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601 lines
19 KiB
C++
601 lines
19 KiB
C++
/*=========================================================================
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Program: Visualization Toolkit
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Module: vtkQuadraticQuad.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 "vtkQuadraticQuad.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 "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(vtkQuadraticQuad);
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//----------------------------------------------------------------------------
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// Construct the quad with eight points.
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vtkQuadraticQuad::vtkQuadraticQuad()
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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->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(9);
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this->Scalars = vtkDoubleArray::New();
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this->Scalars->SetNumberOfTuples(4);
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// We add a fictitious ninth point in order to process the cell. The ninth
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// point is in the center of the cell.
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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->Points->SetNumberOfPoints(8);
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this->PointIds->SetNumberOfIds(8);
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}
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//----------------------------------------------------------------------------
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vtkQuadraticQuad::~vtkQuadraticQuad()
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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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this->PointData->Delete();
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this->CellData->Delete();
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this->CellScalars->Delete();
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}
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//----------------------------------------------------------------------------
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vtkCell *vtkQuadraticQuad::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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void vtkQuadraticQuad::Subdivide(double *weights)
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{
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int i, j;
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double pc[3], x[3];
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pc[0] = pc[1] = 0.5;
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this->InterpolationFunctions(pc, weights);
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double p[3];
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x[0] = x[1] = x[2] = 0.0;
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for (i=0; i<8; 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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}
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this->Points->SetPoint(8,x);
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}
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//----------------------------------------------------------------------------
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int vtkQuadraticQuad::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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// compute the midquad node
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this->Subdivide(weights);
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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(
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0,this->Points->GetPoint(LinearQuads[i][0]));
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this->Quad->Points->SetPoint(
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1,this->Points->GetPoint(LinearQuads[i][1]));
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this->Quad->Points->SetPoint(
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2,this->Points->GetPoint(LinearQuads[i][2]));
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this->Quad->Points->SetPoint(
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3,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->InterpolationFunctions(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 vtkQuadraticQuad::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<8; 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 vtkQuadraticQuad::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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static double MidPoints[1][3] = { {0.5,0.5,0.0} };
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//----------------------------------------------------------------------------
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void vtkQuadraticQuad::InterpolateAttributes(vtkPointData *inPd, vtkCellData *inCd,
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vtkIdType cellId, vtkDataArray *cellScalars)
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{
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int numMidPts, i, j;
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double weights[20];
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double x[3];
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double s;
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//Copy point and cell attribute data, first make sure it's empty:
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this->PointData->Initialize();
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this->CellData->Initialize();
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// 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,9);
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this->CellData->CopyAllocate(inCd,4);
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// copy the point data over into point ids 0->7
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for (i=0; i<8; 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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// copy the cell data over to the linear cell
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this->CellData->CopyData(inCd,cellId,0);
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//Interpolate new values
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double p[3];
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this->Points->Resize(9);
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this->CellScalars->Resize(9);
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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<8; 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(8+numMidPts,x);
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this->CellScalars->SetValue(8+numMidPts,s);
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this->PointData->InterpolatePoint(inPd, 8+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 vtkQuadraticQuad::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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//interpolate point and cell data
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this->InterpolateAttributes(inPd,inCd,cellId,cellScalars);
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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,LinearQuads[i][j]);
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this->Scalars->SetValue(j,this->CellScalars->GetValue(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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this->PointData,outPd,this->CellData,i,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 vtkQuadraticQuad::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,
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vtkCellData* outCd, int insideOut)
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{
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//interpolate point and cell data
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this->InterpolateAttributes(inPd,inCd,cellId,cellScalars);
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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,LinearQuads[i][j]);
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this->Scalars->SetValue(j,this->CellScalars->GetValue(LinearQuads[i][j]));
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}
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this->Quad->Clip(value,this->Scalars,locator,polys,this->PointData,
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outPd,this->CellData,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 vtkQuadraticQuad::IntersectWithLine(double* p1,
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double* p2,
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double tol,
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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 subTest, i;
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subId = 0;
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double weights[8];
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//first define the midquad point
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this->Subdivide(weights);
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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,this->Points->GetPoint(LinearQuads[i][0]));
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this->Quad->Points->SetPoint(1,this->Points->GetPoint(LinearQuads[i][1]));
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this->Quad->Points->SetPoint(2,this->Points->GetPoint(LinearQuads[i][2]));
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this->Quad->Points->SetPoint(3,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 vtkQuadraticQuad::Triangulate(int vtkNotUsed(index), vtkIdList *ptIds,
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vtkPoints *pts)
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{
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pts->Reset();
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ptIds->Reset();
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// Create six linear triangles: one at each corner and two
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// to cover the remaining quadrilateral.
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// First the corner vertices
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ptIds->InsertId(0,this->PointIds->GetId(0));
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ptIds->InsertId(1,this->PointIds->GetId(4));
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ptIds->InsertId(2,this->PointIds->GetId(7));
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pts->InsertPoint(0,this->Points->GetPoint(0));
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pts->InsertPoint(1,this->Points->GetPoint(4));
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pts->InsertPoint(2,this->Points->GetPoint(7));
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ptIds->InsertId(3,this->PointIds->GetId(4));
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ptIds->InsertId(4,this->PointIds->GetId(1));
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ptIds->InsertId(5,this->PointIds->GetId(5));
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pts->InsertPoint(3,this->Points->GetPoint(4));
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pts->InsertPoint(4,this->Points->GetPoint(1));
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pts->InsertPoint(5,this->Points->GetPoint(5));
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ptIds->InsertId(6,this->PointIds->GetId(5));
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ptIds->InsertId(7,this->PointIds->GetId(2));
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ptIds->InsertId(8,this->PointIds->GetId(6));
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pts->InsertPoint(6,this->Points->GetPoint(5));
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pts->InsertPoint(7,this->Points->GetPoint(2));
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pts->InsertPoint(8,this->Points->GetPoint(6));
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ptIds->InsertId(9,this->PointIds->GetId(6));
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ptIds->InsertId(10,this->PointIds->GetId(3));
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ptIds->InsertId(11,this->PointIds->GetId(7));
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pts->InsertPoint(9,this->Points->GetPoint(6));
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pts->InsertPoint(10,this->Points->GetPoint(3));
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pts->InsertPoint(11,this->Points->GetPoint(7));
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// Now the two remaining triangles
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// Choose the triangulation that minimizes the edge length
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// across the cell.
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double x4[3], x5[3], x6[3], x7[3];
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this->Points->GetPoint(4, x4);
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this->Points->GetPoint(5, x5);
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this->Points->GetPoint(6, x6);
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this->Points->GetPoint(7, x7);
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if ( vtkMath::Distance2BetweenPoints(x4,x6) <=
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vtkMath::Distance2BetweenPoints(x5,x7) )
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{
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ptIds->InsertId(12,this->PointIds->GetId(4));
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ptIds->InsertId(13,this->PointIds->GetId(6));
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ptIds->InsertId(14,this->PointIds->GetId(7));
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pts->InsertPoint(12,this->Points->GetPoint(4));
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pts->InsertPoint(13,this->Points->GetPoint(6));
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pts->InsertPoint(14,this->Points->GetPoint(7));
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ptIds->InsertId(15,this->PointIds->GetId(4));
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ptIds->InsertId(16,this->PointIds->GetId(5));
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ptIds->InsertId(17,this->PointIds->GetId(6));
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pts->InsertPoint(15,this->Points->GetPoint(4));
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pts->InsertPoint(16,this->Points->GetPoint(5));
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pts->InsertPoint(17,this->Points->GetPoint(6));
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}
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else
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{
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ptIds->InsertId(12,this->PointIds->GetId(5));
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ptIds->InsertId(13,this->PointIds->GetId(6));
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ptIds->InsertId(14,this->PointIds->GetId(7));
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pts->InsertPoint(12,this->Points->GetPoint(5));
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pts->InsertPoint(13,this->Points->GetPoint(6));
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pts->InsertPoint(14,this->Points->GetPoint(7));
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ptIds->InsertId(15,this->PointIds->GetId(5));
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ptIds->InsertId(16,this->PointIds->GetId(7));
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ptIds->InsertId(17,this->PointIds->GetId(4));
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pts->InsertPoint(15,this->Points->GetPoint(5));
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pts->InsertPoint(16,this->Points->GetPoint(7));
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pts->InsertPoint(17,this->Points->GetPoint(4));
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}
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return 1;
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}
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//----------------------------------------------------------------------------
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void vtkQuadraticQuad::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[8];
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double functionDerivs[16];
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double elemNodes[8][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<8; i++)
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{
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this->Points->GetPoint(i, elemNodes[i]);
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}
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this->InterpolationFunctions(pcoords,weights);
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this->InterpolationDerivs(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<8; i++)
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|
{
|
|
for(int j = 0; j<2; j++)
|
|
{
|
|
for(int k = 0; k<3; k++)
|
|
{
|
|
J[j][k] += elemNodes[i][k] * functionDerivs[j*8+i];
|
|
}
|
|
}
|
|
}
|
|
|
|
// Compute third row vector in transposed Jacobian and normalize it, so that Jacobian determinant stays the same.
|
|
vtkMath::Cross(J0,J1,J2);
|
|
if ( vtkMath::Normalize(J2) == 0.0 || !vtkMath::InvertMatrix(J,JI,3)) //degenerate
|
|
{
|
|
for (int j=0; j < dim; j++ )
|
|
{
|
|
for (int i=0; i < 3; i++ )
|
|
{
|
|
derivs[j*dim + i] = 0.0;
|
|
}
|
|
}
|
|
return;
|
|
}
|
|
|
|
|
|
// Loop over "dim" derivative values. For each set of values,
|
|
// compute derivatives
|
|
// in local system and then transform into modelling system.
|
|
// First compute derivatives in local x'-y' coordinate system
|
|
for (int j=0; j < dim; j++ )
|
|
{
|
|
sum[0] = sum[1] = sum[2] = 0.0;
|
|
for (int i=0; i < 8; i++) //loop over interp. function derivatives
|
|
{
|
|
sum[0] += functionDerivs[i] * values[dim*i + j];
|
|
sum[1] += functionDerivs[8 + i] * values[dim*i + j];
|
|
}
|
|
// dBydx = sum[0]*JI[0][0] + sum[1]*JI[0][1];
|
|
// dBydy = sum[0]*JI[1][0] + sum[1]*JI[1][1];
|
|
|
|
// Transform into global system (dot product with global axes)
|
|
derivs[3*j] = sum[0]*JI[0][0] + sum[1]*JI[0][1];
|
|
derivs[3*j + 1] = sum[0]*JI[1][0] + sum[1]*JI[1][1];
|
|
derivs[3*j + 2] = sum[0]*JI[2][0] + sum[1]*JI[2][1];
|
|
}
|
|
}
|
|
|
|
//----------------------------------------------------------------------------
|
|
// Compute interpolation functions. The first four nodes are the corner
|
|
// vertices; the others are mid-edge nodes.
|
|
void vtkQuadraticQuad::InterpolationFunctions(double pcoords[3],
|
|
double weights[8])
|
|
{
|
|
double r = pcoords[0];
|
|
double s = pcoords[1];
|
|
|
|
//midedge weights
|
|
weights[4] = 4 * r * (1.0 - r) * (1.0 - s);
|
|
weights[5] = 4 * r * (1.0 - s) * s;
|
|
weights[6] = 4 * r * (1.0 - r) * s;
|
|
weights[7] = 4 * (1.0 - r) * (1.0 - s) * s;
|
|
|
|
//corner
|
|
weights[0] = (1.0 - r) * (1.0 - s) - 0.5*(weights[4]+weights[7]);
|
|
weights[1] = r * (1.0 - s) - 0.5*(weights[4]+weights[5]);
|
|
weights[2] = r * s - 0.5*(weights[5]+weights[6]);
|
|
weights[3] = (1.0 - r) * s - 0.5*(weights[6]+weights[7]);
|
|
|
|
}
|
|
|
|
//----------------------------------------------------------------------------
|
|
// Derivatives in parametric space.
|
|
void vtkQuadraticQuad::InterpolationDerivs(double pcoords[3], double derivs[16])
|
|
{
|
|
// Coordinate conversion
|
|
double r = pcoords[0];
|
|
double s = pcoords[1];
|
|
|
|
// Derivatives in the r-direction
|
|
// midedge
|
|
derivs[4] = 4 * (1.0 - s) * (1.0 - 2*r);
|
|
derivs[5] = 4 * (1.0 - s) * s;
|
|
derivs[6] = 4 * s * (1.0 - 2*r);
|
|
derivs[7] =-4 * (1.0 - s) * s;
|
|
derivs[0] =-(1.0 - s) - 0.5 * (derivs[4] + derivs[7]);
|
|
derivs[1] = (1.0 - s) - 0.5 * (derivs[4] + derivs[5]);
|
|
derivs[2] = s - 0.5 * (derivs[5] + derivs[6]);
|
|
derivs[3] = -s - 0.5 * (derivs[6] + derivs[7]);
|
|
|
|
// Derivatives in the s-direction
|
|
// midedge
|
|
derivs[12] =-4 * r * (1.0 - r);
|
|
derivs[13] = 4 * r * (1.0 - 2*s);
|
|
derivs[14] = 4 * r * (1.0 - r);
|
|
derivs[15] = 4 * (1.0 - r) * (1.0 - 2*s);
|
|
derivs[8] = -(1.0 - r) - 0.5 * (derivs[12] + derivs[15]);
|
|
derivs[9] = - r - 0.5 * (derivs[12] + derivs[13]);
|
|
derivs[10] = r - 0.5 * (derivs[13] + derivs[14]);
|
|
derivs[11] = (1.0 - r) - 0.5 * (derivs[14] + derivs[15]);
|
|
}
|
|
|
|
//----------------------------------------------------------------------------
|
|
static double vtkQQuadCellPCoords[24] = {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};
|
|
double *vtkQuadraticQuad::GetParametricCoords()
|
|
{
|
|
return vtkQQuadCellPCoords;
|
|
}
|
|
|
|
//----------------------------------------------------------------------------
|
|
void vtkQuadraticQuad::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());
|
|
}
|