HolomorphicOneForms.h

#pragma once

#include <CGAL/boost/graph/Seam_mesh.h>
#include <CGAL/Surface_mesh_parameterization/Error_code.h>
#include <Eigen/Dense>
#include <Euclid/Topology/Chain.h>

namespace Euclid
{
template<typename Mesh, typename DerivedA, typename DerivedB>
void holomorphic_one_form_basis(const Mesh& mesh,
                                Eigen::MatrixBase<DerivedA>& primal,
                                Eigen::MatrixBase<DerivedB>& conjugate);

template<typename Mesh, typename DerivedA, typename DerivedB>
void holomorphic_one_form_basis(const Mesh& mesh,
                                const VertexChains<Mesh>& homology_generators,
                                Eigen::MatrixBase<DerivedA>& primal,
                                Eigen::MatrixBase<DerivedB>& conjugate);

template<typename Mesh,
         typename Derived,
         typename SEM,
         typename SVM,
         typename VertexUVMap>
void integrate_holomorphic_one_forms(
    const Mesh& mesh,
    const Eigen::MatrixBase<Derived>& one_forms,
    CGAL::Seam_mesh<Mesh, SEM, SVM>& seam_mesh,
    VertexUVMap uvmap);

template<typename Mesh, typename SEM, typename SVM>
class Holomorphic_one_forms_parameterizer3
{
public:
    using TriangleMesh = CGAL::Seam_mesh<Mesh, SEM, SVM>;
    using halfedge_descriptor =
        typename boost::graph_traits<TriangleMesh>::halfedge_descriptor;

public:
    explicit Holomorphic_one_forms_parameterizer3(const Mesh& mesh);

    Holomorphic_one_forms_parameterizer3(
        const Mesh& mesh,
        const VertexChains<Mesh>& homology_generators);

    template<typename Derived>
    void set_coeffs(const Eigen::MatrixBase<Derived>& coeffs);

    template<typename VertexUVMap,
             typename VertexIndexMap,
             typename VertexParameterizedMap>
    CGAL::Surface_mesh_parameterization::Error_code parameterize(
        TriangleMesh& mesh,
        halfedge_descriptor bhd,
        VertexUVMap uvmap,
        VertexIndexMap vimap,
        VertexParameterizedMap vpmap);

private:
    using Scalar = typename CGAL::Kernel_traits<typename boost::property_traits<
        typename boost::property_map<Mesh, boost::vertex_point_t>::type>::
                                                    value_type>::Kernel::FT;
    using Vector = Eigen::Matrix<Scalar, Eigen::Dynamic, 1>;
    using Matrix = Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic>;

private:
    const Mesh& _underlying_mesh;
    Matrix _primal;
    Matrix _conjugate;
    Matrix _one_forms;
};

} // namespace Euclid

#include "src/HolomorphicOneForms.cpp"