itkDiscretePrincipalCurvaturesQuadEdgeMeshFilter.h

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 *  Copyright Insight Software Consortium
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 *  you may not use this file except in compliance with the License.
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 *  See the License for the specific language governing permissions and
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#ifndef itkDiscretePrincipalCurvaturesQuadEdgeMeshFilter_h
#define itkDiscretePrincipalCurvaturesQuadEdgeMeshFilter_h

#include "itkDiscreteCurvatureQuadEdgeMeshFilter.h"
#include "itkQuadEdgeMeshParamMatrixCoefficients.h"

namespace itk
{
template< typename TInputMesh, typename TOutputMesh=TInputMesh >
class DiscretePrincipalCurvaturesQuadEdgeMeshFilter:
  public DiscreteCurvatureQuadEdgeMeshFilter< TInputMesh, TOutputMesh >
{
public:
  using Self = DiscretePrincipalCurvaturesQuadEdgeMeshFilter;
  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;

  itkTypeMacro(DiscretePrincipalCurvaturesQuadEdgeMeshFilter, DiscreteCurvatureQuadEdgeMeshFilter);

  using CoefficientType = ConformalMatrixCoefficients< OutputMeshType >;

#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() override = default;

  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 != 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 &) = delete;
  void operator=(const Self &) = delete;
};
}

#endif