itkQuadEdgeMeshParamMatrixCoefficients.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
 *
 *  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.
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#ifndef itkQuadEdgeMeshParamMatrixCoefficients_h
#define itkQuadEdgeMeshParamMatrixCoefficients_h
 
#include "itkQuadEdgeMesh.h"
#include "itkTriangleHelper.h"
#include "itkMath.h"
 
namespace itk
{
template <typename TInputMesh>
class MatrixCoefficients
{
public:
  using InputMeshType = TInputMesh;
  using InputCoordRepType = typename InputMeshType::CoordRepType;
  using InputQEType = typename InputMeshType::QEType;
 
  MatrixCoefficients() = default;
  virtual ~MatrixCoefficients() = default;
 
  virtual InputCoordRepType
  operator()(const InputMeshType * iMesh, InputQEType * iEdge) const = 0;
};
 
template <typename TInputMesh>
class ITK_TEMPLATE_EXPORT OnesMatrixCoefficients : public MatrixCoefficients<TInputMesh>
{
public:
  using Superclass = MatrixCoefficients<TInputMesh>;
 
  using InputMeshType = TInputMesh;
  using InputCoordRepType = typename InputMeshType::CoordRepType;
  using InputQEType = typename InputMeshType::QEType;
 
  OnesMatrixCoefficients() = default;
 
  InputCoordRepType
  operator()(const InputMeshType * itkNotUsed(iMesh), InputQEType * itkNotUsed(iEdge)) const override
  {
    return 1.0;
  }
};
 
template <typename TInputMesh>
class ITK_TEMPLATE_EXPORT InverseEuclideanDistanceMatrixCoefficients : public MatrixCoefficients<TInputMesh>
{
public:
  using Superclass = MatrixCoefficients<TInputMesh>;
 
  using InputMeshType = TInputMesh;
  using InputCoordRepType = typename InputMeshType::CoordRepType;
  using InputPointType = typename InputMeshType::PointType;
  using InputPointIdentifier = typename InputMeshType::PointIdentifier;
  using InputQEType = typename InputMeshType::QEType;
  using InputVectorType = typename InputMeshType::VectorType;
 
  InverseEuclideanDistanceMatrixCoefficients() = default;
 
  InputCoordRepType
  operator()(const InputMeshType * iMesh, InputQEType * iEdge) const override
  {
    InputPointIdentifier id1 = iEdge->GetOrigin();
    InputPointIdentifier id2 = iEdge->GetDestination();
    InputPointType pt1 = iMesh->GetPoint(id1);
    InputPointType pt2 = iMesh->GetPoint(id2);
 
    InputCoordRepType oValue = 1.0 / pt1.EuclideanDistanceTo(pt2);
 
    return oValue;
  }
};
 
template <typename TInputMesh>
class ITK_TEMPLATE_EXPORT ConformalMatrixCoefficients : public MatrixCoefficients<TInputMesh>
{
public:
  using Superclass = MatrixCoefficients<TInputMesh>;
 
  using InputMeshType = TInputMesh;
  using InputCoordRepType = typename InputMeshType::CoordRepType;
  using InputPointType = typename InputMeshType::PointType;
  using InputPointIdentifier = typename InputMeshType::PointIdentifier;
  using InputQEType = typename InputMeshType::QEType;
 
  ConformalMatrixCoefficients() = default;
 
  InputCoordRepType
  operator()(const InputMeshType * iMesh, InputQEType * iEdge) const override
  {
    InputPointIdentifier id1 = iEdge->GetOrigin();
    InputPointIdentifier id2 = iEdge->GetDestination();
    InputPointType       pt1 = iMesh->GetPoint(id1);
    InputPointType       pt2 = iMesh->GetPoint(id2);
    InputCoordRepType oValue(0.0);
 
    if (iEdge->IsLeftSet())
    {
      InputPointIdentifier idA = iEdge->GetLnext()->GetDestination();
      InputPointType       ptA = iMesh->GetPoint(idA);
      oValue += TriangleHelper<InputPointType>::Cotangent(pt1, ptA, pt2);
    }
    if (iEdge->IsRightSet())
    {
      InputPointIdentifier idB = iEdge->GetRnext()->GetOrigin();
      InputPointType       ptB = iMesh->GetPoint(idB);
      oValue += TriangleHelper<InputPointType>::Cotangent(pt1, ptB, pt2);
    }
 
    return std::max(InputCoordRepType{}, oValue);
  }
};
 
template <typename TInputMesh>
class ITK_TEMPLATE_EXPORT AuthalicMatrixCoefficients : public MatrixCoefficients<TInputMesh>
{
public:
  using Superclass = MatrixCoefficients<TInputMesh>;
 
  using InputMeshType = TInputMesh;
  using InputCoordRepType = typename InputMeshType::CoordRepType;
  using InputPointType = typename InputMeshType::PointType;
  using InputPointIdentifier = typename InputMeshType::PointIdentifier;
  using InputQEType = typename InputMeshType::QEType;
 
  AuthalicMatrixCoefficients() = default;
 
  InputCoordRepType
  operator()(const InputMeshType * iMesh, InputQEType * iEdge) const override
  {
    InputPointIdentifier id1 = iEdge->GetOrigin();
    InputPointType       pt1 = iMesh->GetPoint(id1);
    InputPointIdentifier id2 = iEdge->GetDestination();
    InputPointType       pt2 = iMesh->GetPoint(id2);
 
    InputCoordRepType oValue{};
 
    if (iEdge->IsLeftSet())
    {
      InputPointIdentifier idA = iEdge->GetLnext()->GetDestination();
      InputPointType       ptA = iMesh->GetPoint(idA);
      oValue += TriangleHelper<InputPointType>::Cotangent(pt1, pt2, ptA);
    }
 
    if (iEdge->IsRightSet())
    {
      InputPointIdentifier idB = iEdge->GetRnext()->GetOrigin();
      InputPointType       ptB = iMesh->GetPoint(idB);
      oValue += TriangleHelper<InputPointType>::Cotangent(pt1, pt2, ptB);
    }
 
    return oValue / pt1.SquaredEuclideanDistanceTo(pt2);
  }
};
 
template <typename TInputMesh>
class ITK_TEMPLATE_EXPORT IntrinsicMatrixCoefficients : public MatrixCoefficients<TInputMesh>
{
public:
  using Superclass = MatrixCoefficients<TInputMesh>;
 
  using InputMeshType = TInputMesh;
  using InputCoordRepType = typename InputMeshType::CoordRepType;
  using InputQEType = typename InputMeshType::QEType;
 
  InputCoordRepType m_Lambda;
 
  IntrinsicMatrixCoefficients(const InputCoordRepType & iLambda)
    : m_Lambda(iLambda)
  {}
 
  InputCoordRepType
  operator()(const InputMeshType * iMesh, InputQEType * iEdge) const
  {
    AuthalicMatrixCoefficients<TInputMesh>  authalic;
    ConformalMatrixCoefficients<TInputMesh> conformal;
 
    InputCoordRepType oValue = m_Lambda * conformal(iMesh, iEdge) + (1.0 - m_Lambda) * authalic(iMesh, iEdge);
 
    return oValue;
  }
};
 
template <typename TInputMesh>
class ITK_TEMPLATE_EXPORT HarmonicMatrixCoefficients : public MatrixCoefficients<TInputMesh>
{
public:
  using Superclass = MatrixCoefficients<TInputMesh>;
 
  using InputMeshType = TInputMesh;
  using InputCoordRepType = typename InputMeshType::CoordRepType;
  using InputPointType = typename InputMeshType::PointType;
  using InputVectorType = typename InputPointType::VectorType;
  using InputPointIdentifier = typename InputMeshType::PointIdentifier;
  using InputQEType = typename InputMeshType::QEType;
 
  static constexpr unsigned int PointDimension = InputPointType::PointDimension;
 
  HarmonicMatrixCoefficients() = default;
 
  InputCoordRepType
  operator()(const InputMeshType * iMesh, InputQEType * iEdge) const override
  {
    InputPointIdentifier id1 = iEdge->GetOrigin();
    InputPointIdentifier id2 = iEdge->GetDestination();
 
    InputPointIdentifier idA = iEdge->GetLnext()->GetDestination();
    InputPointIdentifier idB = iEdge->GetRnext()->GetOrigin();
 
    InputPointType pt1 = iMesh->GetPoint(id1);
    InputPointType pt2 = iMesh->GetPoint(id2);
    InputPointType ptA = iMesh->GetPoint(idA);
    InputPointType ptB = iMesh->GetPoint(idB);
 
    InputVectorType v1A = ptA - pt1;
    InputVectorType v1B = ptB - pt1;
    InputVectorType v12 = pt2 - pt1;
 
    InputCoordRepType L1A = v1A * v1A;
    InputCoordRepType L1B = v1B * v1B;
    InputCoordRepType L12 = v12 * v12;
 
    InputCoordRepType L2A = pt2.SquaredEuclideanDistanceTo(ptA);
    InputCoordRepType L2B = pt2.SquaredEuclideanDistanceTo(ptB);
 
    CrossHelper<InputVectorType> cross;
 
    InputCoordRepType AreaA = 0.5 * (cross(v1A, v12).GetNorm());
    InputCoordRepType AreaB = 0.5 * (cross(v1B, v12).GetNorm());
 
    InputCoordRepType oValue = (L1A + L2A - L12) / AreaA + (L1B + L2B - L12) / AreaB;
 
    return oValue;
  }
};
} // namespace itk
#endif