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