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/*=========================================================================
Program: Visualization Toolkit
Module: vtkParametricFigure8Klein.h
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.
=========================================================================*/
// .NAME vtkParametricFigure8Klein - Generate a figure-8 Klein bottle.
// .SECTION Description
// vtkParametricFigure8Klein generates a figure-8 Klein bottle. A Klein bottle
// is a closed surface with no interior and only one surface. It is
// unrealisable in 3 dimensions without intersecting surfaces. It can be
// realised in 4 dimensions by considering the map \f$F:R^2 \rightarrow R^4\f$ given by:
//
// - \f$f(u,v) = ((r*cos(v)+a)*cos(u),(r*cos(v)+a)*sin(u),r*sin(v)*cos(u/2),r*sin(v)*sin(u/2))\f$
//
// This representation of the immersion in \f$R^3\f$ is formed by taking two Mobius
// strips and joining them along their boundaries, this is the so called
// "Figure-8 Klein Bottle"
//
// For further information about this surface, please consult the
// technical description "Parametric surfaces" in http://www.vtk.org/documents.php
// in the "VTK Technical Documents" section in the VTk.org web pages.
//
// .SECTION Thanks
// Andrew Maclean andrew.amaclean@gmail.com for creating and contributing the
// class.
//
#ifndef vtkParametricFigure8Klein_h
#define vtkParametricFigure8Klein_h
#include "vtkCommonComputationalGeometryModule.h" // For export macro
#include "vtkParametricFunction.h"
class VTKCOMMONCOMPUTATIONALGEOMETRY_EXPORT vtkParametricFigure8Klein : public vtkParametricFunction
{
public:
vtkTypeMacro(vtkParametricFigure8Klein,vtkParametricFunction);
void PrintSelf(ostream& os, vtkIndent indent);
// Description:
// Construct a figure-8 Klein Bottle with the following parameters:
// MinimumU = -Pi, MaximumU = Pi,
// MinimumV = -Pi, MaximumV = Pi,
// JoinU = 1, JoinV = 1,
// TwistU = 0, TwistV = 0,
// ClockwiseOrdering = 1,
// DerivativesAvailable = 1,
// Radius = 1
static vtkParametricFigure8Klein *New();
// Description:
// Set/Get the radius of the bottle. Default is 1.
vtkSetMacro(Radius,double);
vtkGetMacro(Radius,double);
// Description
// Return the parametric dimension of the class.
virtual int GetDimension() {return 2;}
// Description:
// A Figure-8 Klein bottle.
//
// This function performs the mapping \f$f(u,v) \rightarrow (x,y,x)\f$, returning it
// as Pt. It also returns the partial derivatives Du and Dv.
// \f$Pt = (x, y, z), Du = (dx/du, dy/du, dz/du), Dv = (dx/dv, dy/dv, dz/dv)\f$ .
// Then the normal is \f$N = Du X Dv\f$ .
virtual void Evaluate(double uvw[3], double Pt[3], double Duvw[9]);
// Description:
// Calculate a user defined scalar using one or all of uvw, Pt, Duvw.
//
// uvw are the parameters with Pt being the the cartesian point,
// Duvw are the derivatives of this point with respect to u, v and w.
// Pt, Duvw are obtained from Evaluate().
//
// This function is only called if the ScalarMode has the value
// vtkParametricFunctionSource::SCALAR_FUNCTION_DEFINED
//
// If the user does not need to calculate a scalar, then the
// instantiated function should return zero.
//
virtual double EvaluateScalar(double uvw[3], double Pt[3], double Duvw[9]);
protected:
vtkParametricFigure8Klein();
~vtkParametricFigure8Klein();
// Variables
double Radius;
private:
vtkParametricFigure8Klein(const vtkParametricFigure8Klein&); // Not implemented.
void operator=(const vtkParametricFigure8Klein&); // Not implemented.
};
#endif
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