text: /*=========================================================================
  
    Program:   Visualization Toolkit
    Module:    vtkParametricBoy.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 vtkParametricBoy - Generate Boy's surface.
  // .SECTION Description
  // vtkParametricBoy generates Boy's surface.
  // This is a Model of the projective plane without singularities.
  // It was found by Werner Boy on assignment from David Hilbert.
  //
  // 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 a.maclean@cas.edu.au for
  // creating and contributing the class.
  //
  #ifndef __vtkParametricBoy_h
  #define __vtkParametricBoy_h
  
  #include "vtkCommonComputationalGeometryModule.h" // For export macro
  #include "vtkParametricFunction.h"
  
  class VTKCOMMONCOMPUTATIONALGEOMETRY_EXPORT vtkParametricBoy : public vtkParametricFunction
  {
  public:
  
    vtkTypeMacro(vtkParametricBoy,vtkParametricFunction);
    void PrintSelf(ostream& os, vtkIndent indent);
  
    // Description:
    // Construct Boy's surface with the following parameters:
    // MinimumU = 0, MaximumU = Pi,
    // MinimumV = 0, MaximumV = Pi,
    // JoinU = 1, JoinV = 1,
    // TwistU = 1, TwistV = 1;
    // ClockwiseOrdering = 1,
    // DerivativesAvailable = 1,
    // ZScale = 0.125.
    static vtkParametricBoy *New();
  
    // Description
    // Return the parametric dimension of the class.
    virtual int GetDimension() {return 2;}
  
    // Description:
    // Set/Get the scale factor for the z-coordinate.
    // Default = 1/8, giving a nice shape.
    vtkSetMacro(ZScale,double);
    vtkGetMacro(ZScale,double);
  
    // Description:
    // Boy's surface.
    //
    // 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:
    vtkParametricBoy();
    ~vtkParametricBoy();
  
    // Variables
    double ZScale;
  
  private:
    vtkParametricBoy(const vtkParametricBoy&);  // Not implemented.
    void operator=(const vtkParametricBoy&);  // Not implemented.
  };
  
  #endif
  