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945 lines
28 KiB
945 lines
28 KiB
2 years ago
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/*=========================================================================
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Program: Visualization Toolkit
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Module: $RCSfile: vtkQuad.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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#include "vtkQuad.h"
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#include "vtkObjectFactory.h"
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#include "vtkCellArray.h"
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#include "vtkCellData.h"
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#include "vtkLine.h"
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#include "vtkTriangle.h"
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#include "vtkMath.h"
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#include "vtkPlane.h"
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#include "vtkPointData.h"
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#include "vtkPointLocator.h"
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#include "vtkPoints.h"
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vtkCxxRevisionMacro(vtkQuad, "$Revision: 1.3.12.1 $");
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vtkStandardNewMacro(vtkQuad);
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static const double VTK_DIVERGED = 1.e6;
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//----------------------------------------------------------------------------
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// Construct the quad with four points.
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vtkQuad::vtkQuad()
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{
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this->Points->SetNumberOfPoints(4);
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this->PointIds->SetNumberOfIds(4);
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for (int i = 0; i < 4; 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->Triangle = vtkTriangle::New();
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}
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//----------------------------------------------------------------------------
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vtkQuad::~vtkQuad()
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{
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this->Line->Delete();
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this->Triangle->Delete();
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}
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//----------------------------------------------------------------------------
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static const int VTK_QUAD_MAX_ITERATION=20;
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static const double VTK_QUAD_CONVERGED=1.e-04;
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inline static void ComputeNormal(vtkQuad *self, double pt1[3], double pt2[3],
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double pt3[3], double n[3])
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{
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vtkTriangle::ComputeNormal (pt1, pt2, pt3, n);
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// If first three points are co-linear, then use fourth point
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//
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double pt4[3];
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if ( n[0] == 0.0 && n[1] == 0.0 && n[2] == 0.0 )
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{
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self->Points->GetPoint(3,pt4);
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vtkTriangle::ComputeNormal (pt2, pt3, pt4, n);
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}
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}
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//----------------------------------------------------------------------------
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int vtkQuad::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 i, j;
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double pt1[3], pt2[3], pt3[3], pt[3], n[3];
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double det;
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double maxComponent;
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int idx=0, indices[2];
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int iteration, converged;
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double params[2];
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double fcol[2], rcol[2], scol[2], cp[3];
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double derivs[8];
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subId = 0;
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pcoords[0] = pcoords[1] = params[0] = params[1] = 0.5;
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// Get normal for quadrilateral
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//
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this->Points->GetPoint(0, pt1);
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this->Points->GetPoint(1, pt2);
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this->Points->GetPoint(2, pt3);
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ComputeNormal (this, pt1, pt2, pt3, n);
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// Project point to plane
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//
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vtkPlane::ProjectPoint(x,pt1,n,cp);
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// Construct matrices. Since we have over determined system, need to find
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// which 2 out of 3 equations to use to develop equations. (Any 2 should
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// work since we've projected point to plane.)
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//
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for (maxComponent=0.0, i=0; i<3; i++)
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{
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if (fabs(n[i]) > maxComponent)
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{
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maxComponent = fabs(n[i]);
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idx = i;
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}
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}
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for (j=0, i=0; i<3; i++)
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{
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if ( i != idx )
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{
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indices[j++] = i;
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}
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}
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// Use Newton's method to solve for parametric coordinates
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//
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for (iteration=converged=0; !converged
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&& (iteration < VTK_QUAD_MAX_ITERATION);
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iteration++)
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{
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// calculate element interpolation functions and derivatives
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//
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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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//
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for (i=0; i<2; i++)
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{
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fcol[i] = rcol[i] = scol[i] = 0.0;
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}
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for (i=0; i<4; i++)
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{
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this->Points->GetPoint(i, pt);
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for (j=0; j<2; j++)
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{
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fcol[j] += pt[indices[j]] * weights[i];
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rcol[j] += pt[indices[j]] * derivs[i];
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scol[j] += pt[indices[j]] * derivs[i+4];
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}
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}
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for (j=0; j<2; j++)
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{
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fcol[j] -= cp[indices[j]];
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}
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// compute determinants and generate improvements
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//
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if ( (det=vtkMath::Determinant2x2(rcol,scol)) == 0.0 )
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{
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return -1;
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}
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pcoords[0] = params[0] - vtkMath::Determinant2x2 (fcol,scol) / det;
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pcoords[1] = params[1] - vtkMath::Determinant2x2 (rcol,fcol) / det;
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// check for convergence
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//
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if ( ((fabs(pcoords[0]-params[0])) < VTK_QUAD_CONVERGED) &&
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((fabs(pcoords[1]-params[1])) < VTK_QUAD_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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{
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return -1;
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}
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// if not converged, repeat
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//
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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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}
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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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//
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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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{
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if (closestPoint)
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{
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dist2 =
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vtkMath::Distance2BetweenPoints(cp,x); //projection distance
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closestPoint[0] = cp[0];
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closestPoint[1] = cp[1];
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closestPoint[2] = cp[2];
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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 t;
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double pt4[3];
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if (closestPoint)
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{
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this->Points->GetPoint(3, pt4);
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if ( pcoords[0] < 0.0 && pcoords[1] < 0.0 )
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{
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dist2 = vtkMath::Distance2BetweenPoints(x,pt1);
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for (i=0; i<3; i++)
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{
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closestPoint[i] = pt1[i];
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}
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}
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else if ( pcoords[0] > 1.0 && pcoords[1] < 0.0 )
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{
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dist2 = vtkMath::Distance2BetweenPoints(x,pt2);
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for (i=0; i<3; i++)
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{
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closestPoint[i] = pt2[i];
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}
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}
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else if ( pcoords[0] > 1.0 && pcoords[1] > 1.0 )
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{
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dist2 = vtkMath::Distance2BetweenPoints(x,pt3);
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for (i=0; i<3; i++)
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{
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closestPoint[i] = pt3[i];
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}
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}
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else if ( pcoords[0] < 0.0 && pcoords[1] > 1.0 )
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{
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dist2 = vtkMath::Distance2BetweenPoints(x,pt4);
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for (i=0; i<3; i++)
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{
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closestPoint[i] = pt4[i];
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}
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}
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else if ( pcoords[0] < 0.0 )
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{
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dist2 = vtkLine::DistanceToLine(x,pt1,pt4,t,closestPoint);
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}
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else if ( pcoords[0] > 1.0 )
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{
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dist2 = vtkLine::DistanceToLine(x,pt2,pt3,t,closestPoint);
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}
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else if ( pcoords[1] < 0.0 )
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{
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dist2 = vtkLine::DistanceToLine(x,pt1,pt2,t,closestPoint);
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}
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else if ( pcoords[1] > 1.0 )
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{
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dist2 = vtkLine::DistanceToLine(x,pt3,pt4,t,closestPoint);
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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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//----------------------------------------------------------------------------
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void vtkQuad::EvaluateLocation(int& vtkNotUsed(subId), 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<4; 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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// Compute iso-parametric interpolation functions
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//
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void vtkQuad::InterpolationFunctions(double pcoords[3], double sf[4])
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{
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double rm, sm;
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rm = 1. - pcoords[0];
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sm = 1. - pcoords[1];
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sf[0] = rm * sm;
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sf[1] = pcoords[0] * sm;
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sf[2] = pcoords[0] * pcoords[1];
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sf[3] = rm * pcoords[1];
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}
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//----------------------------------------------------------------------------
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void vtkQuad::InterpolationDerivs(double pcoords[3], double derivs[8])
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{
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double rm, sm;
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rm = 1. - pcoords[0];
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sm = 1. - pcoords[1];
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derivs[0] = -sm;
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derivs[1] = sm;
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derivs[2] = pcoords[1];
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derivs[3] = -pcoords[1];
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derivs[4] = -rm;
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derivs[5] = -pcoords[0];
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derivs[6] = pcoords[0];
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derivs[7] = rm;
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}
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//----------------------------------------------------------------------------
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int vtkQuad::CellBoundary(int vtkNotUsed(subId), double pcoords[3],
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vtkIdList *pts)
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{
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double t1=pcoords[0]-pcoords[1];
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double t2=1.0-pcoords[0]-pcoords[1];
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pts->SetNumberOfIds(2);
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// compare against two lines in parametric space that divide element
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// into four pieces.
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if ( t1 >= 0.0 && t2 >= 0.0 )
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{
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pts->SetId(0,this->PointIds->GetId(0));
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pts->SetId(1,this->PointIds->GetId(1));
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}
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else if ( t1 >= 0.0 && t2 < 0.0 )
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{
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pts->SetId(0,this->PointIds->GetId(1));
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pts->SetId(1,this->PointIds->GetId(2));
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}
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else if ( t1 < 0.0 && t2 < 0.0 )
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{
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pts->SetId(0,this->PointIds->GetId(2));
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pts->SetId(1,this->PointIds->GetId(3));
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}
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else //( t1 < 0.0 && t2 >= 0.0 )
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{
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pts->SetId(0,this->PointIds->GetId(3));
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pts->SetId(1,this->PointIds->GetId(0));
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}
|
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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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{
|
||
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return 0;
|
||
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}
|
||
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else
|
||
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{
|
||
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return 1;
|
||
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}
|
||
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}
|
||
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|
||
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//----------------------------------------------------------------------------
|
||
|
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// Marching (convex) quadrilaterals
|
||
|
|
//
|
||
|
|
static int edges[4][2] = { {0,1}, {1,2}, {3,2}, {0,3} };
|
||
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|
||
|
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typedef int EDGE_LIST;
|
||
|
|
typedef struct {
|
||
|
|
EDGE_LIST edges[5];
|
||
|
|
} LINE_CASES;
|
||
|
|
|
||
|
|
static LINE_CASES lineCases[] = {
|
||
|
|
{{-1, -1, -1, -1, -1}},
|
||
|
|
{{0, 3, -1, -1, -1}},
|
||
|
|
{{1, 0, -1, -1, -1}},
|
||
|
|
{{1, 3, -1, -1, -1}},
|
||
|
|
{{2, 1, -1, -1, -1}},
|
||
|
|
{{0, 3, 2, 1, -1}},
|
||
|
|
{{2, 0, -1, -1, -1}},
|
||
|
|
{{2, 3, -1, -1, -1}},
|
||
|
|
{{3, 2, -1, -1, -1}},
|
||
|
|
{{0, 2, -1, -1, -1}},
|
||
|
|
{{1, 0, 3, 2, -1}},
|
||
|
|
{{1, 2, -1, -1, -1}},
|
||
|
|
{{3, 1, -1, -1, -1}},
|
||
|
|
{{0, 1, -1, -1, -1}},
|
||
|
|
{{3, 0, -1, -1, -1}},
|
||
|
|
{{-1, -1, -1, -1, -1}}
|
||
|
|
};
|
||
|
|
|
||
|
|
//----------------------------------------------------------------------------
|
||
|
|
void vtkQuad::Contour(double value, vtkDataArray *cellScalars,
|
||
|
|
vtkPointLocator *locator,
|
||
|
|
vtkCellArray *verts,
|
||
|
|
vtkCellArray *lines,
|
||
|
|
vtkCellArray *vtkNotUsed(polys),
|
||
|
|
vtkPointData *inPd, vtkPointData *outPd,
|
||
|
|
vtkCellData *inCd, vtkIdType cellId, vtkCellData *outCd)
|
||
|
|
{
|
||
|
|
static int CASE_MASK[4] = {1,2,4,8};
|
||
|
|
LINE_CASES *lineCase;
|
||
|
|
EDGE_LIST *edge;
|
||
|
|
int i, j, index, *vert;
|
||
|
|
int newCellId;
|
||
|
|
vtkIdType pts[2];
|
||
|
|
int e1, e2;
|
||
|
|
double t, x1[3], x2[3], x[3], deltaScalar;
|
||
|
|
vtkIdType offset = verts->GetNumberOfCells();
|
||
|
|
|
||
|
|
// Build the case table
|
||
|
|
for ( i=0, index = 0; i < 4; i++)
|
||
|
|
{
|
||
|
|
if (cellScalars->GetComponent(i,0) >= value)
|
||
|
|
{
|
||
|
|
index |= CASE_MASK[i];
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
lineCase = lineCases + index;
|
||
|
|
edge = lineCase->edges;
|
||
|
|
|
||
|
|
for ( ; edge[0] > -1; edge += 2 )
|
||
|
|
{
|
||
|
|
for (i=0; i<2; i++) // insert line
|
||
|
|
{
|
||
|
|
vert = edges[edge[i]];
|
||
|
|
// calculate a preferred interpolation direction
|
||
|
|
deltaScalar = (cellScalars->GetComponent(vert[1],0)
|
||
|
|
- cellScalars->GetComponent(vert[0],0));
|
||
|
|
if (deltaScalar > 0)
|
||
|
|
{
|
||
|
|
e1 = vert[0]; e2 = vert[1];
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
e1 = vert[1]; e2 = vert[0];
|
||
|
|
deltaScalar = -deltaScalar;
|
||
|
|
}
|
||
|
|
|
||
|
|
// linear interpolation
|
||
|
|
if (deltaScalar == 0.0)
|
||
|
|
{
|
||
|
|
t = 0.0;
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
t = (value - cellScalars->GetComponent(e1,0)) / deltaScalar;
|
||
|
|
}
|
||
|
|
|
||
|
|
this->Points->GetPoint(e1, x1);
|
||
|
|
this->Points->GetPoint(e2, x2);
|
||
|
|
|
||
|
|
for (j=0; j<3; j++)
|
||
|
|
{
|
||
|
|
x[j] = x1[j] + t * (x2[j] - x1[j]);
|
||
|
|
}
|
||
|
|
if ( locator->InsertUniquePoint(x, pts[i]) )
|
||
|
|
{
|
||
|
|
if ( outPd )
|
||
|
|
{
|
||
|
|
vtkIdType p1 = this->PointIds->GetId(e1);
|
||
|
|
vtkIdType p2 = this->PointIds->GetId(e2);
|
||
|
|
outPd->InterpolateEdge(inPd,pts[i],p1,p2,t);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
// check for degenerate line
|
||
|
|
if ( pts[0] != pts[1] )
|
||
|
|
{
|
||
|
|
newCellId = offset + lines->InsertNextCell(2,pts);
|
||
|
|
outCd->CopyData(inCd,cellId,newCellId);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
//----------------------------------------------------------------------------
|
||
|
|
vtkCell *vtkQuad::GetEdge(int edgeId)
|
||
|
|
{
|
||
|
|
int edgeIdPlus1 = edgeId + 1;
|
||
|
|
|
||
|
|
if (edgeIdPlus1 > 3)
|
||
|
|
{
|
||
|
|
edgeIdPlus1 = 0;
|
||
|
|
}
|
||
|
|
|
||
|
|
// load point id's
|
||
|
|
this->Line->PointIds->SetId(0,this->PointIds->GetId(edgeId));
|
||
|
|
this->Line->PointIds->SetId(1,this->PointIds->GetId(edgeIdPlus1));
|
||
|
|
|
||
|
|
// load coordinates
|
||
|
|
this->Line->Points->SetPoint(0,this->Points->GetPoint(edgeId));
|
||
|
|
this->Line->Points->SetPoint(1,this->Points->GetPoint(edgeIdPlus1));
|
||
|
|
|
||
|
|
return this->Line;
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
//----------------------------------------------------------------------------
|
||
|
|
// Intersect plane; see whether point is in quadrilateral. This code
|
||
|
|
// splits the quad into two triangles and intersects them (because the
|
||
|
|
// quad may be non-planar).
|
||
|
|
//
|
||
|
|
int vtkQuad::IntersectWithLine(double p1[3], double p2[3], double tol, double& t,
|
||
|
|
double x[3], double pcoords[3], int& subId)
|
||
|
|
{
|
||
|
|
int diagonalCase;
|
||
|
|
double d1 = vtkMath::Distance2BetweenPoints(this->Points->GetPoint(0),
|
||
|
|
this->Points->GetPoint(2));
|
||
|
|
double d2 = vtkMath::Distance2BetweenPoints(this->Points->GetPoint(1),
|
||
|
|
this->Points->GetPoint(3));
|
||
|
|
subId = 0;
|
||
|
|
|
||
|
|
// Figure out how to uniquely tessellate the quad. Watch out for
|
||
|
|
// equivalent triangulations (i.e., the triangulation is equivalent
|
||
|
|
// no matter where the diagonal). In this case use the point ids as
|
||
|
|
// a tie breaker to insure unique triangulation across the quad.
|
||
|
|
//
|
||
|
|
if ( d1 == d2 ) //rare case; discriminate based on point id
|
||
|
|
{
|
||
|
|
int i, id, maxId=0, maxIdx=0;
|
||
|
|
for (i=0; i<4; i++) //find the maximum id
|
||
|
|
{
|
||
|
|
if ( (id=this->PointIds->GetId(i)) > maxId )
|
||
|
|
{
|
||
|
|
maxId = id;
|
||
|
|
maxIdx = i;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
if ( maxIdx == 0 || maxIdx == 2) diagonalCase = 0;
|
||
|
|
else diagonalCase = 1;
|
||
|
|
}
|
||
|
|
else if ( d1 < d2 )
|
||
|
|
{
|
||
|
|
diagonalCase = 0;
|
||
|
|
}
|
||
|
|
else //d2 < d1
|
||
|
|
{
|
||
|
|
diagonalCase = 1;
|
||
|
|
}
|
||
|
|
|
||
|
|
// Note: in the following code the parametric coords must be adjusted to
|
||
|
|
// reflect the use of the triangle parametric coordinate system.
|
||
|
|
switch (diagonalCase)
|
||
|
|
{
|
||
|
|
case 0:
|
||
|
|
this->Triangle->Points->SetPoint(0,this->Points->GetPoint(0));
|
||
|
|
this->Triangle->Points->SetPoint(1,this->Points->GetPoint(1));
|
||
|
|
this->Triangle->Points->SetPoint(2,this->Points->GetPoint(2));
|
||
|
|
if (this->Triangle->IntersectWithLine(p1, p2, tol, t, x, pcoords, subId) )
|
||
|
|
{
|
||
|
|
pcoords[0] = pcoords[0] + pcoords[1];
|
||
|
|
return 1;
|
||
|
|
}
|
||
|
|
this->Triangle->Points->SetPoint(0,this->Points->GetPoint(2));
|
||
|
|
this->Triangle->Points->SetPoint(1,this->Points->GetPoint(3));
|
||
|
|
this->Triangle->Points->SetPoint(2,this->Points->GetPoint(0));
|
||
|
|
if (this->Triangle->IntersectWithLine(p1, p2, tol, t, x, pcoords, subId) )
|
||
|
|
{
|
||
|
|
pcoords[0] = 1.0 - (pcoords[0]+pcoords[1]);
|
||
|
|
pcoords[1] = 1.0 - pcoords[1];
|
||
|
|
return 1;
|
||
|
|
}
|
||
|
|
return 0;
|
||
|
|
|
||
|
|
case 1:
|
||
|
|
this->Triangle->Points->SetPoint(0,this->Points->GetPoint(0));
|
||
|
|
this->Triangle->Points->SetPoint(1,this->Points->GetPoint(1));
|
||
|
|
this->Triangle->Points->SetPoint(2,this->Points->GetPoint(3));
|
||
|
|
if (this->Triangle->IntersectWithLine(p1, p2, tol, t, x, pcoords, subId) )
|
||
|
|
{
|
||
|
|
return 1;
|
||
|
|
}
|
||
|
|
this->Triangle->Points->SetPoint(0,this->Points->GetPoint(2));
|
||
|
|
this->Triangle->Points->SetPoint(1,this->Points->GetPoint(3));
|
||
|
|
this->Triangle->Points->SetPoint(2,this->Points->GetPoint(1));
|
||
|
|
if (this->Triangle->IntersectWithLine(p1, p2, tol, t, x, pcoords, subId) )
|
||
|
|
{
|
||
|
|
pcoords[0] = 1.0 - pcoords[0];
|
||
|
|
pcoords[1] = 1.0 - pcoords[1];
|
||
|
|
return 1;
|
||
|
|
}
|
||
|
|
|
||
|
|
return 0;
|
||
|
|
}
|
||
|
|
|
||
|
|
return 0;
|
||
|
|
}
|
||
|
|
|
||
|
|
//----------------------------------------------------------------------------
|
||
|
|
int vtkQuad::Triangulate(int vtkNotUsed(index), vtkIdList *ptIds,
|
||
|
|
vtkPoints *pts)
|
||
|
|
{
|
||
|
|
double d1, d2;
|
||
|
|
|
||
|
|
pts->Reset();
|
||
|
|
ptIds->Reset();
|
||
|
|
|
||
|
|
// use minimum diagonal (Delaunay triangles) - assumed convex
|
||
|
|
d1 = vtkMath::Distance2BetweenPoints(this->Points->GetPoint(0),
|
||
|
|
this->Points->GetPoint(2));
|
||
|
|
d2 = vtkMath::Distance2BetweenPoints(this->Points->GetPoint(1),
|
||
|
|
this->Points->GetPoint(3));
|
||
|
|
|
||
|
|
if ( d1 <= d2 )
|
||
|
|
{
|
||
|
|
ptIds->InsertId(0,this->PointIds->GetId(0));
|
||
|
|
pts->InsertPoint(0,this->Points->GetPoint(0));
|
||
|
|
ptIds->InsertId(1,this->PointIds->GetId(1));
|
||
|
|
pts->InsertPoint(1,this->Points->GetPoint(1));
|
||
|
|
ptIds->InsertId(2,this->PointIds->GetId(2));
|
||
|
|
pts->InsertPoint(2,this->Points->GetPoint(2));
|
||
|
|
|
||
|
|
ptIds->InsertId(3,this->PointIds->GetId(0));
|
||
|
|
pts->InsertPoint(3,this->Points->GetPoint(0));
|
||
|
|
ptIds->InsertId(4,this->PointIds->GetId(2));
|
||
|
|
pts->InsertPoint(4,this->Points->GetPoint(2));
|
||
|
|
ptIds->InsertId(5,this->PointIds->GetId(3));
|
||
|
|
pts->InsertPoint(5,this->Points->GetPoint(3));
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
ptIds->InsertId(0,this->PointIds->GetId(0));
|
||
|
|
pts->InsertPoint(0,this->Points->GetPoint(0));
|
||
|
|
ptIds->InsertId(1,this->PointIds->GetId(1));
|
||
|
|
pts->InsertPoint(1,this->Points->GetPoint(1));
|
||
|
|
ptIds->InsertId(2,this->PointIds->GetId(3));
|
||
|
|
pts->InsertPoint(2,this->Points->GetPoint(3));
|
||
|
|
|
||
|
|
ptIds->InsertId(3,this->PointIds->GetId(1));
|
||
|
|
pts->InsertPoint(3,this->Points->GetPoint(1));
|
||
|
|
ptIds->InsertId(4,this->PointIds->GetId(2));
|
||
|
|
pts->InsertPoint(4,this->Points->GetPoint(2));
|
||
|
|
ptIds->InsertId(5,this->PointIds->GetId(3));
|
||
|
|
pts->InsertPoint(5,this->Points->GetPoint(3));
|
||
|
|
}
|
||
|
|
|
||
|
|
return 1;
|
||
|
|
}
|
||
|
|
|
||
|
|
//----------------------------------------------------------------------------
|
||
|
|
void vtkQuad::Derivatives(int vtkNotUsed(subId), double pcoords[3],
|
||
|
|
double *values, int dim, double *derivs)
|
||
|
|
{
|
||
|
|
double v0[2], v1[2], v2[2], v3[2], v10[3], v20[3], lenX;
|
||
|
|
double x0[3], x1[3], x2[3], x3[3], n[3], vec20[3], vec30[3];
|
||
|
|
double *J[2], J0[2], J1[2];
|
||
|
|
double *JI[2], JI0[2], JI1[2];
|
||
|
|
double funcDerivs[8], sum[2], dBydx, dBydy;
|
||
|
|
int i, j;
|
||
|
|
|
||
|
|
// Project points of quad into 2D system
|
||
|
|
this->Points->GetPoint(0, x0);
|
||
|
|
this->Points->GetPoint(1, x1);
|
||
|
|
this->Points->GetPoint(2, x2);
|
||
|
|
ComputeNormal (this,x0, x1, x2, n);
|
||
|
|
this->Points->GetPoint(3, x3);
|
||
|
|
|
||
|
|
for (i=0; i < 3; i++)
|
||
|
|
{
|
||
|
|
v10[i] = x1[i] - x0[i];
|
||
|
|
vec20[i] = x2[i] - x0[i];
|
||
|
|
vec30[i] = x3[i] - x0[i];
|
||
|
|
}
|
||
|
|
|
||
|
|
vtkMath::Cross(n,v10,v20); //creates local y' axis
|
||
|
|
|
||
|
|
if ( (lenX=vtkMath::Normalize(v10)) <= 0.0
|
||
|
|
|| vtkMath::Normalize(v20) <= 0.0 ) //degenerate
|
||
|
|
{
|
||
|
|
for ( j=0; j < dim; j++ )
|
||
|
|
{
|
||
|
|
for ( i=0; i < 3; i++ )
|
||
|
|
{
|
||
|
|
derivs[j*dim + i] = 0.0;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
return;
|
||
|
|
}
|
||
|
|
|
||
|
|
v0[0] = v0[1] = 0.0; //convert points to 2D (i.e., local system)
|
||
|
|
v1[0] = lenX; v1[1] = 0.0;
|
||
|
|
v2[0] = vtkMath::Dot(vec20,v10);
|
||
|
|
v2[1] = vtkMath::Dot(vec20,v20);
|
||
|
|
v3[0] = vtkMath::Dot(vec30,v10);
|
||
|
|
v3[1] = vtkMath::Dot(vec30,v20);
|
||
|
|
|
||
|
|
this->InterpolationDerivs(pcoords, funcDerivs);
|
||
|
|
|
||
|
|
// Compute Jacobian and inverse Jacobian
|
||
|
|
J[0] = J0; J[1] = J1;
|
||
|
|
JI[0] = JI0; JI[1] = JI1;
|
||
|
|
|
||
|
|
J[0][0] = v0[0]*funcDerivs[0] + v1[0]*funcDerivs[1] +
|
||
|
|
v2[0]*funcDerivs[2] + v3[0]*funcDerivs[3];
|
||
|
|
J[0][1] = v0[1]*funcDerivs[0] + v1[1]*funcDerivs[1] +
|
||
|
|
v2[1]*funcDerivs[2] + v3[1]*funcDerivs[3];
|
||
|
|
J[1][0] = v0[0]*funcDerivs[4] + v1[0]*funcDerivs[5] +
|
||
|
|
v2[0]*funcDerivs[6] + v3[0]*funcDerivs[7];
|
||
|
|
J[1][1] = v0[1]*funcDerivs[4] + v1[1]*funcDerivs[5] +
|
||
|
|
v2[1]*funcDerivs[6] + v3[1]*funcDerivs[7];
|
||
|
|
|
||
|
|
// Compute inverse Jacobian, return if Jacobian is singular
|
||
|
|
if (!vtkMath::InvertMatrix(J,JI,2))
|
||
|
|
{
|
||
|
|
for ( j=0; j < dim; j++ )
|
||
|
|
{
|
||
|
|
for ( 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 ( j=0; j < dim; j++ )
|
||
|
|
{
|
||
|
|
sum[0] = sum[1] = 0.0;
|
||
|
|
for ( i=0; i < 4; i++) //loop over interp. function derivatives
|
||
|
|
{
|
||
|
|
sum[0] += funcDerivs[i] * values[dim*i + j];
|
||
|
|
sum[1] += funcDerivs[4 + 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] = dBydx * v10[0] + dBydy * v20[0];
|
||
|
|
derivs[3*j + 1] = dBydx * v10[1] + dBydy * v20[1];
|
||
|
|
derivs[3*j + 2] = dBydx * v10[2] + dBydy * v20[2];
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
//----------------------------------------------------------------------------
|
||
|
|
// support quad clipping
|
||
|
|
typedef int QUAD_EDGE_LIST;
|
||
|
|
typedef struct {
|
||
|
|
QUAD_EDGE_LIST edges[14];
|
||
|
|
} QUAD_CASES;
|
||
|
|
|
||
|
|
static QUAD_CASES quadCases[] = {
|
||
|
|
{{ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 0
|
||
|
|
{{ 3, 100, 0, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 1
|
||
|
|
{{ 3, 101, 1, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 2
|
||
|
|
{{ 4, 100, 101, 1, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 3
|
||
|
|
{{ 3, 102, 2, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 4
|
||
|
|
{{ 3, 100, 0, 3, 3, 102, 2, 1, 4, 0, 1, 2, 3, -1}}, // 5
|
||
|
|
{{ 4, 101, 102, 2, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 6
|
||
|
|
{{ 3, 100, 101, 3, 3, 101, 2, 3, 3, 101, 102, 2, -1, -1}}, // 7
|
||
|
|
{{ 3, 103, 3, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 8
|
||
|
|
{{ 4, 100, 0, 2, 103, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 9
|
||
|
|
{{ 3, 101, 1, 0, 3, 103, 3, 2, 4, 0, 1, 2, 3, -1}}, // 10
|
||
|
|
{{ 3, 100, 101, 1, 3, 100, 1, 2, 3, 100, 2, 103, -1, -1}}, // 11
|
||
|
|
{{ 4, 102, 103, 3, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 12
|
||
|
|
{{ 3, 100, 0, 103, 3, 0, 1, 103, 3, 1, 102, 103, -1, -1}}, // 13
|
||
|
|
{{ 3, 0, 101, 102, 3, 0, 102, 3, 3, 102, 103, 3, -1, -1}}, // 14
|
||
|
|
{{ 4, 100, 101, 102, 103, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 15
|
||
|
|
};
|
||
|
|
|
||
|
|
static QUAD_CASES quadCasesComplement[] = {
|
||
|
|
{{ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 0
|
||
|
|
{{ 3, 100, 0, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 1
|
||
|
|
{{ 3, 101, 1, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 2
|
||
|
|
{{ 4, 100, 101, 1, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 3
|
||
|
|
{{ 3, 102, 2, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 4
|
||
|
|
{{ 3, 100, 0, 3, 3, 102, 2, 1, -1, -1, -1, -1, -1, -1}}, // 5
|
||
|
|
{{ 4, 101, 102, 2, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 6
|
||
|
|
{{ 3, 100, 101, 3, 3, 101, 2, 3, 3, 101, 102, 2, -1, -1}}, // 7
|
||
|
|
{{ 3, 103, 3, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 8
|
||
|
|
{{ 4, 100, 0, 2, 103, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 9
|
||
|
|
{{ 3, 101, 1, 0, 3, 103, 3, 2, -1, -1, -1, -1, -1, -1}}, // 10
|
||
|
|
{{ 3, 100, 101, 1, 3, 100, 1, 2, 3, 100, 2, 103, -1, -1}}, // 11
|
||
|
|
{{ 4, 102, 103, 3, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 12
|
||
|
|
{{ 3, 100, 0, 103, 3, 0, 1, 103, 3, 1, 102, 103, -1, -1}}, // 13
|
||
|
|
{{ 3, 0, 101, 102, 3, 0, 102, 3, 3, 102, 103, 3, -1, -1}}, // 14
|
||
|
|
{{ 4, 100, 101, 102, 103, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 15
|
||
|
|
};
|
||
|
|
|
||
|
|
//----------------------------------------------------------------------------
|
||
|
|
// Clip this quad using scalar value provided. Like contouring, except
|
||
|
|
// that it cuts the quad to produce other quads and/or triangles.
|
||
|
|
void vtkQuad::Clip(double value, vtkDataArray *cellScalars,
|
||
|
|
vtkPointLocator *locator, vtkCellArray *polys,
|
||
|
|
vtkPointData *inPd, vtkPointData *outPd,
|
||
|
|
vtkCellData *inCd, vtkIdType cellId, vtkCellData *outCd,
|
||
|
|
int insideOut)
|
||
|
|
{
|
||
|
|
static int CASE_MASK[4] = {1,2,4,8};
|
||
|
|
QUAD_CASES *quadCase;
|
||
|
|
QUAD_EDGE_LIST *edge;
|
||
|
|
int i, j, index, *vert;
|
||
|
|
int e1, e2;
|
||
|
|
int newCellId;
|
||
|
|
vtkIdType pts[4];
|
||
|
|
int vertexId;
|
||
|
|
double t, x1[3], x2[3], x[3], deltaScalar;
|
||
|
|
double scalar0, scalar1, e1Scalar;
|
||
|
|
|
||
|
|
// Build the index into the case table
|
||
|
|
if ( insideOut )
|
||
|
|
{
|
||
|
|
for ( i=0, index = 0; i < 4; i++)
|
||
|
|
{
|
||
|
|
if (cellScalars->GetComponent(i,0) <= value)
|
||
|
|
{
|
||
|
|
index |= CASE_MASK[i];
|
||
|
|
}
|
||
|
|
}
|
||
|
|
// Select case based on the index and get the list of edges for this case
|
||
|
|
quadCase = quadCases + index;
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
for ( i=0, index = 0; i < 4; i++)
|
||
|
|
{
|
||
|
|
if (cellScalars->GetComponent(i,0) > value)
|
||
|
|
{
|
||
|
|
index |= CASE_MASK[i];
|
||
|
|
}
|
||
|
|
}
|
||
|
|
// Select case based on the index and get the list of edges for this case
|
||
|
|
quadCase = quadCasesComplement + index;
|
||
|
|
}
|
||
|
|
|
||
|
|
edge = quadCase->edges;
|
||
|
|
|
||
|
|
// generate each quad
|
||
|
|
for ( ; edge[0] > -1; edge += edge[0]+1 )
|
||
|
|
{
|
||
|
|
for (i=0; i < edge[0]; i++) // insert quad or triangle
|
||
|
|
{
|
||
|
|
// vertex exists, and need not be interpolated
|
||
|
|
if (edge[i+1] >= 100)
|
||
|
|
{
|
||
|
|
vertexId = edge[i+1] - 100;
|
||
|
|
this->Points->GetPoint(vertexId, x);
|
||
|
|
if ( locator->InsertUniquePoint(x, pts[i]) )
|
||
|
|
{
|
||
|
|
outPd->CopyData(inPd,this->PointIds->GetId(vertexId),pts[i]);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
else //new vertex, interpolate
|
||
|
|
{
|
||
|
|
vert = edges[edge[i+1]];
|
||
|
|
|
||
|
|
// calculate a preferred interpolation direction
|
||
|
|
scalar0 = cellScalars->GetComponent(vert[0],0);
|
||
|
|
scalar1 = cellScalars->GetComponent(vert[1],0);
|
||
|
|
deltaScalar = scalar1 - scalar0;
|
||
|
|
|
||
|
|
if (deltaScalar > 0)
|
||
|
|
{
|
||
|
|
e1 = vert[0]; e2 = vert[1];
|
||
|
|
e1Scalar = scalar0;
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
e1 = vert[1]; e2 = vert[0];
|
||
|
|
e1Scalar = scalar1;
|
||
|
|
deltaScalar = -deltaScalar;
|
||
|
|
}
|
||
|
|
|
||
|
|
// linear interpolation
|
||
|
|
if (deltaScalar == 0.0)
|
||
|
|
{
|
||
|
|
t = 0.0;
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
t = (value - e1Scalar) / deltaScalar;
|
||
|
|
}
|
||
|
|
|
||
|
|
this->Points->GetPoint(e1, x1);
|
||
|
|
this->Points->GetPoint(e2, x2);
|
||
|
|
|
||
|
|
for (j=0; j<3; j++)
|
||
|
|
{
|
||
|
|
x[j] = x1[j] + t * (x2[j] - x1[j]);
|
||
|
|
}
|
||
|
|
|
||
|
|
if ( locator->InsertUniquePoint(x, pts[i]) )
|
||
|
|
{
|
||
|
|
vtkIdType p1 = this->PointIds->GetId(e1);
|
||
|
|
vtkIdType p2 = this->PointIds->GetId(e2);
|
||
|
|
outPd->InterpolateEdge(inPd,pts[i],p1,p2,t);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
// check for degenerate output
|
||
|
|
if ( edge[0] == 3 ) //i.e., a triangle
|
||
|
|
{
|
||
|
|
if (pts[0] == pts[1] || pts[0] == pts[2] || pts[1] == pts[2] )
|
||
|
|
{
|
||
|
|
continue;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
else // a quad
|
||
|
|
{
|
||
|
|
if ((pts[0] == pts[3] && pts[1] == pts[2]) ||
|
||
|
|
(pts[0] == pts[1] && pts[3] == pts[2]) )
|
||
|
|
{
|
||
|
|
continue;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
newCellId = polys->InsertNextCell(edge[0],pts);
|
||
|
|
outCd->CopyData(inCd,cellId,newCellId);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
//----------------------------------------------------------------------------
|
||
|
|
static double vtkQuadCellPCoords[12] = {0.0,0.0,0.0, 1.0,0.0,0.0,
|
||
|
|
1.0,1.0,0.0, 0.0,1.0,0.0};
|
||
|
|
double *vtkQuad::GetParametricCoords()
|
||
|
|
{
|
||
|
|
return vtkQuadCellPCoords;
|
||
|
|
}
|
||
|
|
|
||
|
|
//----------------------------------------------------------------------------
|
||
|
|
void vtkQuad::PrintSelf(ostream& os, vtkIndent indent)
|
||
|
|
{
|
||
|
|
this->Superclass::PrintSelf(os,indent);
|
||
|
|
|
||
|
|
os << indent << "Line:\n";
|
||
|
|
this->Line->PrintSelf(os,indent.GetNextIndent());
|
||
|
|
os << indent << "Triangle:\n";
|
||
|
|
this->Triangle->PrintSelf(os,indent.GetNextIndent());
|
||
|
|
}
|