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// SPDX-FileCopyrightText: Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen
// SPDX-License-Identifier: BSD-3-Clause
/**
* @class vtkParametricFigure8Klein
* @brief Generate a figure-8 Klein bottle.
*
* 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/publications
* in the "VTK Technical Documents" section in the VTk.org web pages.
*
* @par 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"
VTK_ABI_NAMESPACE_BEGIN
class VTKCOMMONCOMPUTATIONALGEOMETRY_EXPORT vtkParametricFigure8Klein : public vtkParametricFunction
{
public:
vtkTypeMacro(vtkParametricFigure8Klein, vtkParametricFunction);
void PrintSelf(ostream& os, vtkIndent indent) override;
/**
* 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 = 0,
* DerivativesAvailable = 1,
* Radius = 1
*/
static vtkParametricFigure8Klein* New();
///@{
/**
* Set/Get the radius of the bottle. Default is 1.
*/
vtkSetMacro(Radius, double);
vtkGetMacro(Radius, double);
///@}
/**
* Return the parametric dimension of the class.
*/
int GetDimension() override { return 2; }
/**
* 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$N = Du X Dv\f$ .
*/
void Evaluate(double uvw[3], double Pt[3], double Duvw[9]) override;
/**
* Calculate a user defined scalar using one or all of uvw, Pt, Duvw.
* uvw are the parameters with Pt being 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.
*/
double EvaluateScalar(double uvw[3], double Pt[3], double Duvw[9]) override;
protected:
vtkParametricFigure8Klein();
~vtkParametricFigure8Klein() override;
// Variables
double Radius;
private:
vtkParametricFigure8Klein(const vtkParametricFigure8Klein&) = delete;
void operator=(const vtkParametricFigure8Klein&) = delete;
};
VTK_ABI_NAMESPACE_END
#endif
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