text: /*=========================================================================
  
    Program:   Visualization Toolkit
    Module:    vtkParametricKlein.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 vtkParametricKlein - Generates a "classical" representation of a Klein bottle.
  // .SECTION Description
  // vtkParametricKlein generates a "classical" representation of a 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$f(u,v) = ((r*cos(v)+a)*cos(u),(r*cos(v)+a)*sin(u),r*sin(v)*cos(u/2),r*sin(v)*sin(u/2))\f$
  //
  // The classical representation of the immersion in \f$R^3\f$ is returned by this function.
  //
  //
  // 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 vtkParametricKlein_h
  #define vtkParametricKlein_h
  
  #include "vtkCommonComputationalGeometryModule.h" // For export macro
  #include "vtkParametricFunction.h"
  
  class VTKCOMMONCOMPUTATIONALGEOMETRY_EXPORT vtkParametricKlein : public vtkParametricFunction
  {
  public:
    vtkTypeMacro(vtkParametricKlein,vtkParametricFunction);
    void PrintSelf(ostream& os, vtkIndent indent) VTK_OVERRIDE;
  
    // Description:
    // Construct a Klein Bottle with the following parameters:
    // MinimumU = 0, MaximumU = 2*Pi,
    // MinimumV = -Pi, MaximumV = Pi,
    // JoinU = 0, JoinV = 1,
    // TwistU = 0, TwistV = 0,
    // ClockwiseOrdering = 1,
    // DerivativesAvailable = 1,
    static vtkParametricKlein *New();  //! Initialise the parameters for the Klein bottle
  
    // Description
    // Return the parametric dimension of the class.
    virtual int GetDimension() {return 2;}
  
    // Description:
    // A 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:
    vtkParametricKlein();
    ~vtkParametricKlein();
  
  private:
    vtkParametricKlein(const vtkParametricKlein&) VTK_DELETE_FUNCTION;
    void operator=(const vtkParametricKlein&) VTK_DELETE_FUNCTION;
  };
  
  #endif
  