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524 lines
17 KiB
C++
524 lines
17 KiB
C++
/*=========================================================================
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Program: Visualization Toolkit
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Module: vtkBiQuadraticQuad.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 "vtkBiQuadraticQuad.h"
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#include "vtkObjectFactory.h"
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#include "vtkDoubleArray.h"
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#include "vtkMath.h"
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#include "vtkPointData.h"
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#include "vtkQuad.h"
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#include "vtkQuadraticEdge.h"
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#include "vtkPoints.h"
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vtkStandardNewMacro(vtkBiQuadraticQuad);
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//----------------------------------------------------------------------------
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// Construct the quad with nine points.
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vtkBiQuadraticQuad::vtkBiQuadraticQuad()
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{
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this->Edge = vtkQuadraticEdge::New();
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this->Quad = vtkQuad::New();
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this->Points->SetNumberOfPoints(9);
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this->PointIds->SetNumberOfIds(9);
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for (int i = 0; i < 9; 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->Scalars = vtkDoubleArray::New();
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this->Scalars->SetNumberOfTuples(4);
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}
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//----------------------------------------------------------------------------
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vtkBiQuadraticQuad::~vtkBiQuadraticQuad()
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{
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this->Edge->Delete();
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this->Quad->Delete();
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this->Scalars->Delete();
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}
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//----------------------------------------------------------------------------
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vtkCell *vtkBiQuadraticQuad::GetEdge(int edgeId)
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{
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edgeId = (edgeId < 0 ? 0 : (edgeId > 3 ? 3 : edgeId));
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int p = (edgeId + 1) % 4;
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// load point id's
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this->Edge->PointIds->SetId (0, this->PointIds->GetId(edgeId));
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this->Edge->PointIds->SetId (1, this->PointIds->GetId(p));
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this->Edge->PointIds->SetId (2, this->PointIds->GetId(edgeId + 4));
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// load coordinates
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this->Edge->Points->SetPoint (0, this->Points->GetPoint(edgeId));
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this->Edge->Points->SetPoint (1, this->Points->GetPoint(p));
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this->Edge->Points->SetPoint (2, this->Points->GetPoint(edgeId + 4));
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return this->Edge;
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}
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//----------------------------------------------------------------------------
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static int LinearQuads[4][4] = { {0, 4, 8, 7}, {4, 1, 5, 8},
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{8, 5, 2, 6}, {7, 8, 6, 3} };
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//----------------------------------------------------------------------------
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int vtkBiQuadraticQuad::EvaluatePosition (double *x,
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double *closestPoint,
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int &subId, double pcoords[3],
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double &minDist2, double *weights)
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{
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double pc[3], dist2;
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int ignoreId, i, returnStatus = 0, status;
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double tempWeights[4];
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double closest[3];
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//four linear quads are used
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for (minDist2 = VTK_DOUBLE_MAX, i = 0; i < 4; i++)
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{
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this->Quad->Points->SetPoint (0,
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this->Points->GetPoint (LinearQuads[i][0]));
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this->Quad->Points->SetPoint (1,
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this->Points->GetPoint (LinearQuads[i][1]));
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this->Quad->Points->SetPoint (2,
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this->Points->GetPoint (LinearQuads[i][2]));
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this->Quad->Points->SetPoint (3,
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this->Points->GetPoint (LinearQuads[i][3]));
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status = this->Quad->EvaluatePosition (x, closest, ignoreId, pc, dist2,
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tempWeights);
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if (status != -1 && dist2 < minDist2)
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{
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returnStatus = status;
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minDist2 = dist2;
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subId = i;
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pcoords[0] = pc[0];
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pcoords[1] = pc[1];
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}
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}
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// adjust parametric coordinates
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if (returnStatus != -1)
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{
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if (subId == 0)
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{
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pcoords[0] /= 2.0;
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pcoords[1] /= 2.0;
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}
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else if (subId == 1)
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{
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pcoords[0] = 0.5 + (pcoords[0] / 2.0);
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pcoords[1] /= 2.0;
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}
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else if (subId == 2)
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{
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pcoords[0] = 0.5 + (pcoords[0] / 2.0);
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pcoords[1] = 0.5 + (pcoords[1] / 2.0);
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}
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else
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{
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pcoords[0] /= 2.0;
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pcoords[1] = 0.5 + (pcoords[1] / 2.0);
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}
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pcoords[2] = 0.0;
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if(closestPoint!=0)
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{
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// Compute both closestPoint and weights
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this->EvaluateLocation(subId,pcoords,closestPoint,weights);
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}
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else
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{
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// Compute weigths only
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this->InterpolationFunctionsPrivate(pcoords,weights);
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}
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}
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return returnStatus;
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}
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//----------------------------------------------------------------------------
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void vtkBiQuadraticQuad::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->InterpolationFunctionsPrivate(pcoords,weights);
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x[0] = x[1] = x[2] = 0.0;
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for (i=0; i<9; 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 vtkBiQuadraticQuad::CellBoundary (int subId, double pcoords[3], vtkIdList * pts)
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{
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return this->Quad->CellBoundary (subId, pcoords, pts);
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}
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//----------------------------------------------------------------------------
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void
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vtkBiQuadraticQuad::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, vtkIdType cellId, vtkCellData * outCd)
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{
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//contour each linear quad separately
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for (int i=0; i<4; i++)
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{
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for (int j=0; j<4; j++)
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{
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this->Quad->Points->SetPoint(j,this->Points->GetPoint(LinearQuads[i][j]));
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this->Quad->PointIds->SetId(j,this->PointIds->GetId(LinearQuads[i][j]));
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this->Scalars->SetValue(j,cellScalars->GetTuple1(LinearQuads[i][j]));
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}
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this->Quad->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 quadratic quad using scalar value provided. Like contouring,
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// except that it cuts the quad to produce other quads and triangles.
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void
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vtkBiQuadraticQuad::Clip (double value, vtkDataArray * cellScalars,
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vtkIncrementalPointLocator * locator, vtkCellArray * polys,
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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 quad separately
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for (int i=0; i<4; i++)
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{
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for ( int j=0; j<4; j++) //for each of the four vertices of the linear quad
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{
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this->Quad->Points->SetPoint(j,this->Points->GetPoint(LinearQuads[i][j]));
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this->Quad->PointIds->SetId(j,this->PointIds->GetId(LinearQuads[i][j]));
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this->Scalars->SetValue(j,cellScalars->GetTuple1(LinearQuads[i][j]));
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}
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this->Quad->Clip(value,this->Scalars,locator,polys,inPd,
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outPd,inCd,cellId,outCd,insideOut);
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}
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}
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//----------------------------------------------------------------------------
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// Line-line intersection. Intersection has to occur within [0,1] parametric
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// coordinates and with specified tolerance.
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int
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vtkBiQuadraticQuad::IntersectWithLine (double *p1,
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double *p2, double tol, double &t, double *x, double *pcoords, int &subId)
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{
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int subTest, i;
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subId = 0;
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//intersect the four linear quads
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for (i = 0; i < 4; i++)
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{
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this->Quad->Points->SetPoint (0,
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this->Points->GetPoint(LinearQuads[i][0]));
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this->Quad->Points->SetPoint (1,
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this->Points->GetPoint(LinearQuads[i][1]));
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this->Quad->Points->SetPoint (2,
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this->Points->GetPoint(LinearQuads[i][2]));
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this->Quad->Points->SetPoint (3,
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this->Points->GetPoint(LinearQuads[i][3]));
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if (this->Quad->IntersectWithLine (p1, p2, tol, t, x, pcoords, subTest))
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{
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return 1;
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}
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}
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return 0;
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}
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//----------------------------------------------------------------------------
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int vtkBiQuadraticQuad::Triangulate (int vtkNotUsed(index),
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vtkIdList *ptIds,
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vtkPoints *pts)
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{
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pts->SetNumberOfPoints(24);
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ptIds->SetNumberOfIds(24);
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// First the corner vertices
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ptIds->SetId(0,this->PointIds->GetId(0));
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ptIds->SetId(1,this->PointIds->GetId(4));
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ptIds->SetId(2,this->PointIds->GetId(7));
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pts->SetPoint(0,this->Points->GetPoint(0));
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pts->SetPoint(1,this->Points->GetPoint(4));
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pts->SetPoint(2,this->Points->GetPoint(7));
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ptIds->SetId(3,this->PointIds->GetId(4));
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ptIds->SetId(4,this->PointIds->GetId(1));
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ptIds->SetId(5,this->PointIds->GetId(5));
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pts->SetPoint(3,this->Points->GetPoint(4));
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pts->SetPoint(4,this->Points->GetPoint(1));
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pts->SetPoint(5,this->Points->GetPoint(5));
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ptIds->SetId(6,this->PointIds->GetId(5));
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ptIds->SetId(7,this->PointIds->GetId(2));
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ptIds->SetId(8,this->PointIds->GetId(6));
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pts->SetPoint(6,this->Points->GetPoint(5));
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pts->SetPoint(7,this->Points->GetPoint(2));
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pts->SetPoint(8,this->Points->GetPoint(6));
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ptIds->SetId(9,this->PointIds->GetId(6));
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ptIds->SetId(10,this->PointIds->GetId(3));
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ptIds->SetId(11,this->PointIds->GetId(7));
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pts->SetPoint(9,this->Points->GetPoint(6));
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pts->SetPoint(10,this->Points->GetPoint(3));
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pts->SetPoint(11,this->Points->GetPoint(7));
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//Now the triangles in the middle
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ptIds->SetId(12,this->PointIds->GetId(4));
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ptIds->SetId(13,this->PointIds->GetId(8));
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ptIds->SetId(14,this->PointIds->GetId(7));
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pts->SetPoint(12,this->Points->GetPoint(4));
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pts->SetPoint(13,this->Points->GetPoint(8));
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pts->SetPoint(14,this->Points->GetPoint(7));
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ptIds->SetId(15,this->PointIds->GetId(4));
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ptIds->SetId(16,this->PointIds->GetId(5));
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ptIds->SetId(17,this->PointIds->GetId(8));
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pts->SetPoint(15,this->Points->GetPoint(4));
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pts->SetPoint(16,this->Points->GetPoint(5));
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pts->SetPoint(17,this->Points->GetPoint(8));
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ptIds->SetId(18,this->PointIds->GetId(5));
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ptIds->SetId(19,this->PointIds->GetId(6));
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ptIds->SetId(20,this->PointIds->GetId(8));
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pts->SetPoint(18,this->Points->GetPoint(5));
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pts->SetPoint(19,this->Points->GetPoint(6));
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pts->SetPoint(20,this->Points->GetPoint(8));
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ptIds->SetId(21,this->PointIds->GetId(6));
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ptIds->SetId(22,this->PointIds->GetId(7));
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ptIds->SetId(23,this->PointIds->GetId(8));
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pts->SetPoint(21,this->Points->GetPoint(6));
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pts->SetPoint(22,this->Points->GetPoint(7));
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pts->SetPoint(23,this->Points->GetPoint(8));
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return 1;
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}
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//----------------------------------------------------------------------------
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void
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vtkBiQuadraticQuad::Derivatives (int vtkNotUsed (subId),
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double pcoords[3], double *values,
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int dim, double *derivs)
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{
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double sum[3], weights[9];
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double functionDerivs[18];
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double elemNodes[9][3];
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double *J[3], J0[3], J1[3], J2[3];
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double *JI[3], JI0[3], JI1[3], JI2[3];
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for(int i = 0; i<9; i++)
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{
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this->Points->GetPoint(i, elemNodes[i]);
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}
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this->InterpolationFunctionsPrivate(pcoords,weights);
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this->InterpolationDerivsPrivate(pcoords,functionDerivs);
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// Compute transposed Jacobian and inverse Jacobian
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J[0] = J0; J[1] = J1; J[2] = J2;
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JI[0] = JI0; JI[1] = JI1; JI[2] = JI2;
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for(int k = 0; k<3; k++)
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{
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J0[k] = J1[k] = 0.0;
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}
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for(int i = 0; i<9; i++)
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{
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for(int j = 0; j<2; j++)
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{
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for(int k = 0; k<3; k++)
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{
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J[j][k] += elemNodes[i][k] * functionDerivs[j*9+i];
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}
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}
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}
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// Compute third row vector in transposed Jacobian and normalize it, so that Jacobian determinant stays the same.
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vtkMath::Cross(J0,J1,J2);
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if ( vtkMath::Normalize(J2) == 0.0 || !vtkMath::InvertMatrix(J,JI,3)) //degenerate
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{
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for (int j=0; j < dim; j++ )
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{
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for (int i=0; i < 3; i++ )
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{
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derivs[j*dim + i] = 0.0;
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}
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}
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return;
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}
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// Loop over "dim" derivative values. For each set of values,
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// compute derivatives
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// in local system and then transform into modelling system.
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// First compute derivatives in local x'-y' coordinate system
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for (int j=0; j < dim; j++ )
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{
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sum[0] = sum[1] = sum[2] = 0.0;
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for (int i=0; i < 9; i++) //loop over interp. function derivatives
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{
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sum[0] += functionDerivs[i] * values[dim*i + j];
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sum[1] += functionDerivs[9 + i] * values[dim*i + j];
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}
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// dBydx = sum[0]*JI[0][0] + sum[1]*JI[0][1];
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// dBydy = sum[0]*JI[1][0] + sum[1]*JI[1][1];
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// Transform into global system (dot product with global axes)
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derivs[3*j] = sum[0]*JI[0][0] + sum[1]*JI[0][1];
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derivs[3*j + 1] = sum[0]*JI[1][0] + sum[1]*JI[1][1];
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derivs[3*j + 2] = sum[0]*JI[2][0] + sum[1]*JI[2][1];
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}
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}
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//----------------------------------------------------------------------------
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// Compute interpolation functions. The first four nodes are the corner
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// vertices; the others are mid-edge nodes, the last one is the mid-center
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// node.
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void vtkBiQuadraticQuad::InterpolationFunctionsPrivate (double pcoords[3],
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double weights[9])
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{
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//Normally these coordinates are named r and s, but I chose x and y,
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//because you can easily mark and paste these functions to the
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//gnuplot splot function. :D
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double x = pcoords[0];
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double y = pcoords[1];
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//midedge weights
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weights[0] = 4.0 * (1.0 - x) * (x - 0.5) * (1.0 - y) * (y - 0.5);
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weights[1] = -4.0 * (x) * (x - 0.5) * (1.0 - y) * (y - 0.5);
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weights[2] = 4.0 * (x) * (x - 0.5) * (y) * (y - 0.5);
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weights[3] = -4.0 * (1.0 - x) * (x - 0.5) * (y) * (y - 0.5);
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//corner weights
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weights[4] = 8.0 * (x) * (1.0 - x) * (1.0 - y) * (0.5 - y);
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weights[5] = -8.0 * (x) * (0.5 - x) * (1.0 - y) * (y);
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weights[6] = -8.0 * (x) * (1.0 - x) * (y) * (0.5 - y);
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weights[7] = 8.0 * (1.0 - x) * (0.5 - x) * (1.0 - y) * (y);
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//surface center weight
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weights[8] = 16.0 * (x) * (1.0 - x) * (1.0 - y) * (y);
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}
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//----------------------------------------------------------------------------
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#if !defined(VTK_LEGACY_REMOVE)
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void vtkBiQuadraticQuad::InterpolationFunctions (double pcoords[3],
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double weights[9])
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{
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VTK_LEGACY_REPLACED_BODY(InterpolationFunctions, "VTK 5.2",
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InterpolateFunctions);
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vtkBiQuadraticQuad::InterpolationFunctionsPrivate(pcoords, weights);
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}
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#endif
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//----------------------------------------------------------------------------
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// Derivatives in parametric space.
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void vtkBiQuadraticQuad::InterpolationDerivsPrivate (double pcoords[3],
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double derivs[18])
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{
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// Coordinate conversion
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double x = pcoords[0];
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double y = pcoords[1];
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// Derivatives in the x-direction
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// edge
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derivs[0] = 4.0 * (1.5 - 2.0 * x) * (1.0 - y) * (y - 0.5);
|
|
derivs[1] =-4.0 * (2.0 * x - 0.5) * (1.0 - y) * (y - 0.5);
|
|
derivs[2] = 4.0 * (2.0 * x - 0.5) * (y) * (y - 0.5);
|
|
derivs[3] =-4.0 * (1.5 - 2.0 * x) * (y) * (y - 0.5);
|
|
// midedge
|
|
derivs[4] = 8.0 * (1.0 - 2.0 * x) * (1.0 - y) * (0.5 - y);
|
|
derivs[5] =-8.0 * (0.5 - 2.0 * x) * (1.0 - y) * (y);
|
|
derivs[6] =-8.0 * (1.0 - 2.0 * x) * (y) * (0.5 - y);
|
|
derivs[7] = 8.0 * (2.0 * x - 1.5) * (1.0 - y) * (y);
|
|
// center
|
|
derivs[8] =16.0 * (1.0 - 2.0 * x) * (1.0 - y) * (y);
|
|
|
|
// Derivatives in the y-direction
|
|
// edge
|
|
derivs[9] = 4.0 * (1.0 - x) * (x - 0.5) * (1.5 - 2.0 * y);
|
|
derivs[10]=-4.0 * (x) * (x - 0.5) * (1.5 - 2.0 * y);
|
|
derivs[11]= 4.0 * (x) * (x - 0.5) * (2.0 * y - 0.5);
|
|
derivs[12]=-4.0 * (1.0 - x) * (x - 0.5) * (2.0 * y - 0.5);
|
|
// midedge
|
|
derivs[13]= 8.0 * (x) * (1.0 - x) * (2.0 * y - 1.5);
|
|
derivs[14]=-8.0 * (x) * (0.5 - x) * (1.0 - 2.0 * y);
|
|
derivs[15]=-8.0 * (x) * (1.0 - x) * (0.5 - 2.0 * y);
|
|
derivs[16]= 8.0 * (1.0 - x) * (0.5 - x) * (1.0 - 2.0 * y);
|
|
// center
|
|
derivs[17]=16.0 * (x) * (1.0 - x) * (1.0 - 2.0 * y);
|
|
|
|
}
|
|
|
|
//----------------------------------------------------------------------------
|
|
#if !defined(VTK_LEGACY_REMOVE)
|
|
void vtkBiQuadraticQuad::InterpolationDerivs (double pcoords[3],
|
|
double derivs[18])
|
|
{
|
|
VTK_LEGACY_REPLACED_BODY(InterpolationDerivs, "VTK 5.2",
|
|
InterpolateDerivs);
|
|
|
|
vtkBiQuadraticQuad::InterpolationDerivsPrivate(pcoords, derivs);
|
|
}
|
|
#endif
|
|
|
|
//----------------------------------------------------------------------------
|
|
static double vtkQQuadCellPCoords[27] = { 0.0, 0.0, 0.0, 1.0, 0.0, 0.0,
|
|
1.0, 1.0, 0.0, 0.0, 1.0, 0.0,
|
|
0.5, 0.0, 0.0, 1.0, 0.5, 0.0,
|
|
0.5, 1.0, 0.0, 0.0, 0.5, 0.0,
|
|
0.5, 0.5, 0.0 };
|
|
|
|
double * vtkBiQuadraticQuad::GetParametricCoords ()
|
|
{
|
|
return vtkQQuadCellPCoords;
|
|
}
|
|
|
|
//----------------------------------------------------------------------------
|
|
void vtkBiQuadraticQuad::PrintSelf(ostream & os, vtkIndent indent)
|
|
{
|
|
this->Superclass::PrintSelf(os, indent);
|
|
|
|
os << indent << "Edge:\n";
|
|
this->Edge->PrintSelf (os, indent.GetNextIndent ());
|
|
os << indent << "Quad:\n";
|
|
this->Quad->PrintSelf (os, indent.GetNextIndent ());
|
|
os << indent << "Scalars:\n";
|
|
this->Scalars->PrintSelf (os, indent.GetNextIndent ());
|
|
}
|