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/*=========================================================================
Program: Visualization Toolkit
Module: vtkParametricFigure8Klein.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 "vtkParametricFigure8Klein.h"
#include "vtkObjectFactory.h"
#include "vtkMath.h"
vtkStandardNewMacro(vtkParametricFigure8Klein);
//----------------------------------------------------------------------------
vtkParametricFigure8Klein::vtkParametricFigure8Klein()
{
// Preset triangulation parameters
this->MinimumU = -vtkMath::Pi();
this->MinimumV = -vtkMath::Pi();
this->MaximumU = vtkMath::Pi();
this->MaximumV = vtkMath::Pi();
this->JoinU = 1;
this->JoinV = 1;
this->TwistU = 1;
this->TwistV = 0;
this->ClockwiseOrdering = 1;
this->DerivativesAvailable = 1;
this->Radius = 1;
}
//----------------------------------------------------------------------------
vtkParametricFigure8Klein::~vtkParametricFigure8Klein()
{
}
//----------------------------------------------------------------------------
void vtkParametricFigure8Klein::Evaluate(double uvw[3], double Pt[3], double Duvw[9])
{
double u = uvw[0];
double v = uvw[1];
double *Du = Duvw;
double *Dv = Duvw + 3;
double cu = cos(u);
double cu2 = cos(u / 2);
double su = sin(u);
double su2 = sin(u / 2);
double cv = cos(v);
double c2v = cos(2 * v);
double s2v = sin(2 * v);
double sv = sin(v);
double t = this->Radius + sv * cu2 - s2v * su2 / 2;
// The point
Pt[0] = cu * t;
Pt[1] = su * t;
Pt[2] = su2 * sv + cu2 * s2v / 2;
//The derivatives are:
Du[0] = -Pt[1] - cu * ( 2 * sv * su2 + s2v * cu2 ) / 4;
Du[1] = Pt[0] - su * ( 2 * sv * su2 + s2v * cu2 ) / 4;
Du[2] = cu2 * sv / 2 - su2 * s2v / 4;
Dv[0] = cu * ( cv * cu2 - c2v * su2);
Dv[1] = su * ( cv * cu2 - c2v * su2);
Dv[2] = su2 * cv / 2 + cu2 * c2v;
}
//----------------------------------------------------------------------------
double vtkParametricFigure8Klein::EvaluateScalar(double*, double*, double*)
{
return 0;
}
//----------------------------------------------------------------------------
void vtkParametricFigure8Klein::PrintSelf(ostream& os, vtkIndent indent)
{
this->Superclass::PrintSelf(os,indent);
os << indent << "Radius: " << this->Radius << "\n";
}
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