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745 lines
22 KiB
745 lines
22 KiB
/*=========================================================================
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Program: Visualization Toolkit
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Module: $RCSfile: vtkHexagonalPrism.cxx,v $
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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 Philippe Guerville who developed this class.
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// Thanks to Charles Pignerol (CEA-DAM, France) who ported this class under
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// VTK 4.
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// Thanks to Jean Favre (CSCS, Switzerland) who contributed to integrate this
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// class in VTK.
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// Please address all comments to Jean Favre (jfavre at cscs.ch).
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#include "vtkHexagonalPrism.h"
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#include "vtkObjectFactory.h"
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#include "vtkLine.h"
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#include "vtkQuad.h"
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#include "vtkPolygon.h"
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#include "vtkMath.h"
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#include "vtkPoints.h"
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vtkCxxRevisionMacro(vtkHexagonalPrism, "$Revision: 1.4 $");
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vtkStandardNewMacro(vtkHexagonalPrism);
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static const double VTK_DIVERGED = 1.e6;
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// You can recompute the value by doing:
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// const double a = sqrt(3.0)/4.0 + 0.5;
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#define EXPRA 0.933012701892219298
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// You can recompute the value by doing:
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// const double b = 0.5 - sqrt(3.0)/4.0;
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// Thus EXPRA + EXPRB = 1.0
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#define EXPRB 0.066987298107780702
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//----------------------------------------------------------------------------
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// Construct the prism with twelve points.
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vtkHexagonalPrism::vtkHexagonalPrism()
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{
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int i;
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this->Points->SetNumberOfPoints(12);
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this->PointIds->SetNumberOfIds(12);
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for (i = 0; i < 12; 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->Line = vtkLine::New();
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this->Quad = vtkQuad::New();
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this->Polygon = vtkPolygon::New();
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this->Polygon->PointIds->SetNumberOfIds(6);
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this->Polygon->Points->SetNumberOfPoints(6);
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for (i = 0; i < 6; i++)
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{
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this->Polygon->Points->SetPoint(i, 0.0, 0.0, 0.0);
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this->Polygon->PointIds->SetId(i,0);
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}
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}
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//----------------------------------------------------------------------------
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vtkHexagonalPrism::~vtkHexagonalPrism()
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{
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this->Line->Delete();
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this->Quad->Delete();
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this->Polygon->Delete();
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}
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// Method to calculate parametric coordinates in an eight noded
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// linear hexahedron element from global coordinates.
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//
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static const int VTK_HEX_MAX_ITERATION=10;
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static const double VTK_HEX_CONVERGED=1.e-03;
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//----------------------------------------------------------------------------
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int vtkHexagonalPrism::EvaluatePosition(double x[3], double* closestPoint,
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int& subId, double pcoords[3],
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double& dist2, double *weights)
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{
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int 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[36];
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// set initial position for Newton's method
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subId = 0;
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pcoords[0] = pcoords[1] = pcoords[2] = params[0] = params[1] = params[2]=0.5;
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// enter iteration loop
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for (iteration=converged=0;
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!converged && (iteration < VTK_HEX_MAX_ITERATION); iteration++)
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{
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// calculate element interpolation functions and derivatives
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this->InterpolationFunctions(pcoords, weights);
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this->InterpolationDerivs(pcoords, derivs);
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// calculate newton functions
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for (i=0; i<3; i++)
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{
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fcol[i] = rcol[i] = scol[i] = tcol[i] = 0.0;
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}
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for (i=0; i<12; 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+12];
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tcol[j] += pt[j] * derivs[i+24];
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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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return -1;
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}
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pcoords[0] = params[0] - vtkMath::Determinant3x3 (fcol,scol,tcol) / d;
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pcoords[1] = params[1] - vtkMath::Determinant3x3 (rcol,fcol,tcol) / d;
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pcoords[2] = params[2] - vtkMath::Determinant3x3 (rcol,scol,fcol) / d;
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// check for convergence
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if ( ((fabs(pcoords[0]-params[0])) < VTK_HEX_CONVERGED) &&
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((fabs(pcoords[1]-params[1])) < VTK_HEX_CONVERGED) &&
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((fabs(pcoords[2]-params[2])) < VTK_HEX_CONVERGED) )
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{
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converged = 1;
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}
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// Test for bad divergence (S.Hirschberg 11.12.2001)
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else if ((fabs(pcoords[0]) > VTK_DIVERGED) ||
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(fabs(pcoords[1]) > VTK_DIVERGED) ||
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(fabs(pcoords[2]) > VTK_DIVERGED))
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{
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return -1;
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}
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// if not converged, repeat
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else
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{
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params[0] = pcoords[0];
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params[1] = pcoords[1];
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params[2] = pcoords[2];
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}
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}
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// if not converged, set the parametric coordinates to arbitrary values
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// outside of element
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if ( !converged )
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{
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return -1;
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}
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this->InterpolationFunctions(pcoords, weights);
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if ( pcoords[0] >= -0.001 && pcoords[0] <= 1.001 &&
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pcoords[1] >= -0.001 && pcoords[1] <= 1.001 &&
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pcoords[2] >= -0.001 && pcoords[2] <= 1.001 )
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{
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if (closestPoint)
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{
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closestPoint[0] = x[0]; closestPoint[1] = x[1]; closestPoint[2] = x[2];
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dist2 = 0.0; //inside hexahedron
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}
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return 1;
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}
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else
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{
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double pc[3], w[12];
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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, (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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//
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// Compute iso-parametric interpolation functions
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//
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void vtkHexagonalPrism::InterpolationFunctions(double pcoords[3], double sf[12])
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{
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double r, s, t;
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r = pcoords[0];
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s = pcoords[1];
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t = pcoords[2];
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const double a = EXPRA;
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const double b = EXPRB;
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//First hexagon
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sf[0] = -16./3.*(r - a )*(r - b)*(s - 1.0 )*(t - 1.0);
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sf[1] = 16./3.*(r - 0.5)*(r - b)*(s - 0.75)*(t - 1.0);
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sf[2] = -16./3.*(r - 0.5)*(r - b)*(s - 0.25)*(t - 1.0);
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sf[3] = 16./3.*(r - a )*(r - b)*(s - 0.0 )*(t - 1.0);
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sf[4] = -16./3.*(r - 0.5)*(r - a)*(s - 0.25)*(t - 1.0);
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sf[5] = 16./3.*(r - 0.5)*(r - a)*(s - 0.75)*(t - 1.0);
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//Second hexagon
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sf[6] = 16./3.*(r - a )*(r - b)*(s - 1.0 )*(t - 0.0);
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sf[7] = -16./3.*(r - 0.5)*(r - b)*(s - 0.75)*(t - 0.0);
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sf[8] = 16./3.*(r - 0.5)*(r - b)*(s - 0.25)*(t - 0.0);
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sf[9] = -16./3.*(r - a )*(r - b)*(s - 0.0 )*(t - 0.0);
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sf[10] = 16./3.*(r - 0.5)*(r - a)*(s - 0.25)*(t - 0.0);
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sf[11] = -16./3.*(r - 0.5)*(r - a)*(s - 0.75)*(t - 0.0);
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}
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//----------------------------------------------------------------------------
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void vtkHexagonalPrism::InterpolationDerivs(double pcoords[3], double derivs[36])
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{
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double r, s, t;
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r = pcoords[0];
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s = pcoords[1];
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t = pcoords[2];
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const double a = EXPRA;
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const double b = EXPRB;
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//note: a+b=1.0
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// r-derivatives
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//First hexagon
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derivs[0] = -16./3.*( 2*r - 1.0) *(s - 1.0 )*(t - 1.0);
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derivs[1] = 16./3.*( 2*r - b - 0.5)*(s - 0.75)*(t - 1.0);
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derivs[2] = -16./3.*( 2*r - b - 0.5)*(s - 0.25)*(t - 1.0);
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derivs[3] = 16./3.*( 2*r - 1.0) *(s - 0.0 )*(t - 1.0);
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derivs[4] = -16./3.*( 2*r - a - 0.5)*(s - 0.25)*(t - 1.0);
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derivs[5] = 16./3.*( 2*r - a - 0.5)*(s - 0.75)*(t - 1.0);
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//Second hexagon
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derivs[6] = 16./3.*( 2*r - 1.0) *(s - 1.0 )*(t - 0.0);
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derivs[7] = -16./3.*( 2*r - b - 0.5)*(s - 0.75)*(t - 0.0);
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derivs[8] = 16./3.*( 2*r - b - 0.5)*(s - 0.25)*(t - 0.0);
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derivs[9] = -16./3.*( 2*r - 1.0) *(s - 0.0 )*(t - 0.0);
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derivs[10] = 16./3.*( 2*r - a - 0.5)*(s - 0.25)*(t - 0.0);
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derivs[11] = -16./3.*( 2*r - a - 0.5)*(s - 0.75)*(t - 0.0);
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// s-derivatives
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//First hexagon
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derivs[12] = -16./3.*(r - a )*(r - b)*(t - 1.0);
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derivs[13] = 16./3.*(r - 0.5)*(r - b)*(t - 1.0);
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derivs[14] = -16./3.*(r - 0.5)*(r - b)*(t - 1.0);
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derivs[15] = 16./3.*(r - a )*(r - b)*(t - 1.0);
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derivs[16] = -16./3.*(r - 0.5)*(r - a)*(t - 1.0);
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derivs[17] = 16./3.*(r - 0.5)*(r - a)*(t - 1.0);
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//Second hexagon
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derivs[18] = 16./3.*(r - a )*(r - b)*(t - 0.0);
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derivs[19] = -16./3.*(r - 0.5)*(r - b)*(t - 0.0);
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derivs[20] = 16./3.*(r - 0.5)*(r - b)*(t - 0.0);
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derivs[21] = -16./3.*(r - a )*(r - b)*(t - 0.0);
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derivs[22] = 16./3.*(r - 0.5)*(r - a)*(t - 0.0);
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derivs[23] = -16./3.*(r - 0.5)*(r - a)*(t - 0.0);
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// t-derivatives
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//First hexagon
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derivs[24] = -16./3.*(r - a )*(r - b)*(s - 1.0 );
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derivs[25] = 16./3.*(r - 0.5)*(r - b)*(s - 0.75);
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derivs[26] = -16./3.*(r - 0.5)*(r - b)*(s - 0.25);
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derivs[27] = 16./3.*(r - a )*(r - b)*(s - 0.0 );
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derivs[28] = -16./3.*(r - 0.5)*(r - a)*(s - 0.25);
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derivs[29] = 16./3.*(r - 0.5)*(r - a)*(s - 0.75);
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//Second hexagon
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derivs[30] = 16./3.*(r - a )*(r - b)*(s - 1.0 );
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derivs[31] = -16./3.*(r - 0.5)*(r - b)*(s - 0.75);
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derivs[32] = 16./3.*(r - 0.5)*(r - b)*(s - 0.25);
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derivs[33] = -16./3.*(r - a )*(r - b)*(s - 0.0 );
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derivs[34] = 16./3.*(r - 0.5)*(r - a)*(s - 0.25);
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derivs[35] = -16./3.*(r - 0.5)*(r - a)*(s - 0.75);
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}
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//----------------------------------------------------------------------------
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void vtkHexagonalPrism::EvaluateLocation(int& vtkNotUsed(subId),
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double pcoords[3], double x[3],
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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 < 12; 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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static int edges[18][2] = { {0,1}, {1, 2}, {2, 3},
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{3,4}, {4, 5}, {5, 0},
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{6,7}, {7, 8}, {8, 9},
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{9,10}, {10,11}, {11, 6},
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{0,6}, {1, 7}, {2, 8},
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{3,9}, {4, 10}, {5, 11} };
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static int faces[8][6] = { {0,5,4,3,2,1}, {6,7,8,9,10,11},
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{0,1,7,6,-1,-1}, {1,2,8,7,-1,-1},
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{2,3,9,8,-1,-1}, {3,4,10,9,-1,-1},
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{4,5,11,10,-1,-1}, {5,0,6,11,-1,-1} };
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#define VTK_MAX(a,b) (((a)>(b))?(a):(b))
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#define VTK_MIN(a,b) (((a)<(b))?(a):(b))
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//----------------------------------------------------------------------------
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// Returns the closest face to the point specified. Closeness is measured
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// parametrically.
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int vtkHexagonalPrism::CellBoundary(int subId, double pcoords[3],
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vtkIdList *pts)
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{
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// load coordinates
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double *points = this->GetParametricCoords();
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for(int i=0;i<6;i++)
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{
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this->Polygon->PointIds->SetId(i, i);
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this->Polygon->Points->SetPoint(i, &points[3*i]);
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}
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this->Polygon->CellBoundary( subId, pcoords, pts);
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int min = VTK_MIN(pts->GetId( 0 ), pts->GetId( 1 ));
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int max = VTK_MAX(pts->GetId( 0 ), pts->GetId( 1 ));
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//Base on the edge find the quad that correspond:
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int index;
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if( (index = (max - min)) > 1)
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{
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index = 7;
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}
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else
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{
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index += min + 1;
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}
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double a[3], b[3], u[3], v[3];
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this->Polygon->Points->GetPoint(pts->GetId( 0 ), a);
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this->Polygon->Points->GetPoint(pts->GetId( 1 ), b);
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u[0] = b[0] - a[0];
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u[1] = b[1] - a[1];
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v[0] = pcoords[0] - a[0];
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v[1] = pcoords[1] - a[1];
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double dot = vtkMath::Dot2D(v, u);
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double uNorm = vtkMath::Norm2D( u );
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if (uNorm)
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{
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dot /= uNorm;
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}
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dot = (v[0]*v[0] + v[1]*v[1]) - dot*dot;
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// mathematically dot must be >= zero but, suprise suprise, it can actually
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// be negative
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if (dot > 0)
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{
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dot = sqrt( dot );
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}
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else
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{
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dot = 0;
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}
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int *verts;
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if(pcoords[2] < 0.5)
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{
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//could be closer to face 1
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//compare that distance to the distance to the quad.
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if(dot < pcoords[2])
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{
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//We are closer to the quad face
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verts = faces[index];
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for(int i=0; i<4; i++)
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{
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pts->InsertId(i, verts[i]);
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}
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}
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else
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{
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//we are closer to the hexa face 1
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for(int i=0; i<6; i++)
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{
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pts->InsertId(i, faces[0][i]);
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}
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}
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}
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else
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{
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//could be closer to face 2
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//compare that distance to the distance to the quad.
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if(dot < (1. - pcoords[2]) )
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{
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//We are closer to the quad face
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verts = faces[index];
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for(int i=0; i<4; i++)
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{
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pts->InsertId(i, verts[i]);
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}
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}
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else
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{
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//we are closer to the hexa face 2
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for(int i=0; i<6; i++)
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{
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pts->InsertId(i, faces[1][i]);
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}
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}
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}
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// determine whether point is inside of hexagon
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if ( pcoords[0] < 0.0 || pcoords[0] > 1.0 ||
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pcoords[1] < 0.0 || pcoords[1] > 1.0 ||
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pcoords[2] < 0.0 || pcoords[2] > 1.0 )
|
|
{
|
|
return 0;
|
|
}
|
|
else
|
|
{
|
|
return 1;
|
|
}
|
|
}
|
|
//----------------------------------------------------------------------------
|
|
int *vtkHexagonalPrism::GetEdgeArray(int edgeId)
|
|
{
|
|
return edges[edgeId];
|
|
}
|
|
|
|
//----------------------------------------------------------------------------
|
|
vtkCell *vtkHexagonalPrism::GetEdge(int edgeId)
|
|
{
|
|
int *verts;
|
|
|
|
verts = edges[edgeId];
|
|
|
|
// load point id's
|
|
this->Line->PointIds->SetId(0,this->PointIds->GetId(verts[0]));
|
|
this->Line->PointIds->SetId(1,this->PointIds->GetId(verts[1]));
|
|
|
|
// load coordinates
|
|
this->Line->Points->SetPoint(0,this->Points->GetPoint(verts[0]));
|
|
this->Line->Points->SetPoint(1,this->Points->GetPoint(verts[1]));
|
|
|
|
return this->Line;
|
|
}
|
|
//----------------------------------------------------------------------------
|
|
int *vtkHexagonalPrism::GetFaceArray(int faceId)
|
|
{
|
|
return faces[faceId];
|
|
}
|
|
//----------------------------------------------------------------------------
|
|
vtkCell *vtkHexagonalPrism::GetFace(int faceId)
|
|
{
|
|
int *verts;
|
|
|
|
verts = faces[faceId];
|
|
|
|
if ( verts[4] != -1 ) // polys cell
|
|
{
|
|
// load point id's
|
|
this->Polygon->PointIds->SetId(0,this->PointIds->GetId(verts[0]));
|
|
this->Polygon->PointIds->SetId(1,this->PointIds->GetId(verts[1]));
|
|
this->Polygon->PointIds->SetId(2,this->PointIds->GetId(verts[2]));
|
|
this->Polygon->PointIds->SetId(3,this->PointIds->GetId(verts[3]));
|
|
this->Polygon->PointIds->SetId(4,this->PointIds->GetId(verts[4]));
|
|
this->Polygon->PointIds->SetId(5,this->PointIds->GetId(verts[5]));
|
|
|
|
// load coordinates
|
|
this->Polygon->Points->SetPoint(0,this->Points->GetPoint(verts[0]));
|
|
this->Polygon->Points->SetPoint(1,this->Points->GetPoint(verts[1]));
|
|
this->Polygon->Points->SetPoint(2,this->Points->GetPoint(verts[2]));
|
|
this->Polygon->Points->SetPoint(3,this->Points->GetPoint(verts[3]));
|
|
this->Polygon->Points->SetPoint(4,this->Points->GetPoint(verts[4]));
|
|
this->Polygon->Points->SetPoint(5,this->Points->GetPoint(verts[5]));
|
|
|
|
return this->Polygon;
|
|
}
|
|
else
|
|
{
|
|
// load point id's
|
|
this->Quad->PointIds->SetId(0,this->PointIds->GetId(verts[0]));
|
|
this->Quad->PointIds->SetId(1,this->PointIds->GetId(verts[1]));
|
|
this->Quad->PointIds->SetId(2,this->PointIds->GetId(verts[2]));
|
|
this->Quad->PointIds->SetId(3,this->PointIds->GetId(verts[3]));
|
|
|
|
// load coordinates
|
|
this->Quad->Points->SetPoint(0,this->Points->GetPoint(verts[0]));
|
|
this->Quad->Points->SetPoint(1,this->Points->GetPoint(verts[1]));
|
|
this->Quad->Points->SetPoint(2,this->Points->GetPoint(verts[2]));
|
|
this->Quad->Points->SetPoint(3,this->Points->GetPoint(verts[3]));
|
|
|
|
return this->Quad;
|
|
}
|
|
}
|
|
//----------------------------------------------------------------------------
|
|
//
|
|
// Intersect prism faces against line. Each prism face is a quadrilateral.
|
|
//
|
|
int vtkHexagonalPrism::IntersectWithLine(double p1[3], double p2[3], double tol,
|
|
double &t, double x[3], double pcoords[3],
|
|
int& subId)
|
|
{
|
|
int intersection=0;
|
|
double pt1[3], pt2[3], pt3[3], pt4[3], pt5[3], pt6[3];
|
|
double tTemp;
|
|
double pc[3], xTemp[3], dist2, weights[12];
|
|
int faceNum;
|
|
|
|
t = VTK_DOUBLE_MAX;
|
|
|
|
//first intersect the penta faces
|
|
for (faceNum=0; faceNum<2; faceNum++)
|
|
{
|
|
this->Points->GetPoint(faces[faceNum][0], pt1);
|
|
this->Points->GetPoint(faces[faceNum][1], pt2);
|
|
this->Points->GetPoint(faces[faceNum][2], pt3);
|
|
this->Points->GetPoint(faces[faceNum][3], pt4);
|
|
this->Points->GetPoint(faces[faceNum][4], pt5);
|
|
this->Points->GetPoint(faces[faceNum][5], pt6);
|
|
|
|
this->Polygon->Points->SetPoint(0,pt1);
|
|
this->Polygon->Points->SetPoint(1,pt2);
|
|
this->Polygon->Points->SetPoint(2,pt3);
|
|
this->Polygon->Points->SetPoint(3,pt4);
|
|
this->Polygon->Points->SetPoint(4,pt5);
|
|
this->Polygon->Points->SetPoint(5,pt6);
|
|
|
|
if ( this->Polygon->IntersectWithLine(p1, p2, tol, tTemp, xTemp,
|
|
pc, subId) )
|
|
{
|
|
intersection = 1;
|
|
if ( tTemp < t )
|
|
{
|
|
t = tTemp;
|
|
x[0] = xTemp[0]; x[1] = xTemp[1]; x[2] = xTemp[2];
|
|
switch (faceNum)
|
|
{
|
|
case 0:
|
|
pcoords[0] = pc[0]; pcoords[1] = pc[1]; pcoords[2] = 0.0;
|
|
break;
|
|
|
|
case 1:
|
|
pcoords[0] = pc[0]; pcoords[1] = pc[1]; pcoords[2] = 1.0;
|
|
break;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
//now intersect the quad faces
|
|
for (faceNum=2; faceNum<8; faceNum++)
|
|
{
|
|
this->Points->GetPoint(faces[faceNum][0], pt1);
|
|
this->Points->GetPoint(faces[faceNum][1], pt2);
|
|
this->Points->GetPoint(faces[faceNum][2], pt3);
|
|
this->Points->GetPoint(faces[faceNum][3], pt4);
|
|
|
|
this->Quad->Points->SetPoint(0,pt1);
|
|
this->Quad->Points->SetPoint(1,pt2);
|
|
this->Quad->Points->SetPoint(2,pt3);
|
|
this->Quad->Points->SetPoint(3,pt4);
|
|
|
|
if ( this->Quad->IntersectWithLine(p1, p2, tol, tTemp, xTemp, pc, subId) )
|
|
{
|
|
intersection = 1;
|
|
if ( tTemp < t )
|
|
{
|
|
t = tTemp;
|
|
x[0] = xTemp[0]; x[1] = xTemp[1]; x[2] = xTemp[2];
|
|
this->EvaluatePosition(x, xTemp, subId, pcoords, dist2, weights);
|
|
}
|
|
}
|
|
}
|
|
|
|
return intersection;
|
|
}
|
|
//----------------------------------------------------------------------------
|
|
int vtkHexagonalPrism::Triangulate(int vtkNotUsed(index), vtkIdList *ptIds, vtkPoints *pts)
|
|
{
|
|
ptIds->Reset();
|
|
pts->Reset();
|
|
|
|
for ( int i=0; i < 4; i++ )
|
|
{
|
|
ptIds->InsertId(i,this->PointIds->GetId(i));
|
|
pts->InsertPoint(i,this->Points->GetPoint(i));
|
|
}
|
|
|
|
return 1;
|
|
}
|
|
//----------------------------------------------------------------------------
|
|
//
|
|
// Compute derivatives in x-y-z directions. Use chain rule in combination
|
|
// with interpolation function derivatives.
|
|
//
|
|
void vtkHexagonalPrism::Derivatives(int vtkNotUsed(subId), double pcoords[3],
|
|
double *values, int dim, double *derivs)
|
|
{
|
|
double *jI[3], j0[3], j1[3], j2[3];
|
|
double functionDerivs[36], sum[3], value;
|
|
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 < 12; i++) //loop over interp. function derivatives
|
|
{
|
|
value = values[dim*i + k];
|
|
sum[0] += functionDerivs[i] * value;
|
|
sum[1] += functionDerivs[12 + i] * value;
|
|
sum[2] += functionDerivs[24 + i] * value;
|
|
}
|
|
|
|
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];
|
|
}
|
|
}
|
|
}
|
|
//----------------------------------------------------------------------------
|
|
// Given parametric coordinates compute inverse Jacobian transformation
|
|
// matrix. Returns 9 elements of 3x3 inverse Jacobian plus interpolation
|
|
// function derivatives.
|
|
void vtkHexagonalPrism::JacobianInverse(double pcoords[3], double **inverse,
|
|
double derivs[36])
|
|
{
|
|
int i, j;
|
|
double *m[3], m0[3], m1[3], m2[3];
|
|
double x[3];
|
|
|
|
// compute interpolation function derivatives
|
|
this->InterpolationDerivs(pcoords, derivs);
|
|
|
|
// create Jacobian matrix
|
|
m[0] = m0; m[1] = m1; m[2] = m2;
|
|
for (i=0; i < 3; i++) //initialize matrix
|
|
{
|
|
m0[i] = m1[i] = m2[i] = 0.0;
|
|
}
|
|
|
|
for ( j=0; j < 12; j++ )
|
|
{
|
|
this->Points->GetPoint(j, x);
|
|
for ( i=0; i < 3; i++ )
|
|
{
|
|
m0[i] += x[i] * derivs[j];
|
|
m1[i] += x[i] * derivs[12 + j];
|
|
m2[i] += x[i] * derivs[24 + j];
|
|
}
|
|
}
|
|
|
|
// now find the inverse
|
|
if ( vtkMath::InvertMatrix(m,inverse,3) == 0 )
|
|
{
|
|
vtkErrorMacro(<<"Jacobian inverse not found");
|
|
return;
|
|
}
|
|
}
|
|
|
|
//----------------------------------------------------------------------------
|
|
void vtkHexagonalPrism::GetEdgePoints(int edgeId, int* &pts)
|
|
{
|
|
pts = this->GetEdgeArray(edgeId);
|
|
}
|
|
|
|
//----------------------------------------------------------------------------
|
|
void vtkHexagonalPrism::GetFacePoints(int faceId, int* &pts)
|
|
{
|
|
pts = this->GetFaceArray(faceId);
|
|
}
|
|
|
|
static double vtkHexagonalPrismCellPCoords[36] = {
|
|
0.5, 0.0 , 0.0,
|
|
EXPRA, 0.25, 0.0,
|
|
EXPRA, 0.75, 0.0,
|
|
0.5, 1.0 , 0.0,
|
|
EXPRB, 0.75, 0.0,
|
|
EXPRB, 0.25, 0.0,
|
|
0.5, 0.0 , 1.0,
|
|
EXPRA, 0.25, 1.0,
|
|
EXPRA, 0.75, 1.0,
|
|
0.5, 1.0 , 1.0,
|
|
EXPRB, 0.75, 1.0,
|
|
EXPRB, 0.25, 1.0,
|
|
};
|
|
|
|
//----------------------------------------------------------------------------
|
|
double *vtkHexagonalPrism::GetParametricCoords()
|
|
{
|
|
return vtkHexagonalPrismCellPCoords;
|
|
}
|
|
|
|
//----------------------------------------------------------------------------
|
|
void vtkHexagonalPrism::PrintSelf(ostream& os, vtkIndent indent)
|
|
{
|
|
this->Superclass::PrintSelf(os,indent);
|
|
|
|
os << indent << "Line:\n";
|
|
this->Line->PrintSelf(os,indent.GetNextIndent());
|
|
os << indent << "Quad:\n";
|
|
this->Quad->PrintSelf(os,indent.GetNextIndent());
|
|
os << indent << "Polygon:\n";
|
|
this->Polygon->PrintSelf(os,indent.GetNextIndent());
|
|
}
|
|
|
|
|