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491 lines
14 KiB
C++
491 lines
14 KiB
C++
/*=========================================================================
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Program: Visualization Toolkit
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Module: vtkCubicLine.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 "vtkCubicLine.h"
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#include "vtkNonLinearCell.h"
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#include "vtkCellArray.h"
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#include "vtkCellData.h"
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#include "vtkCell.h"
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#include "vtkMath.h"
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#include "vtkObjectFactory.h"
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#include "vtkIncrementalPointLocator.h"
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#include "vtkLine.h"
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#include "vtkDoubleArray.h"
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#include "vtkPoints.h"
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#include "vtkPointData.h"
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vtkStandardNewMacro(vtkCubicLine);
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//----------------------------------------------------------------------------
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// Construct the line with four points.
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vtkCubicLine::vtkCubicLine()
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{
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this->Scalars = vtkDoubleArray::New();
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this->Scalars->SetNumberOfTuples(4);
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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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}
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//----------------------------------------------------------------------------
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// Delete the Line
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vtkCubicLine::~vtkCubicLine()
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{
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this->Line->Delete();
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this->Scalars->Delete();
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}
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//----------------------------------------------------------------------------
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int vtkCubicLine::EvaluatePosition(double x[3], 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 closest[3];
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double pc[3], dist2;
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int ignoreId, i, returnStatus, status;
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double lineWeights[2];
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pcoords[1] = pcoords[2] = 0.0;
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returnStatus = -1;
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weights[0] = 0.0;
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for (minDist2=VTK_DOUBLE_MAX,i=0; i < 3; i++)
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{
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if ( i == 0)
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{
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this->Line->Points->SetPoint(0,this->Points->GetPoint(0));
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this->Line->Points->SetPoint(1,this->Points->GetPoint(2));
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}
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else if (i == 1)
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{
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this->Line->Points->SetPoint(0,this->Points->GetPoint(2));
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this->Line->Points->SetPoint(1,this->Points->GetPoint(3));
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}
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else
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{
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this->Line->Points->SetPoint(0,this->Points->GetPoint(3));
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this->Line->Points->SetPoint(1,this->Points->GetPoint(1));
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}
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status = this->Line->EvaluatePosition(x,closest,ignoreId,pc,
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dist2,lineWeights);
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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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}
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}
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// adjust parametric coordinate
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if ( returnStatus != -1 )
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{
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if ( subId == 0 ) //first part : -1 <= pcoords <= -1/3
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{
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pcoords[0] = pcoords[0]*(2.0/3.0) - 1;
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}
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else if ( subId == 1 ) //second part : -1/3 <= pcoords <= 1/3
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{
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pcoords[0] = pcoords[0]*(2.0/3.0) -(1.0/3.0) ;
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}
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else // third part : 1/3 <= pcoords <= 1
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{
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pcoords[0] = pcoords[0]*(2.0/3.0) + (1.0/3.0);
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}
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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 weights 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 vtkCubicLine::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;
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double a0[3], a1[3], a2[3], a3[3];
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this->Points->GetPoint(0, a0);
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this->Points->GetPoint(1, a1);
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this->Points->GetPoint(2, a2); //first midside node
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this->Points->GetPoint(3, a3); //second midside node
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this->InterpolationFunctions(pcoords,weights);
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for (i=0; i<3; i++)
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{
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x[i] = a0[i]*weights[0] + a1[i]*weights[1] + a2[i]*weights[2] + a3[i]*weights[3];
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}
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}
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//----------------------------------------------------------------------------
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int vtkCubicLine::CellBoundary(int vtkNotUsed(subId), double pcoords[3],
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vtkIdList *pts)
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{
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pts->SetNumberOfIds(1);
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if ( pcoords[0] >= 0.0 )
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{
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pts->SetId(0,this->PointIds->GetId(1)); // The edge points IDs are 0 and 1.
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if ( pcoords[0] > 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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else
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{
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pts->SetId(0,this->PointIds->GetId(0));
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if ( pcoords[0] < -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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//LinearLines for the Contour and the Clip Algorithm
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//-----------------------------------------------------------------------------
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static int LinearLines[3][2] = { {0,2}, {2,3}, {3,1} };
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void vtkCubicLine::Contour(double value, vtkDataArray *cellScalars,
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vtkIncrementalPointLocator *locator, vtkCellArray *verts,
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vtkCellArray *lines, vtkCellArray *polys,
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vtkPointData *inPd, vtkPointData *outPd,
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vtkCellData *inCd, vtkIdType cellId,
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vtkCellData *outCd)
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{
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for (int i=0; i < 3; i++) //for each subdivided line
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{
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for ( int j=0; j<2; j++) //for each of the four vertices of the line
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{
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this->Line->Points->SetPoint(j,this->Points->GetPoint(LinearLines[i][j]));
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this->Line->PointIds->SetId(j,this->PointIds->GetId(LinearLines[i][j]));
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this->Scalars->SetValue(j,cellScalars->GetTuple1(LinearLines[i][j]));
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}
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this->Line->Contour(value, this->Scalars, locator, verts,
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lines, polys, inPd, outPd, inCd, cellId, outCd);
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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 vtkCubicLine::IntersectWithLine(double p1[3], double p2[3], double tol, double& t,
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double x[3], double pcoords[3], int& subId)
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{
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int subTest, numLines=3;
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for (subId=0; subId < numLines; subId++)
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{
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if ( subId == 0)
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{
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this->Line->Points->SetPoint(0,this->Points->GetPoint(0));
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this->Line->Points->SetPoint(1,this->Points->GetPoint(2));
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}
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else if (subId == 1)
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{
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this->Line->Points->SetPoint(0,this->Points->GetPoint(2));
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this->Line->Points->SetPoint(1,this->Points->GetPoint(3));
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}
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else
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{
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this->Line->Points->SetPoint(0,this->Points->GetPoint(3));
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this->Line->Points->SetPoint(1,this->Points->GetPoint(1));
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}
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if ( this->Line->IntersectWithLine(p1, p2, tol, t, x, pcoords, subTest) )
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{
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// adjust parametric coordinate
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if ( subId == 0 ) //first part : -1 <= pcoords <= -1/3
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{
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pcoords[0] = pcoords[0]*(2.0/3.0) - 1;
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}
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else if ( subId == 1 ) //second part : -1/3 <= pcoords <= 1/3
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{
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pcoords[0] = pcoords[0]*(2.0/3.0) - (1.0/3.0) ;
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}
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else // third part : 1/3 <= pcoords <= 1
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{
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pcoords[0] = pcoords[0]*(2.0/3.0) + (1.0/3.0);
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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 vtkCubicLine::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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// The first line
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ptIds->InsertId(0,this->PointIds->GetId(0));
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pts->InsertPoint(0,this->Points->GetPoint(0));
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ptIds->InsertId(1,this->PointIds->GetId(2));
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pts->InsertPoint(1,this->Points->GetPoint(2));
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// The second line
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ptIds->InsertId(2,this->PointIds->GetId(2));
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pts->InsertPoint(2,this->Points->GetPoint(2));
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ptIds->InsertId(3,this->PointIds->GetId(3));
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pts->InsertPoint(3,this->Points->GetPoint(3));
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// The third line
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ptIds->InsertId(4,this->PointIds->GetId(3));
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pts->InsertPoint(4,this->Points->GetPoint(3));
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ptIds->InsertId(5,this->PointIds->GetId(1));
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pts->InsertPoint(5,this->Points->GetPoint(1));
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return 1;
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}
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//----------------------------------------------------------------------------
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void vtkCubicLine::Derivatives(int vtkNotUsed(subId),
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double pcoords[3],
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double *values,
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int dim,
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double *derivs)
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{
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double v0, v1, v2, v3; // Local coordinates of Each point.
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double v10[3], lenX; // Reesentation of local Axis
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double x0[3], x1[3], x2[3], x3[3]; // Points of the model
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double vec20[3], vec30[3]; // Normal and vector of each point.
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double J; // Jacobian Matrix
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double JI; // Inverse of the Jacobian Matrix
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double funcDerivs[4], sum, dBydx; // Derivated values
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// Project points of vtkCubicLine into a 1D system
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this->Points->GetPoint(0, x0);
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this->Points->GetPoint(1, x1);
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this->Points->GetPoint(2, x2);
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this->Points->GetPoint(3, x3);
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for (int i=0; i < 3; i++) // Compute the vector for each point
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{
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v10[i] = x1[i] - x0[i];
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vec20[i] = x2[i] - x0[i];
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vec30[i] = x3[i] - x0[i];
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}
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if ( (lenX=vtkMath::Normalize(v10)) <= 0.0 ) //degenerate
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{
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for (int j=0; j < dim; j++ )
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{
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for (int i=0; i < 3; i++ )
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{
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derivs[j*dim + i] = 0.0;
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}
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}
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return;
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}
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v0 = 0.0; //convert points to 1D (i.e., local system)
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v1 = lenX;
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v2 = vtkMath::Dot(vec20,v10);
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v3 = vtkMath::Dot(vec30,v10);
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this->InterpolationDerivs(pcoords, funcDerivs);
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J = v0*funcDerivs[0] + v1*funcDerivs[1] +
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v2*funcDerivs[2] + v3*funcDerivs[3];
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// Compute inverse Jacobian, return if Jacobian is singular
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if(J != 0)
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{
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JI = 1.0 / J;
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}
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else
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{
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for (int j=0; j < dim; j++ )
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{
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for (int i=0; i < 3; i++ )
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{
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derivs[j*dim + i] = 0.0;
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}
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}
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return;
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}
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// Loop over "dim" derivative values. For each set of values,
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// compute derivatives
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// in local system and then transform into modelling system.
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// First compute derivatives in local x' coordinate system
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for (int j=0; j < dim; j++ )
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{
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sum = 0.0;
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for (int i=0; i < 4; i++) //loop over interp. function derivatives
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{
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sum += funcDerivs[i] * values[dim*i + j];
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}
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dBydx = sum*JI;
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// Transform into global system (dot product with global axes)
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derivs[3*j] = dBydx * v10[0] ;
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derivs[3*j + 1] = dBydx * v10[1] ;
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derivs[3*j + 2] = dBydx * v10[2] ;
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}
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}
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//--------------------------------------------------------------------------
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// Clip this line using scalar value provided. Like contouring, except
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// that it cuts the line to produce other lines.
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void vtkCubicLine::Clip(double value, vtkDataArray *cellScalars,
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vtkIncrementalPointLocator *locator, vtkCellArray *lines,
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vtkPointData *inPd, vtkPointData *outPd,
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vtkCellData *inCd, vtkIdType cellId, vtkCellData *outCd,
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int insideOut)
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{
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for (int i=0; i < 3; i++) //for each subdivided line
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{
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for ( int j=0; j<2; j++) //for each of the four vertices of the line
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{
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this->Line->Points->SetPoint(j,this->Points->GetPoint(LinearLines[i][j]));
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this->Line->PointIds->SetId(j,this->PointIds->GetId(LinearLines[i][j]));
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this->Scalars->SetValue(j,cellScalars->GetTuple1(LinearLines[i][j]));
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}
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this->Line->Clip(value, this->Scalars, locator, lines, inPd, outPd,
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inCd, cellId, outCd, insideOut);
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}
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}
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//----------------------------------------------------------------------------
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//
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// Compute interpolation functions
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//
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void vtkCubicLine::InterpolationFunctions(double pcoords[3], double weights[4]) // N2 and N3 are the middle points
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{
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// pcoords[0] = t, weights need to be set in accordance with the definition of the standard cubic line finite element
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double t = pcoords[0];
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weights[0] = (9.0/16.0)*(1.0 - t)*(t + (1.0/3.0))*(t - (1.0/3.0));
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weights[1] = (-9.0/16.0)*(1.0 + t)*((1.0/3.0) - t)*(t + (1.0/3.0));
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weights[2] = (27.0/16.0)*(t - 1.0)*(t + 1.0)*(t - (1.0/3.0));
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weights[3] = (-27.0/16.0)*(t - 1.0)*(t + 1.0)*(t + (1.0/3.0));
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}
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//----------------------------------------------------------------------------
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void vtkCubicLine::InterpolationDerivs(double pcoords[3], double derivs[4]) //N2 and N3 are the middle points
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{
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double t = pcoords[0];
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derivs[0] = (1.0/16.0)*(1.0 + 18.0*t - 27.0*t*t);
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derivs[1] = (1.0/16.0)*(-1.0 + 18.0*t + 27.0*t*t);
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derivs[2] = (1.0/16.0)*(-27.0 - 18.0*t + 81.0*t*t);
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derivs[3] = (1.0/16.0)*(27.0 - 18.0*t - 81.0*t*t);
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}
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//----------------------------------------------------------------------------
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static double vtkCubicLineCellPCoords[12] = {-1.0,0.0,0.0, 1.0,0.0,0.0, -(1.0/3.0),0.0,0.0, (1.0/3.0),0.0,0.0};
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double *vtkCubicLine::GetParametricCoords()
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{
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return vtkCubicLineCellPCoords;
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}
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//----------------------------------------------------------------------------
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double vtkCubicLine::GetParametricDistance(double pcoords[3])
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{
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double pc;
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pc = pcoords[0];
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if ( pc <= -1.0)
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{
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return pc * (-1.0) - 1.0;
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}
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else if (pc >= 1.0)
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{
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return pc - 1.0;
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}
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return pc; // the parametric coordintate lies between -1.0 and 1.0.
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}
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//----------------------------------------------------------------------------
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void vtkCubicLine::PrintSelf(ostream& os, vtkIndent indent)
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{
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this->Superclass::PrintSelf(os,indent);
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os << indent << "Line: " << this->Line << endl;
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}
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