/*=========================================================================

  Program:   Visualization Toolkit
  Module:    vtkParametricSuperToroid.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.

=========================================================================*/
/**
 * @class   vtkParametricSuperToroid
 * @brief   Generate a supertoroid.
 *
 * vtkParametricSuperToroid generates a supertoroid.  Essentially a
 * supertoroid is a torus with the sine and cosine terms raised to a power.
 * A supertoroid is a versatile primitive that is controlled by four
 * parameters r0, r1, n1 and n2. r0, r1 determine the type of torus whilst
 * the value of n1 determines the shape of the torus ring and n2 determines
 * the shape of the cross section of the ring. It is the different values of
 * these powers which give rise to a family of 3D shapes that are all
 * basically toroidal in shape.
 *
 * 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.
 *
 * Also see: http://paulbourke.net/geometry/torus/#super.
 *
 * @warning
 * Care needs to be taken specifying the bounds correctly. You may need to
 * carefully adjust MinimumU, MinimumV, MaximumU, MaximumV.
 *
 * @par Thanks:
 * Andrew Maclean andrew.amaclean@gmail.com for creating and contributing the
 * class.
 *
*/

#ifndef vtkParametricSuperToroid_h
#define vtkParametricSuperToroid_h

#include "vtkCommonComputationalGeometryModule.h" // For export macro
#include "vtkParametricFunction.h"

class VTKCOMMONCOMPUTATIONALGEOMETRY_EXPORT vtkParametricSuperToroid :
  public vtkParametricFunction
{
  public:
    vtkTypeMacro(vtkParametricSuperToroid, vtkParametricFunction);
    void PrintSelf(ostream& os, vtkIndent indent) VTK_OVERRIDE;

    /**
     * Construct a supertoroid with the following parameters:
     * MinimumU = 0, MaximumU = 2*Pi,
     * MinimumV = 0, MaximumV = 2*Pi,
     * JoinU = 0, JoinV = 0,
     * TwistU = 0, TwistV = 0,
     * ClockwiseOrdering = 1,
     * DerivativesAvailable = 0,
     * RingRadius = 1, CrossSectionRadius = 0.5,
     * N1 = 1, N2 = 1, XRadius = 1,
     * YRadius = 1, ZRadius = 1, a torus in this case.
     */
    static vtkParametricSuperToroid *New();

    /**
     * Return the parametric dimension of the class.
     */
    int GetDimension() VTK_OVERRIDE {return 2;}

    //@{
    /**
     * Set/Get the radius from the center to the middle of the ring of the
     * supertoroid. Default is 1.
     */
    vtkSetMacro(RingRadius, double);
    vtkGetMacro(RingRadius, double);
    //@}

    //@{
    /**
     * Set/Get the radius of the cross section of ring of the supertoroid.
     * Default = 0.5.
     */
    vtkSetMacro(CrossSectionRadius, double);
    vtkGetMacro(CrossSectionRadius, double);
    //@}

    //@{
    /**
     * Set/Get the scaling factor for the x-axis. Default is 1.
     */
    vtkSetMacro(XRadius, double);
    vtkGetMacro(XRadius, double);
    //@}

    //@{
    /**
     * Set/Get the scaling factor for the y-axis. Default is 1.
     */
    vtkSetMacro(YRadius, double);
    vtkGetMacro(YRadius, double);
    //@}

    //@{
    /**
     * Set/Get the scaling factor for the z-axis. Default is 1.
     */
    vtkSetMacro(ZRadius, double);
    vtkGetMacro(ZRadius, double);
    //@}

    //@{
    /**
     * Set/Get the shape of the torus ring.  Default is 1.
     */
    vtkSetMacro(N1, double);
    vtkGetMacro(N1, double);
    //@}

    //@{
    /**
     * Set/Get the shape of the cross section of the ring. Default is 1.
     */
    vtkSetMacro(N2, double);
    vtkGetMacro(N2, double);
    //@}

    /**
     * A supertoroid.

     * 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]) VTK_OVERRIDE;

    /**
     * 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.
     */
    double EvaluateScalar(double uvw[3], double Pt[3],
                          double Duvw[9]) VTK_OVERRIDE;

  protected:
    vtkParametricSuperToroid();
    ~vtkParametricSuperToroid() VTK_OVERRIDE;

    // Variables
    double RingRadius;
    double CrossSectionRadius;
    double XRadius;
    double YRadius;
    double ZRadius;
    double N1;
    double N2;

  private:
    vtkParametricSuperToroid(const vtkParametricSuperToroid&) VTK_DELETE_FUNCTION;
    void operator=(const vtkParametricSuperToroid&) VTK_DELETE_FUNCTION;

};

#endif

