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/*=========================================================================
Program: Visualization Toolkit
Module: vtkParametricKuen.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 "vtkParametricKuen.h"
#include "vtkMath.h"
#include "vtkObjectFactory.h"
#include <cfloat>
#include <cmath>
VTK_ABI_NAMESPACE_BEGIN
vtkStandardNewMacro(vtkParametricKuen);
//----------------------------------------------------------------------------//
vtkParametricKuen::vtkParametricKuen()
{
// Preset triangulation parameters
this->MinimumU = -4.5;
this->MaximumU = 4.5;
this->MinimumV = 0.0;
this->MaximumV = vtkMath::Pi();
this->JoinU = 0;
this->JoinV = 0;
this->TwistU = 0;
this->TwistV = 0;
this->ClockwiseOrdering = 0;
this->DerivativesAvailable = 1;
this->DeltaV0 = 0.05;
}
//----------------------------------------------------------------------------//
vtkParametricKuen::~vtkParametricKuen() = default;
//----------------------------------------------------------------------------//
void vtkParametricKuen::Evaluate(double uvw[3], double Pt[3], double Duvw[9])
{
// Copy the parameters out of the vector, for the sake of convenience.
double u = uvw[0];
double v = uvw[1];
// This is needed to prevent Pt[2] going to -inf.
v = (v == 0 ? this->DeltaV0 : v);
// We're only going to need the u and v partial derivatives.
// The w partial derivatives are not needed.
double* Du = Duvw;
double* Dv = Duvw + 3;
// Instead of a bunch of calls to the trig library,
// just call it once and store the results.
double cosu = cos(u);
double cosv = cos(v);
double sinu = sin(u);
double sinv = sin(v);
double denom_1 = 1. + u * u * sinv * sinv;
double denom_2;
if (std::abs(sinv) < 1.0e-9)
{
denom_2 = 0;
}
else
{
denom_2 = u * u + 1. / (sinv * sinv);
}
// Location of the point. This parametrization was taken from:
// http://mathworld.wolfram.com/KuenSurface.html
// Conditional is needed to prevent Pt[2] going to inf (due to log(tan(Pi/2))).
// Limit of log(tan(0))=1.
double logTanvO2 =
((vtkMath::Pi() - FLT_EPSILON <= v) && (v <= vtkMath::Pi() + FLT_EPSILON) ? 1.0
: log(tan(v / 2.0)));
Pt[0] = 2. * sinv * (sinu - u * cosu) / denom_1;
Pt[1] = 2. * sinv * (cosu + u * sinu) / denom_1;
Pt[2] = logTanvO2 + 2. * cosv / denom_1;
// The derivative with respect to u:
Du[1] = (2. * u * sinv * (cosu + ((u * u - 2.) * cosu - 2. * u * sinu) * sinv * sinv)) /
(denom_1 * denom_1);
// Avoid division by 0
if (denom_2 == 0.0 || sinv == 0.0)
{
Du[0] = 0.0;
Du[2] = 0.0;
}
else
{
Du[0] = (2. * u / sinv * (2. * u * cosu + (u * u - 2. + 1 / (sinv * sinv)) * sinu)) /
(denom_2 * denom_2);
Du[2] = -4. * u * cosv / (denom_2 * denom_2 * sinv * sinv);
}
// The derivative with respect to v:
Dv[0] = 2. * cosv * (u * u * sinv * sinv - 1.) * (u * cosu - sinu) / (denom_1 * denom_1);
Dv[1] = 2. * cosv * (1. - u * u * sinv * sinv) * (cosu + u * sinu) / (denom_1 * denom_1);
Dv[2] = 1. / sinv - (2. + u * u * (3. + cos(2 * u))) * sinv / (denom_1 * denom_1);
}
//----------------------------------------------------------------------------//
double vtkParametricKuen::EvaluateScalar(double*, double*, double*)
{
return 0;
}
//----------------------------------------------------------------------------//
void vtkParametricKuen::PrintSelf(ostream& os, vtkIndent indent)
{
this->Superclass::PrintSelf(os, indent);
os << indent << "DeltaV0: " << this->DeltaV0 << "\n";
}
VTK_ABI_NAMESPACE_END
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