text: /*=========================================================================
   *
   *  Copyright Insight Software Consortium
   *
   *  Licensed under the Apache License, Version 2.0 (the "License");
   *  you may not use this file except in compliance with the License.
   *  You may obtain a copy of the License at
   *
   *         http://www.apache.org/licenses/LICENSE-2.0.txt
   *
   *  Unless required by applicable law or agreed to in writing, software
   *  distributed under the License is distributed on an "AS IS" BASIS,
   *  WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
   *  See the License for the specific language governing permissions and
   *  limitations under the License.
   *
   *=========================================================================*/
  #ifndef itkDiscreteGaussianCurvatureQuadEdgeMeshFilter_h
  #define itkDiscreteGaussianCurvatureQuadEdgeMeshFilter_h
  
  #include "itkDiscreteCurvatureQuadEdgeMeshFilter.h"
  #include "itkMath.h"
  
  
  namespace itk
  {
  /**
   * \class DiscreteGaussianCurvatureQuadEdgeMeshFilter
   * \brief see the following paper
   * title: Discrete Differential-Geometry Operators for Triangulated 2-Manifolds
   * authors: Mark Meyer, Mathieu Desbrun, Peter Schroder, Alan H. Barr
   * conference: VisMath '02
   * location: Berlin (Germany)
   * \author: Arnaud Gelas, Alexandre Gouaillard
   * \ingroup ITKQuadEdgeMeshFiltering
   */
  template< typename TInputMesh, typename TOutputMesh=TInputMesh >
  class DiscreteGaussianCurvatureQuadEdgeMeshFilter:
    public DiscreteCurvatureQuadEdgeMeshFilter< TInputMesh, TOutputMesh >
  {
  public:
    ITK_DISALLOW_COPY_AND_ASSIGN(DiscreteGaussianCurvatureQuadEdgeMeshFilter);
  
    using Self = DiscreteGaussianCurvatureQuadEdgeMeshFilter;
    using Pointer = SmartPointer< Self >;
    using ConstPointer = SmartPointer< const Self >;
    using Superclass = DiscreteCurvatureQuadEdgeMeshFilter<
      TInputMesh, TOutputMesh >;
  
    using InputMeshType = typename Superclass::InputMeshType;
    using InputMeshPointer = typename Superclass::InputMeshPointer;
  
    using OutputMeshType = typename Superclass::OutputMeshType;
    using OutputMeshPointer = typename Superclass::OutputMeshPointer;
    using OutputPointsContainerPointer = typename Superclass::OutputPointsContainerPointer;
    using OutputPointsContainerIterator = typename Superclass::OutputPointsContainerIterator;
    using OutputPointType = typename Superclass::OutputPointType;
    using OutputVectorType = typename Superclass::OutputVectorType;
    using OutputCoordType = typename Superclass::OutputCoordType;
    using OutputPointIdentifier = typename Superclass::OutputPointIdentifier;
    using OutputCellIdentifier = typename Superclass::OutputCellIdentifier;
    using OutputQEType = typename Superclass::OutputQEType;
    using OutputMeshTraits = typename Superclass::OutputMeshTraits;
    using OutputCurvatureType = typename Superclass::OutputCurvatureType;
    using TriangleType = typename Superclass::TriangleType;
  
    /** Run-time type information (and related methods).   */
    itkTypeMacro(DiscreteGaussianCurvatureQuadEdgeMeshFilter, DiscreteCurvatureQuadEdgeMeshFilter);
  
    /** New macro for creation of through a Smart Pointer   */
    itkNewMacro(Self);
  
  #ifdef ITK_USE_CONCEPT_CHECKING
    // Begin concept checking
    itkConceptMacro( OutputIsFloatingPointCheck,
                     ( Concept::IsFloatingPoint< OutputCurvatureType > ) );
    // End concept checking
  #endif
  
  protected:
    DiscreteGaussianCurvatureQuadEdgeMeshFilter() {}
    ~DiscreteGaussianCurvatureQuadEdgeMeshFilter() override {}
  
    OutputCurvatureType EstimateCurvature(const OutputPointType & iP) override
    {
      OutputMeshPointer output = this->GetOutput();
  
      OutputQEType *qe = iP.GetEdge();
  
      if ( qe != nullptr )
        {
        OutputQEType *qe_it = qe;
        OutputQEType *qe_it2;
  
        OutputPointType q0, q1;
  
        OutputCurvatureType sum_theta = 0.;
        OutputCurvatureType area = 0.;
  
        do
          {
          // cell_id = qe_it->GetLeft();
          qe_it2 = qe_it->GetOnext();
          q0 = output->GetPoint( qe_it->GetDestination() );
          q1 = output->GetPoint( qe_it2->GetDestination() );
  
          // Compute Angle;
          sum_theta += static_cast< OutputCurvatureType >(
            TriangleType::ComputeAngle(q0, iP, q1) );
          area += this->ComputeMixedArea(qe_it, qe_it2);
          qe_it = qe_it2;
          }
        while ( qe_it != qe );
  
        return ( 2.0 * itk::Math::pi - sum_theta ) / area;
        }
  
      return 0.;
    }
  };
  }
  
  #endif
  