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/*=========================================================================
Program: Visualization Toolkit
Module: vtkParametricKlein.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 "vtkParametricKlein.h"
#include "vtkObjectFactory.h"
#include "vtkMath.h"
vtkStandardNewMacro(vtkParametricKlein);
//----------------------------------------------------------------------------
vtkParametricKlein::vtkParametricKlein()
{
// Preset triangulation parameters
this->MinimumU = 0;
this->MinimumV = 0;
this->MaximumU = vtkMath::Pi();
this->MaximumV = 2.0 * vtkMath::Pi();
this->JoinU = 0;
this->JoinV = 1;
this->TwistU = 0;
this->TwistV = 0;
this->ClockwiseOrdering = 1;
this->DerivativesAvailable = 1;
}
//----------------------------------------------------------------------------
vtkParametricKlein::~vtkParametricKlein()
{
}
//----------------------------------------------------------------------------
void vtkParametricKlein::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 su = sin(u);
double cv = cos(v);
double sv = sin(v);
double subX = 3*cv+5*su*cv*cu-30*su-60*su*pow(cu,6)
+90*su*pow(cu,4);
double subY = 80*cv*pow(cu,7)*su+48*cv*pow(cu,6)
-80*cv*pow(cu,5)*su
-48*cv*pow(cu,4)-5*cv*pow(cu,3)*su-3*cv*pow(cu,2)+
5*su*cv*cu+3*cv-60*su;
double subZ = 3+5*su*cu;
// The point
Pt[0] = -2.0/15.0*cu*subX;
Pt[1] = -1.0/15.0*su*subY;
Pt[2] = 2.0/15.0*sv*subZ;
// The derivatives
Du[0] = 2.0/15.0*su*subX -2.0/15.0*cu*(5.0*cv*pow(cu,2)
-5.0*pow(su,2)*cv-30.0*cu-60.0*pow(cu,7)
+360.0*pow(su,2)*pow(cu,5)
+90.0*pow(cu,5)-360.0*pow(su,2)*pow(cu,3));
Dv[0] = -2.0/15.0*cu*(-3.0*sv-5.0*su*sv*cu);
Du[1] = -1.0/15.0*cu*subY-1.0/15.0*su*(
-560.0*cv*pow(cu,6)*pow(su,2)
+80.0*cv*pow(cu,8)-288*cv*pow(cu,5)*su+
400*cv*pow(cu,4)*pow(su,2)
-80.0*cv*pow(cu,6)+192*cv*pow(cu,3)*su
+15.0*pow(su,2)*cv*pow(cu,2)
-5.0*cv*pow(cu,4)+6.0*su*cv*cu+5.0*cv*pow(cu,2)
-5.0*pow(su,2)*cv-60.0*cu);
Dv[1] = -1.0/15.0*su*(-80.0*sv*pow(cu,7)*su-48.0*sv*pow(cu,6)
+80.0*sv*pow(cu,5)*su+48.0*sv*pow(cu,4)+5.0*sv*pow(cu,3)*su
+3.0*sv*pow(cu,2)-5.0*su*sv*cu-3.0*sv);
Du[2] = 2.0/15.0*sv*(5.0*pow(cu,2)-5.0*pow(su,2));
Dv[2] = 2.0/15.0*cv*subZ;
}
//----------------------------------------------------------------------------
double vtkParametricKlein::EvaluateScalar(double*, double*, double*)
{
return 0;
}
//----------------------------------------------------------------------------
void vtkParametricKlein::PrintSelf(ostream& os, vtkIndent indent)
{
this->Superclass::PrintSelf(os,indent);
}
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