itkDiscretePrincipalCurvaturesQuadEdgeMeshFilter.h

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 *  Copyright NumFOCUS
 *
 *  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
 *
 *         https://www.apache.org/licenses/LICENSE-2.0.txt
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 *  distributed under the License is distributed on an "AS IS" BASIS,
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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:
  ITK_DISALLOW_COPY_AND_MOVE(DiscretePrincipalCurvaturesQuadEdgeMeshFilter);
 
  using Self = DiscretePrincipalCurvaturesQuadEdgeMeshFilter;
  using Pointer = SmartPointer<Self>;
  using ConstPointer = SmartPointer<const Self>;
  using Superclass = DiscreteCurvatureQuadEdgeMeshFilter<TInputMesh, TOutputMesh>;
 
  using typename Superclass::InputMeshType;
  using typename Superclass::InputMeshPointer;
  using typename Superclass::OutputMeshType;
  using typename Superclass::OutputMeshPointer;
  using typename Superclass::OutputPointsContainerPointer;
  using typename Superclass::OutputPointsContainerIterator;
  using typename Superclass::OutputPointType;
  using typename Superclass::OutputVectorType;
  using typename Superclass::OutputCoordType;
  using typename Superclass::OutputPointIdentifier;
  using typename Superclass::OutputCellIdentifier;
  using typename Superclass::OutputQEType;
  using typename Superclass::OutputMeshTraits;
  using typename Superclass::OutputCurvatureType;
 
  using typename Superclass::TriangleType;
 
  itkOverrideGetNameOfClassMacro(DiscretePrincipalCurvaturesQuadEdgeMeshFilter);
 
  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{};
 
      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{};
 
        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);
  }
};
} // namespace itk
 
#endif