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