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101 lines
3.2 KiB
C++
101 lines
3.2 KiB
C++
/*=========================================================================
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Program: Visualization Toolkit
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Module: vtkParametricKuen.cxx
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Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen
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All rights reserved.
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See Copyright.txt or http://www.kitware.com/Copyright.htm for details.
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This software is distributed WITHOUT ANY WARRANTY; without even
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the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
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PURPOSE. See the above copyright notice for more information.
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=========================================================================*/
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#include "vtkParametricKuen.h"
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#include "vtkObjectFactory.h"
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#include "vtkMath.h"
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vtkStandardNewMacro(vtkParametricKuen);
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//----------------------------------------------------------------------------//
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vtkParametricKuen::vtkParametricKuen()
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{
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// Preset triangulation parameters
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this->MinimumU = -3.*vtkMath::Pi();
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this->MinimumV = 0.;
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this->MaximumU = 3.*vtkMath::Pi();
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this->MaximumV = vtkMath::Pi();
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this->JoinU = 0;
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this->JoinV = 0;
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this->TwistU = 0;
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this->TwistV = 0;
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this->ClockwiseOrdering = 1;
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this->DerivativesAvailable = 1;
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}
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//----------------------------------------------------------------------------//
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vtkParametricKuen::~vtkParametricKuen()
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{
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}
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//----------------------------------------------------------------------------//
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void vtkParametricKuen::Evaluate(double uvw[3], double Pt[3], double Duvw[9])
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{
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// Copy the parameters out of the vector, for the sake of convenience.
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double u = uvw[0];
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double v = uvw[1];
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// We're only going to need the u and v partial derivatives.
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// The w partial derivatives are not needed.
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double *Du = Duvw;
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double *Dv = Duvw + 3;
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// Instead of a bunch of calls to the trig library,
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// just call it once and store the results.
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double cosu = cos(u);
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double cosv = cos(v);
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double sinu = sin(u);
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double sinv = sin(v);
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double denom_1 = 1. + u*u*sinv*sinv;
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double denom_2 = u*u + 1./(sinv*sinv);
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// Location of the point. This parametrization was taken from:
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// http://mathworld.wolfram.com/KuenSurface.html
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Pt[0] = 2.*sinv*(cosu + u*sinu)/denom_1;
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Pt[1] = 2.*sinv*(sinu - u*cosu)/denom_1;
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Pt[2] = log(tan(v/2.)) + 2.*cosv/denom_1;
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// The derivative with respect to u:
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Du[0] = (2.*u*sinv*(cosu + ((u*u - 2.)*cosu - 2.*u*sinu)*sinv*sinv))/(denom_1*denom_1);
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// Avoid division by 0
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if (denom_2 == 0.0 || sinv == 0.0)
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{
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Du[1] = 0.0;
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Du[2] = 0.0;
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}
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else
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{
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Du[1] = (2.*u/sinv*(2.*u*cosu + (u*u - 2. + 1/(sinv*sinv))*sinu))/(denom_2*denom_2);
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Du[2] = -4.*u*cosv/(denom_2*denom_2*sinv*sinv);
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}
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// The derivative with respect to v:
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Dv[0] = 2.*cosv*(1. - u*u*sinv*sinv)*(cosu + u*sinu)/(denom_1*denom_1);
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Dv[1] = 2.*cosv*(u*u*sinv*sinv - 1.)*(u*cosu - sinu)/(denom_1*denom_1);
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Dv[2] = 1./sinv - (2. + u*u*(3. + cos(2*u)))*sinv/(denom_1*denom_1);
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}
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//----------------------------------------------------------------------------//
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double vtkParametricKuen::EvaluateScalar(double *, double *, double *)
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{
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return 0;
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}
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//----------------------------------------------------------------------------//
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void vtkParametricKuen::PrintSelf(ostream& os, vtkIndent indent)
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{
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this->Superclass::PrintSelf(os,indent);
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}
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