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 itkDiscretePrincipalCurvaturesQuadEdgeMeshFilter_h
  #define itkDiscretePrincipalCurvaturesQuadEdgeMeshFilter_h
  
  #include "itkDiscreteCurvatureQuadEdgeMeshFilter.h"
  #include "itkQuadEdgeMeshParamMatrixCoefficients.h"
  
  namespace itk
  {
  /**
   * \class DiscretePrincipalCurvaturesQuadEdgeMeshFilter
   *
   * \brief  FIXME   add documentation here
   *
   * \ingroup ITKQuadEdgeMeshFiltering
   */
  template< typename TInputMesh, typename TOutputMesh=TInputMesh >
  class DiscretePrincipalCurvaturesQuadEdgeMeshFilter:
    public DiscreteCurvatureQuadEdgeMeshFilter< TInputMesh, TOutputMesh >
  {
  public:
    typedef DiscretePrincipalCurvaturesQuadEdgeMeshFilter     Self;
    typedef SmartPointer< Self >                              Pointer;
    typedef SmartPointer< const Self >                        ConstPointer;
    typedef DiscreteCurvatureQuadEdgeMeshFilter<
      TInputMesh, TOutputMesh >                               Superclass;
  
    typedef typename Superclass::InputMeshType                 InputMeshType;
    typedef typename Superclass::InputMeshPointer              InputMeshPointer;
    typedef typename Superclass::OutputMeshType                OutputMeshType;
    typedef typename Superclass::OutputMeshPointer             OutputMeshPointer;
    typedef typename Superclass::OutputPointsContainerPointer  OutputPointsContainerPointer;
    typedef typename Superclass::OutputPointsContainerIterator OutputPointsContainerIterator;
    typedef typename Superclass::OutputPointType               OutputPointType;
    typedef typename Superclass::OutputVectorType              OutputVectorType;
    typedef typename Superclass::OutputCoordType               OutputCoordType;
    typedef typename Superclass::OutputPointIdentifier         OutputPointIdentifier;
    typedef typename Superclass::OutputCellIdentifier          OutputCellIdentifier;
    typedef typename Superclass::OutputQEType                  OutputQEType;
    typedef typename Superclass::OutputMeshTraits              OutputMeshTraits;
    typedef typename Superclass::OutputCurvatureType           OutputCurvatureType;
  
    typedef typename Superclass::TriangleType TriangleType;
  
    /** Run-time type information (and related methods).   */
    itkTypeMacro(DiscretePrincipalCurvaturesQuadEdgeMeshFilter, DiscreteCurvatureQuadEdgeMeshFilter);
  
    typedef ConformalMatrixCoefficients< OutputMeshType > CoefficientType;
  
  #ifdef ITK_USE_CONCEPT_CHECKING
    // Begin concept checking
    itkConceptMacro( OutputIsFloatingPointCheck,
                     ( Concept::IsFloatingPoint< OutputCurvatureType > ) );
    // End concept checking
  #endif
  
  protected:
    DiscretePrincipalCurvaturesQuadEdgeMeshFilter():
      m_Gaussian(0.0), m_Mean(0.0){}
    ~DiscretePrincipalCurvaturesQuadEdgeMeshFilter() {}
  
    OutputCurvatureType m_Gaussian;
    OutputCurvatureType m_Mean;
  
    void ComputeMeanAndGaussianCurvatures(const OutputPointType & iP)
    {
      OutputMeshPointer output = this->GetOutput();
  
      OutputQEType *qe = iP.GetEdge();
  
      m_Mean = 0.;
      m_Gaussian = 0.;
  
      if ( qe != ITK_NULLPTR )
        {
        OutputVectorType Laplace;
        Laplace.Fill(0.);
  
        OutputQEType *qe_it = qe;
  
        OutputCurvatureType area(0.), sum_theta(0.);
  
        if ( qe_it != qe_it->GetOnext() )
          {
          qe_it = qe;
          OutputQEType *qe_it2;
  
          OutputPointType  q0, q1;
          OutputVectorType face_normal;
  
          OutputVectorType normal;
          normal.Fill(0.);
  
          OutputCurvatureType temp_area;
          OutputCoordType     temp_coeff;
  
          CoefficientType coefficent;
  
          do
            {
            qe_it2 = qe_it->GetOnext();
            q0 = output->GetPoint( qe_it->GetDestination() );
            q1 = output->GetPoint( qe_it2->GetDestination() );
  
            temp_coeff = coefficent(output, qe_it);
            Laplace += temp_coeff * ( iP - q0 );
  
            // Compute Angle;
            sum_theta += static_cast< OutputCurvatureType >(
              TriangleType::ComputeAngle(q0, iP, q1) );
  
            temp_area = this->ComputeMixedArea(qe_it, qe_it2);
            area += temp_area;
  
            face_normal = TriangleType::ComputeNormal(q0, iP, q1);
            normal += face_normal;
  
            qe_it = qe_it2;
            }
          while ( qe_it != qe );
  
          if ( area > 1e-10 )
            {
            area = 1. / area;
            Laplace *= 0.25 * area;
            m_Mean = Laplace * normal;
            m_Gaussian = ( 2. * itk::Math::pi - sum_theta ) * area;
            }
          }
        }
    }
  
    virtual OutputCurvatureType ComputeDelta()
    {
      return std::max( static_cast<OutputCurvatureType>( 0. ),
                           m_Mean * m_Mean - m_Gaussian );
    }
  
  private:
    DiscretePrincipalCurvaturesQuadEdgeMeshFilter(const Self &); // purposely
                                                                    // not
                                                                    // implemented
    void operator=(const Self &);                                   // purposely
                                                                    // not
                                                                    // implemented
  };
  }
  
  #endif
  