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

  Program:   Visualization Toolkit
  Module:    vtkCurvatures.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   vtkCurvatures
 * @brief   compute curvatures (Gauss and mean) of a Polydata object
 *
 * vtkCurvatures takes a polydata input and computes the curvature of the
 * mesh at each point. Four possible methods of computation are available :
 *
 * Gauss Curvature
 * discrete Gauss curvature (K) computation,
 * \f$K(vertex v) = 2*PI-\sum_{facet neighbs f of v} (angle_f at v)\f$
 * The contribution of every facet is for the moment weighted by \f$Area(facet)/3\f$
 * The units of Gaussian Curvature are \f$[1/m^2]\f$
 *
 * Mean Curvature
 * \f$H(vertex v) = average over edges neighbs e of H(e)\f$
 * \f$H(edge e) = length(e)*dihedral_angle(e)\f$
 * NB: dihedral_angle is the ORIENTED angle between -PI and PI,
 * this means that the surface is assumed to be orientable
 * the computation creates the orientation
 * The units of Mean Curvature are [1/m]
 *
 * Maximum (\f$k_max\f$) and Minimum (\f$k_min\f$) Principal Curvatures
 * \f$k_max = H + sqrt(H^2 - K)\f$
 * \f$k_min = H - sqrt(H^2 - K)\f$
 * Excepting spherical and planar surfaces which have equal principal curvatures,
 * the curvature at a point on a surface varies with the direction one "sets off"
 * from the point. For all directions, the curvature will pass through two extrema:
 * a minimum (\f$k_min\f$) and a maximum (\f$k_max\f$) which occur at mutually orthogonal
 * directions to each other.
 *
 * NB. The sign of the Gauss curvature is a geometric ivariant, it should be +ve
 * when the surface looks like a sphere, -ve when it looks like a saddle,
 * however, the sign of the Mean curvature is not, it depends on the
 * convention for normals - This code assumes that normals point outwards (ie
 * from the surface of a sphere outwards). If a given mesh produces curvatures
 * of opposite senses then the flag InvertMeanCurvature can be set and the
 * Curvature reported by the Mean calculation will be inverted.
 *
 * @par Thanks:
 * Philip Batchelor philipp.batchelor@kcl.ac.uk for creating and contributing
 * the class and Andrew Maclean a.maclean@acfr.usyd.edu.au for cleanups and
 * fixes. Thanks also to Goodwin Lawlor for contributing patch to calculate
 * principal curvatures
 *
 *
 *
*/

#ifndef vtkCurvatures_h
#define vtkCurvatures_h

#include "vtkFiltersGeneralModule.h" // For export macro
#include "vtkPolyDataAlgorithm.h"

#define VTK_CURVATURE_GAUSS 0
#define VTK_CURVATURE_MEAN  1
#define VTK_CURVATURE_MAXIMUM 2
#define VTK_CURVATURE_MINIMUM 3

class VTKFILTERSGENERAL_EXPORT vtkCurvatures : public vtkPolyDataAlgorithm
{
public:
  vtkTypeMacro(vtkCurvatures,vtkPolyDataAlgorithm);
  void PrintSelf(ostream& os, vtkIndent indent) VTK_OVERRIDE;

  /**
   * Construct with curvature type set to Gauss
   */
  static vtkCurvatures *New();

  //@{
  /**
   * Set/Get Curvature type
   * VTK_CURVATURE_GAUSS: Gaussian curvature, stored as
   * DataArray "Gauss_Curvature"
   * VTK_CURVATURE_MEAN : Mean curvature, stored as
   * DataArray "Mean_Curvature"
   */
  vtkSetMacro(CurvatureType,int);
  vtkGetMacro(CurvatureType,int);
  void SetCurvatureTypeToGaussian()
  { this->SetCurvatureType(VTK_CURVATURE_GAUSS); }
  void SetCurvatureTypeToMean()
  { this->SetCurvatureType(VTK_CURVATURE_MEAN); }
  void SetCurvatureTypeToMaximum()
  { this->SetCurvatureType(VTK_CURVATURE_MAXIMUM); }
  void SetCurvatureTypeToMinimum()
  { this->SetCurvatureType(VTK_CURVATURE_MINIMUM); }
  //@}

  //@{
  /**
   * Set/Get the flag which inverts the mean curvature calculation for
   * meshes with inward pointing normals (default false)
   */
  vtkSetMacro(InvertMeanCurvature,int);
  vtkGetMacro(InvertMeanCurvature,int);
  vtkBooleanMacro(InvertMeanCurvature,int);
  //@}

protected:
  vtkCurvatures();

  // Usual data generation method
  int RequestData(vtkInformation *, vtkInformationVector **, vtkInformationVector *) VTK_OVERRIDE;

  /**
   * discrete Gauss curvature (K) computation,
   * cf http://www-ipg.umds.ac.uk/p.batchelor/curvatures/curvatures.html
   */
  void GetGaussCurvature(vtkPolyData *output);

  // discrete Mean curvature (H) computation,
  // cf http://www-ipg.umds.ac.uk/p.batchelor/curvatures/curvatures.html
  void GetMeanCurvature(vtkPolyData *output);

  /**
   * Maximum principal curvature \f$k_max = H + sqrt(H^2 -K)\f$
   */
  void GetMaximumCurvature(vtkPolyData *input, vtkPolyData *output);

  /**
   * Minimum principal curvature \f$k_min = H - sqrt(H^2 -K)\f$
   */
  void GetMinimumCurvature(vtkPolyData *input, vtkPolyData *output);


  // Vars
  int CurvatureType;
  int InvertMeanCurvature;

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

};

#endif