vtkQuadraticEdge.cxx

/*=========================================================================

  Program:   Visualization Toolkit
  Module:    vtkQuadraticEdge.cxx

  Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen
  All rights reserved.
  See Copyright.txt or http://www.kitware.com/Copyright.htm for details.

     This software is distributed WITHOUT ANY WARRANTY; without even
     the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
     PURPOSE.  See the above copyright notice for more information.

=========================================================================*/
#include "vtkQuadraticEdge.h"

#include "vtkObjectFactory.h"
#include "vtkMath.h"
#include "vtkLine.h"
#include "vtkDoubleArray.h"
#include "vtkPoints.h"

vtkStandardNewMacro(vtkQuadraticEdge);

//----------------------------------------------------------------------------
// Construct the line with two points.
vtkQuadraticEdge::vtkQuadraticEdge()
{
  this->Scalars = vtkDoubleArray::New();
  this->Scalars->SetNumberOfTuples(2);
  this->Points->SetNumberOfPoints(3);
  this->PointIds->SetNumberOfIds(3);
  for (int i = 0; i < 3; i++)
    {
    this->Points->SetPoint(i, 0.0, 0.0, 0.0);
    this->PointIds->SetId(i,0);
    }
  this->Line = vtkLine::New();
}

//----------------------------------------------------------------------------
vtkQuadraticEdge::~vtkQuadraticEdge()
{
  this->Line->Delete();
  this->Scalars->Delete();
}


//----------------------------------------------------------------------------
int vtkQuadraticEdge::EvaluatePosition(double* x, double* closestPoint, 
                                       int& subId, double pcoords[3],
                                       double& minDist2, double *weights)
{
  double closest[3];
  double pc[3], dist2;
  int ignoreId, i, returnStatus, status;
  double lineWeights[2];

  pcoords[1] = pcoords[2] = 0.0;

  returnStatus = -1;
  weights[0] = 0.0;
  for (minDist2=VTK_DOUBLE_MAX,i=0; i < 2; i++)
    {
    if ( i == 0)
      {
      this->Line->Points->SetPoint(0,this->Points->GetPoint(0));
      this->Line->Points->SetPoint(1,this->Points->GetPoint(2));
      }
    else
      {
      this->Line->Points->SetPoint(0,this->Points->GetPoint(2));
      this->Line->Points->SetPoint(1,this->Points->GetPoint(1));
      }
    
    status = this->Line->EvaluatePosition(x,closest,ignoreId,pc,
                                          dist2,lineWeights);
    if ( status != -1 && dist2 < minDist2 )
      {
      returnStatus = status;
      minDist2 = dist2;
      subId = i;
      pcoords[0] = pc[0];
      }
    }

  // adjust parametric coordinate
  if ( returnStatus != -1 )
    {
    if ( subId == 0 ) //first part
      {
      pcoords[0] = pcoords[0]/2.0;
      }
    else
      {
      pcoords[0] = 0.5 + pcoords[0]/2.0;
      }
    if(closestPoint!=0)
      {
      // Compute both closestPoint and weights
      this->EvaluateLocation(subId,pcoords,closestPoint,weights);
      }
    else
      {
      // Compute weights only
      this->InterpolationFunctions(pcoords,weights);
      }
    }

  return returnStatus;
}

//----------------------------------------------------------------------------
void vtkQuadraticEdge::EvaluateLocation(int& vtkNotUsed(subId), 
                                        double pcoords[3], 
                                        double x[3], double *weights)
{
  int i;
  double a0[3], a1[3], a2[3];
  this->Points->GetPoint(0, a0);
  this->Points->GetPoint(1, a1);
  this->Points->GetPoint(2, a2); //midside node

  this->InterpolationFunctions(pcoords,weights);
  
  for (i=0; i<3; i++) 
    {
    x[i] = a0[i]*weights[0] + a1[i]*weights[1] + a2[i]*weights[2];
    }
}

//----------------------------------------------------------------------------
int vtkQuadraticEdge::CellBoundary(int subId, double pcoords[3], 
                                   vtkIdList *pts)
{
  return this->Line->CellBoundary(subId, pcoords, pts);
}

//----------------------------------------------------------------------------
static int LinearLines[2][2] = { {0,2}, {2,1} };                             
    

void vtkQuadraticEdge::Contour(double value, vtkDataArray *cellScalars,
                               vtkIncrementalPointLocator *locator, vtkCellArray *verts,
                               vtkCellArray *lines, vtkCellArray *polys, 
                               vtkPointData *inPd, vtkPointData *outPd,
                               vtkCellData *inCd, vtkIdType cellId,
                               vtkCellData *outCd)
{
  for (int i=0; i < 2; i++) //for each subdivided line
    {
    for ( int j=0; j<2; j++) //for each of the four vertices of the line
      {
      this->Line->Points->SetPoint(j,this->Points->GetPoint(LinearLines[i][j]));
      this->Line->PointIds->SetId(j,this->PointIds->GetId(LinearLines[i][j]));
      this->Scalars->SetValue(j,cellScalars->GetTuple1(LinearLines[i][j]));
      }
    this->Line->Contour(value, this->Scalars, locator, verts,
                       lines, polys, inPd, outPd, inCd, cellId, outCd);
    }
}

//----------------------------------------------------------------------------
// Line-line intersection. Intersection has to occur within [0,1] parametric
// coordinates and with specified tolerance.

// The following arguments were modified to avoid warnings:
// double p1[3], double p2[3], double x[3], double pcoords[3], 

int vtkQuadraticEdge::IntersectWithLine(double p1[3], double p2[3], 
                                        double tol, double& t, 
                                        double x[3], double pcoords[3],
                                        int& subId)
{
  int subTest, numLines=2;

  for (subId=0; subId < numLines; subId++)
    {
    if ( subId == 0)
      {
      this->Line->Points->SetPoint(0,this->Points->GetPoint(0));
      this->Line->Points->SetPoint(1,this->Points->GetPoint(2));
      }
    else
      {
      this->Line->Points->SetPoint(0,this->Points->GetPoint(2));
      this->Line->Points->SetPoint(1,this->Points->GetPoint(1));
      }

    if ( this->Line->IntersectWithLine(p1, p2, tol, t, x, pcoords, subTest) )
      {
      return 1;
      }
    }

  return 0;
}

//----------------------------------------------------------------------------
int vtkQuadraticEdge::Triangulate(int vtkNotUsed(index), vtkIdList *ptIds, 
                                  vtkPoints *pts)
{
  pts->Reset();
  ptIds->Reset();

  // The first line
  ptIds->InsertId(0,this->PointIds->GetId(0));
  pts->InsertPoint(0,this->Points->GetPoint(0));

  ptIds->InsertId(1,this->PointIds->GetId(2));
  pts->InsertPoint(1,this->Points->GetPoint(2));

  // The second line
  ptIds->InsertId(2,this->PointIds->GetId(2));
  pts->InsertPoint(2,this->Points->GetPoint(2));

  ptIds->InsertId(3,this->PointIds->GetId(1));
  pts->InsertPoint(3,this->Points->GetPoint(1));

  return 1;
}

//----------------------------------------------------------------------------
void vtkQuadraticEdge::Derivatives(int vtkNotUsed(subId), 
                                   double pcoords[3], double *values,
                                   int dim, double *derivs)
{
  double x0[3], x1[3], x2[3];
  this->Points->GetPoint(0, x0);
  this->Points->GetPoint(1, x1);
  this->Points->GetPoint(2, x2); //midside node

  // set up Jacobian matrix and inverse matrix
  double *jTj[3], jTj0[3], jTj1[3], jTj2[3];
  jTj[0] = jTj0; jTj[1] = jTj1; jTj[2] = jTj2;
  double *jI[3], jI0[3], jI1[3], jI2[3];
  jI[0] = jI0; jI[1] = jI1; jI[2] = jI2;
  /*
  double *iI[3], iI0[3], iI1[3], iI2[3];
  iI[0] = iI0; iI[1] = iI1; iI[2] = iI2;
  */
  // Compute dx/dt, dy/dt, dz/dt
  this->InterpolationDerivs(pcoords,derivs);
  double dxdt = x0[0]*derivs[0] + x1[0]*derivs[1] + x2[0]*derivs[2];
  double dydt = x0[1]*derivs[0] + x1[1]*derivs[1] + x2[1]*derivs[2];
  double dzdt = x0[2]*derivs[0] + x1[2]*derivs[1] + x2[2]*derivs[2];
  
  // Compute the psuedo inverse (we are dealing with an overconstrained system,
  // i.e., a non-square Jacobian matrix). The pseudo inverse is ((jT*j)-1)*jT
  // with jT Jacobian transpose, -1 notation means inverse.
  // Compute jT * j
  jTj[0][0] = dxdt*dxdt;
  jTj[0][1] = dxdt*dydt;
  jTj[0][2] = dxdt*dzdt;
  jTj[1][0] = dydt*dxdt;
  jTj[1][1] = dydt*dydt;
  jTj[1][2] = dydt*dzdt;
  jTj[2][0] = dzdt*dxdt;
  jTj[2][1] = dzdt*dydt;
  jTj[2][2] = dzdt*dzdt;
  
  // Compute (jT * j) inverse
  // now find the inverse
  if ( vtkMath::InvertMatrix(jTj,jI,3) == 0 )
    {
    vtkErrorMacro(<<"Jacobian inverse not found");
    return;
    }
  
  // Multiply inverse by transpose (jT * j) * jT to yield pseudo inverse.
  // Here the pseudo inverse is a 3x1 matrix.
  double inv[3];
  inv[0] = jI[0][0]*dxdt + jI[0][1]*dydt + jI[0][2]*dzdt;
  inv[1] = jI[1][0]*dxdt + jI[1][1]*dydt + jI[1][2]*dzdt;
  inv[2] = jI[2][0]*dxdt + jI[2][1]*dydt + jI[2][2]*dzdt;

  //now compute the derivates of the data values
  double sum;
  int i, j, k;
  for (k=0; k<dim; k++)
    {
    sum = 0.0;
    for ( i=0; i < 3; i++) //loop over interp. function derivatives
      {
      sum += derivs[i] * values[dim*i + k]; 
      }
    for (j=0; j < 3; j++) //loop over derivative directions
      {
      derivs[3*k + j] = sum*inv[j];
      }
    }
}


//----------------------------------------------------------------------------
// Clip this quadratic edge using scalar value provided. Like contouring, 
// except that it cuts the edge to produce linear line segments.
void vtkQuadraticEdge::Clip(double value, vtkDataArray *cellScalars, 
                            vtkIncrementalPointLocator *locator, vtkCellArray *lines,
                            vtkPointData *inPd, vtkPointData *outPd,
                            vtkCellData *inCd, vtkIdType cellId, 
                            vtkCellData *outCd, int insideOut)
{
  for (int i=0; i < 2; i++) //for each subdivided line
    {
    for ( int j=0; j<2; j++) //for each of the four vertices of the line
      {
      this->Line->Points->SetPoint(j,this->Points->GetPoint(LinearLines[i][j]));
      this->Line->PointIds->SetId(j,this->PointIds->GetId(LinearLines[i][j]));
      this->Scalars->SetValue(j,cellScalars->GetTuple1(LinearLines[i][j]));
      }
    this->Line->Clip(value, this->Scalars, locator, lines, inPd, outPd, 
                     inCd, cellId, outCd, insideOut);
    }
}

//----------------------------------------------------------------------------
// Compute interpolation functions. Node [2] is the mid-edge node.
void vtkQuadraticEdge::InterpolationFunctions(double pcoords[3], 
                                              double weights[3])
{
  double r = pcoords[0];

  weights[0] = 2.0 * (r - 0.5) * (r - 1.0);
  weights[1] = 2.0 * r * (r - 0.5);
  weights[2] = 4.0 * r * (1.0 - r);
}

//----------------------------------------------------------------------------
// Derivatives in parametric space.
void vtkQuadraticEdge::InterpolationDerivs(double pcoords[3], double derivs[3])
{
  double r = pcoords[0];

  derivs[0] = 4.0 * r - 3.0;
  derivs[1] = 4.0 * r - 1.0;
  derivs[2] = 4.0 - r * 8.0;
}

//----------------------------------------------------------------------------
static double vtkQEdgeCellPCoords[9] = {0.0,0.0,0.0, 1.0,0.0,0.0, 0.5,0.0,0.0};
double *vtkQuadraticEdge::GetParametricCoords()
{
  return vtkQEdgeCellPCoords;
}

//----------------------------------------------------------------------------
void vtkQuadraticEdge::PrintSelf(ostream& os, vtkIndent indent)
{
  this->Superclass::PrintSelf(os,indent);
  
  os << indent << "Line:\n";
  this->Line->PrintSelf(os,indent.GetNextIndent());
}