeFaces[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_WEDGE_MAX_ITERATION = 20;
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static const double VTK_WEDGE_CONVERGED = 1.e-03;
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int vtkBiQuadraticQuadraticWedge::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, pt[3];
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double derivs[3 * 18];
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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; !converged && (iteration < VTK_WEDGE_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 < 18; 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 + 18];
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tcol[j] += pt[j] * derivs[i + 36];
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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_WEDGE_CONVERGED) &&
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((fabs (pcoords[1] - params[1])) < VTK_WEDGE_CONVERGED) &&
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((fabs (pcoords[2] - params[2])) < VTK_WEDGE_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 wedge
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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[18];
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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 vtkBiQuadraticQuadraticWedge::EvaluateLocation (int &vtkNotUsed (subId),
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double pcoords[3], double x[3], double *weights)
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{
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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 (int i = 0; i < 18; i++)
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{
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this->Points->GetPoint (i, pt);
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for (int 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 vtkBiQuadraticQuadraticWedge::CellBoundary (int subId,
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double pcoords[3], vtkIdList * pts)
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{
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return this->Wedge->CellBoundary (subId, pcoords, pts);
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}
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//----------------------------------------------------------------------------
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void vtkBiQuadraticQuadraticWedge::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, vtkCellData * inCd,
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vtkIdType cellId, vtkCellData * outCd)
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{
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//contour each linear wedge separately
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for (int i=0; i<8; i++) //for each wedge
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{
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for (int j=0; j<6; j++) //for each point of wedge
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{
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this->Wedge->Points->SetPoint(j,this->Points->GetPoint(LinearWedges[i][j]));
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this->Wedge->PointIds->SetId(j,this->PointIds->GetId(LinearWedges[i][j]));
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this->Scalars->SetValue(j,cellScalars->GetTuple1(LinearWedges[i][j]));
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}
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this->Wedge->Contour(value,this->Scalars,locator,verts,lines,polys, inPd,outPd,inCd,cellId,outCd);
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}
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}
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//----------------------------------------------------------------------------
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// Clip this biquadratic wedge using scalar value provided. Like contouring,
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// except that it cuts the wedge to produce tetrahedra.
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void
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vtkBiQuadraticQuadraticWedge::Clip (double value, vtkDataArray *cellScalars,
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vtkIncrementalPointLocator * locator, vtkCellArray * tets,
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vtkPointData * inPd, vtkPointData * outPd,
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vtkCellData * inCd, vtkIdType cellId, vtkCellData * outCd, int insideOut)
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{
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//contour each linear wedge separately
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for (int i=0; i<8; i++) //for each wedge
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{
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for (int j=0; j<6; j++) //for each of the six vertices of the wedge
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{
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this->Wedge->Points->SetPoint(j,this->Points->GetPoint(LinearWedges[i][j]));
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this->Wedge->PointIds->SetId(j,this->PointIds->GetId(LinearWedges[i][j]));
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this->Scalars->SetValue(j,cellScalars->GetTuple1(LinearWedges[i][j]));
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}
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this->Wedge->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 vtkBiQuadraticQuadraticWedge::IntersectWithLine (double *p1, double *p2,
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double tol, double &t,
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double *x,
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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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int inter;
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t = VTK_DOUBLE_MAX;
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for (faceNum = 0; faceNum < 5; faceNum++)
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{
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// We have 9 nodes on biquad face
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// and 6 on triangle faces
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if (faceNum < 2)
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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 (WedgeFaces[faceNum][i]));
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this->TriangleFace->Points->SetPoint (i, this->Points->GetPoint (WedgeFaces[faceNum][i]));
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}
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inter = this->TriangleFace->IntersectWithLine (p1, p2, tol, tTemp, xTemp,
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pc, subId);
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}
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else
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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->Points->SetPoint (i, this->Points->GetPoint (WedgeFaces[faceNum][i]));
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}
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inter = this->Face->IntersectWithLine (p1, p2, tol, tTemp, xTemp, pc,
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subId);
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}
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if (inter)
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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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default:
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assert("check:impossible case" && 0); // reaching this line is a bug
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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 vtkBiQuadraticQuadraticWedge::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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for (int i = 0; i < 8; i++)
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{
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for (int j = 0; j < 6; j++)
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{
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ptIds->InsertId (6 * i + j, this->PointIds->GetId (LinearWedges[i][j]));
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pts->InsertPoint (6 * i + j, this->Points->GetPoint (LinearWedges[i][j]));
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}
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}
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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 vtkBiQuadraticQuadraticWedge::JacobianInverse(double pcoords[3],
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double **inverse, double derivs[54])
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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 < 18; j++)
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{
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this->Points->GetPoint (j, x);
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for (i = 0; i < 3; i++)
|
|
{
|
|
m0[i] += x[i] * derivs[j];
|
|
m1[i] += x[i] * derivs[18 + j];
|
|
m2[i] += x[i] * derivs[36 + j];
|
|
}
|
|
}
|
|
|
|
// now find the inverse
|
|
if (vtkMath::InvertMatrix(m, inverse, 3) == 0)
|
|
{
|
|
vtkErrorMacro (<<"Jacobian inverse not found");
|
|
return;
|
|
}
|
|
}
|
|
|
|
//----------------------------------------------------------------------------
|
|
void vtkBiQuadraticQuadraticWedge::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 * 18], 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 < 18; i++) //loop over interp. function derivatives
|
|
{
|
|
sum[0] += functionDerivs[i] * values[dim * i + k];
|
|
sum[1] += functionDerivs[18 + i] * values[dim * i + k];
|
|
sum[2] += functionDerivs[36 + 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 fifteen nodes.
|
|
void vtkBiQuadraticQuadraticWedge::InterpolationFunctions (double pcoords[3], double weights[18])
|
|
{
|
|
// VTK needs parametric coordinates to be between (0,1). Isoparametric
|
|
// shape functions are formulated between (-1,1). Here we do a
|
|
// coordinate system conversion from (0,1) to (-1,1).
|
|
double x = 2*(pcoords[0]- 0.5);
|
|
double y = 2*(pcoords[1]- 0.5);
|
|
double z = 2*(pcoords[2]- 0.5);
|
|
|
|
// corners
|
|
weights[0] =-0.25 * (x + y) * (x + y + 1) * z * (1 - z);
|
|
weights[1] =-0.25 * x * (x + 1) * z * (1 - z);
|
|
weights[2] =-0.25 * y * (1 + y) * z * (1 - z);
|
|
weights[3] = 0.25 * (x + y) * (x + y + 1) * z * (1 + z);
|
|
weights[4] = 0.25 * x * (x + 1) * z * (1 + z);
|
|
weights[5] = 0.25 * y * (1 + y) * z * (1 + z);
|
|
|
|
// midsides of quadratic triangles
|
|
weights[6] = (x + 1)*(x + y) * 0.5 * z * (1 - z);
|
|
weights[7] = -(x + 1)*(y + 1) * 0.5 * z * (1 - z);
|
|
weights[8] = (y + 1)*(x + y) * 0.5 * z * (1 - z);
|
|
weights[9] = -(x + 1)*(x + y) * 0.5 * z * (1 + z);
|
|
weights[10]= (x + 1)*(y + 1) * 0.5 * z * (1 + z);
|
|
weights[11]= -(y + 1)*(x + y) * 0.5 * z * (1 + z);
|
|
|
|
// midsides of edges between the two triangles
|
|
weights[12] = 0.5 * (x + y) * (x + y + 1) * (1 + z)*(1 - z);
|
|
weights[13] = 0.5 * x * (x + 1) * (1 + z)*(1 - z);
|
|
weights[14] = 0.5 * y * (1 + y) * (1 + z)*(1 - z);
|
|
|
|
//Centerpoints of the biquadratic quads
|
|
weights[15] = -(x + 1)*(x + y) * (1 + z)*(1 - z);
|
|
weights[16] = (x + 1)*(y + 1) * (1 + z)*(1 - z);
|
|
weights[17] = -(y + 1)*(x + y) * (1 + z)*(1 - z);
|
|
}
|
|
|
|
//----------------------------------------------------------------------------
|
|
// Derivatives in parametric space.
|
|
void vtkBiQuadraticQuadraticWedge::InterpolationDerivs (double pcoords[3], double derivs[54])
|
|
{
|
|
//VTK needs parametric coordinates to be between (0,1). Isoparametric
|
|
//shape functions are formulated between (-1,1). Here we do a
|
|
//coordinate system conversion from (0,1) to (-1,1).
|
|
double x = 2*(pcoords[0]- 0.5);
|
|
double y = 2*(pcoords[1]- 0.5);
|
|
double z = 2*(pcoords[2]- 0.5);
|
|
|
|
//Derivatives in x-direction
|
|
// corners
|
|
derivs[0] = -0.25 * (2 * x + 2 * y + 1) * z * (1 - z);
|
|
derivs[1] = -0.25 * (2 * x + 1) * z * (1 - z);
|
|
derivs[2] = 0;
|
|
derivs[3] = 0.25 * (2 * x + 2 * y + 1) * z * (1 + z);
|
|
derivs[4] = 0.25 * (2 * x + 1) * z * (1 + z);
|
|
derivs[5] = 0;
|
|
// midsides of quadratic triangles
|
|
derivs[6] = (2 * x + y + 1) * 0.5 * z * (1 - z);
|
|
derivs[7] = -(y + 1) * 0.5 * z * (1 - z);
|
|
derivs[8] = (y + 1) * 0.5 * z * (1 - z);
|
|
derivs[9] = -(2 * x + y + 1) * 0.5 * z * (1 + z);
|
|
derivs[10] = (y + 1) * 0.5 * z * (1 + z) ;
|
|
derivs[11] =-(y + 1) * 0.5 * z * (1 + z) ;
|
|
// midsides of edges between the two triangles
|
|
derivs[12] = 0.5 * (2 * x + 2 * y + 1) * (1 + z)*(1 - z);
|
|
derivs[13] = 0.5 * (2 * x + 1) * (1 + z)*(1 - z);
|
|
derivs[14] = 0;
|
|
//Centerpoints of the biquadratic quads
|
|
derivs[15] = -(2 * x + y + 1) * (1 + z)*(1 - z);
|
|
derivs[16] = (y + 1) * (1 + z)*(1 - z);
|
|
derivs[17] = -(y + 1) * (1 + z)*(1 - z);
|
|
|
|
//Derivatives in y-direction
|
|
// corners
|
|
derivs[18] = -0.25 * (2 * y + 2 * x + 1) * z * (1 - z);
|
|
derivs[19] = 0;
|
|
derivs[20] = -0.25 * (2 * y + 1) * z * (1 - z);
|
|
derivs[21] = 0.25 * (2 * y + 2 * x + 1) * z * (1 + z);
|
|
derivs[22] = 0;
|
|
derivs[23] = 0.25 * (2 * y + 1) * z * (1 + z);
|
|
// midsides of quadratic triangles
|
|
derivs[24] = (x + 1) * 0.5 * z * (1 - z);
|
|
derivs[25] = -(x + 1) * 0.5 * z * (1 - z);
|
|
derivs[26] = (2 * y + x + 1) * 0.5 * z * (1 - z);
|
|
derivs[27] = -(x + 1) * 0.5 * z * (1 + z);
|
|
derivs[28] = (x + 1) * 0.5 * z * (1 + z);
|
|
derivs[29] = -(2 * y + x + 1) * 0.5 * z * (1 + z);
|
|
// midsides of edges between the two triangles
|
|
derivs[30] = 0.5 * (2 * y + 2 * x + 1) * (1 + z)*(1 - z);
|
|
derivs[31] = 0;
|
|
derivs[32] = 0.5 * (2 * y + 1) * (1 + z)*(1 - z);
|
|
//Centerpoints of the biquadratic quads
|
|
derivs[33] = -(x + 1) * (1 + z)*(1 - z);
|
|
derivs[34] = (x + 1) * (1 + z)*(1 - z);
|
|
derivs[35] = -(2 * y + x + 1) * (1 + z)*(1 - z);
|
|
|
|
//Derivatives in z-direction
|
|
// corners
|
|
derivs[36] = -0.25 * (x + y) * (x + y + 1) * (1 - 2 * z);
|
|
derivs[37] = -0.25 * x * (x + 1) * (1 - 2 * z);
|
|
derivs[38] = -0.25 * y * (1 + y) * (1 - 2 * z);
|
|
derivs[39] = 0.25 * (x + y) * (x + y + 1) * (1 + 2 * z);
|
|
derivs[40] = 0.25 * x * (x + 1) * (1 + 2 * z);
|
|
derivs[41] = 0.25 * y * (1 + y) * (1 + 2 * z);
|
|
// midsides of quadratic triangles
|
|
derivs[42] = (x + 1)*(x + y) * 0.5 * (1 - 2 * z);
|
|
derivs[43] = -(x + 1)*(y + 1) * 0.5 * (1 - 2 * z);
|
|
derivs[44] = (y + 1)*(x + y) * 0.5 * (1 - 2 * z);
|
|
derivs[45] = -(x + 1)*(x + y) * 0.5 * (1 + 2 * z);
|
|
derivs[46] = (x + 1)*(y + 1) * 0.5 * (1 + 2 * z);
|
|
derivs[47] = -(y + 1)*(x + y) * 0.5 * (1 + 2 * z);
|
|
// midsides of edges between the two triangles
|
|
derivs[48] = 0.5 * (x + y) * (x + y + 1) * (-2 * z);
|
|
derivs[49] = 0.5 * x * (x + 1) * (-2 * z);
|
|
derivs[50] = 0.5 * y * (1 + y) * (-2 * z);
|
|
//Centerpoints of the biquadratic quads
|
|
derivs[51] = -(x + 1)*(x + y) * (-2 * z);
|
|
derivs[52] = (x + 1)*(y + 1) * (-2 * z);
|
|
derivs[53] = -(y + 1)*(x + y) * (-2 * z);
|
|
|
|
// we compute derivatives in [-1; 1] but we need them in [ 0; 1]
|
|
for(int i = 0; i < 54; i++)
|
|
derivs[i] *= 2;
|
|
}
|
|
|
|
//----------------------------------------------------------------------------
|
|
static double vtkQWedgeCellPCoords[54] = {
|
|
0.0,0.0,0.0, 1.0,0.0,0.0, 0.0,1.0,0.0,
|
|
0.0,0.0,1.0, 1.0,0.0,1.0, 0.0,1.0,1.0,
|
|
0.5,0.0,0.0, 0.5,0.5,0.0, 0.0,0.5,0.0,
|
|
0.5,0.0,1.0, 0.5,0.5,1.0, 0.0,0.5,1.0,
|
|
0.0,0.0,0.5, 1.0,0.0,0.5, 0.0,1.0,0.5,
|
|
0.5,0.0,0.5, 0.5,0.5,0.5, 0.0,0.5,0.5
|
|
};
|
|
|
|
double *vtkBiQuadraticQuadraticWedge::GetParametricCoords()
|
|
{
|
|
return vtkQWedgeCellPCoords;
|
|
}
|
|
|
|
//----------------------------------------------------------------------------
|
|
void vtkBiQuadraticQuadraticWedge::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 << "Wedge:\n";
|
|
this->Wedge->PrintSelf (os, indent.GetNextIndent ());
|
|
os << indent << "Scalars:\n";
|
|
this->Scalars->PrintSelf (os, indent.GetNextIndent ());
|
|
}
|