FEM_PCC_1D_LocalSpace.hpp

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//
// Copyright (C) 2019 - 2025.
// Terms register on the GPL-3.0 license.
//
// This file can be redistributed and/or modified under the license terms.
//
// See top level LICENSE file for more details.
//
// This file can be used citing references in CITATION.cff file.
 
#ifndef __FEM_PCC_1D_LocalSpace_HPP
#define __FEM_PCC_1D_LocalSpace_HPP
 
#include "FEM_PCC_1D_ReferenceElement.hpp"
 
namespace Polydim
{
namespace FEM
{
namespace PCC
{
struct FEM_PCC_1D_Segment_Geometry final
{
    double Tolerance1D;
 
    Eigen::Vector3d Origin;
    Eigen::Vector3d Tangent;
    double Length;
};
 
struct FEM_PCC_1D_LocalSpace_Data final
{
    struct SegmentMapData
    {
        Eigen::Vector3d Origin;
        Eigen::Vector3d Tangent;
        double Length;
        double SquaredLength;
    };
 
    Polydim::FEM::PCC::FEM_PCC_1D_LocalSpace_Data::SegmentMapData MapData;
    unsigned int Order;
    unsigned int NumberOfBasisFunctions;
    Eigen::MatrixXd Dofs;
    std::vector<unsigned int> DofsMeshOrder;
    std::array<unsigned int, 3> Dof0DsIndex;
    std::array<unsigned int, 2> Dof1DsIndex;
    Gedim::Quadrature::QuadratureData InternalQuadrature;
};
 
class FEM_PCC_1D_LocalSpace final
{
  private:
    Eigen::MatrixXd F(const Polydim::FEM::PCC::FEM_PCC_1D_LocalSpace_Data::SegmentMapData &mapData, const Eigen::MatrixXd &x) const
    {
        Eigen::MatrixXd points(3, x.cols());
 
        for (unsigned int p = 0; p < x.cols(); ++p)
            points.col(p) << mapData.Origin + mapData.Tangent * x(0, p);
 
        return points;
    }
 
    Eigen::MatrixXd FInv(const Polydim::FEM::PCC::FEM_PCC_1D_LocalSpace_Data::SegmentMapData &mapData, const Eigen::MatrixXd &x) const
    {
        Eigen::MatrixXd points(3, x.cols());
 
        for (unsigned int p = 0; p < x.cols(); ++p)
            points(0, p) = (x.col(p) - mapData.Origin).dot(mapData.Tangent) / mapData.SquaredLength;
 
        return points;
    }
 
    inline Eigen::VectorXd DetJ(const Polydim::FEM::PCC::FEM_PCC_1D_LocalSpace_Data::SegmentMapData &mapData,
                                const Eigen::MatrixXd &x) const
    {
        return Eigen::VectorXd::Constant(x.cols(), mapData.Length);
    }
 
    Eigen::MatrixXd MapValues(const Polydim::FEM::PCC::FEM_PCC_1D_LocalSpace_Data &local_space,
                              const Eigen::MatrixXd &referenceValues) const;
 
    std::vector<Eigen::MatrixXd> MapDerivativeValues(const Polydim::FEM::PCC::FEM_PCC_1D_LocalSpace_Data &local_space,
                                                     const std::vector<Eigen::MatrixXd> &referenceDerivateValues) const;
 
    Gedim::Quadrature::QuadratureData InternalQuadrature(const Gedim::Quadrature::QuadratureData &reference_quadrature,
                                                         const Polydim::FEM::PCC::FEM_PCC_1D_LocalSpace_Data::SegmentMapData &mapData) const;
 
  public:
    Polydim::FEM::PCC::FEM_PCC_1D_LocalSpace_Data CreateLocalSpace(const Polydim::FEM::PCC::FEM_PCC_1D_ReferenceElement_Data &reference_element_data,
                                                                   const Polydim::FEM::PCC::FEM_PCC_1D_Segment_Geometry &segment) const;
 
    inline Eigen::MatrixXd ComputeBasisFunctionsValues(const Polydim::FEM::PCC::FEM_PCC_1D_ReferenceElement_Data &reference_element_data,
                                                       const Polydim::FEM::PCC::FEM_PCC_1D_LocalSpace_Data &local_space) const
    {
        return MapValues(local_space, reference_element_data.ReferenceBasisFunctionValues);
    }
 
    inline std::vector<Eigen::MatrixXd> ComputeBasisFunctionsDerivativeValues(
        const Polydim::FEM::PCC::FEM_PCC_1D_ReferenceElement_Data &reference_element_data,
        const Polydim::FEM::PCC::FEM_PCC_1D_LocalSpace_Data &local_space) const
    {
        return MapDerivativeValues(local_space, reference_element_data.ReferenceBasisFunctionDerivativeValues);
    }
 
    inline Eigen::MatrixXd ComputeBasisFunctionsValues(const Polydim::FEM::PCC::FEM_PCC_1D_ReferenceElement_Data &reference_element_data,
                                                       const Polydim::FEM::PCC::FEM_PCC_1D_LocalSpace_Data &local_space,
                                                       const Eigen::MatrixXd &points) const
    {
        const Eigen::MatrixXd referencePoints = FInv(local_space.MapData, points);
 
        Polydim::FEM::PCC::FEM_PCC_1D_ReferenceElement reference_element;
 
        return MapValues(local_space, reference_element.EvaluateBasisFunctions(referencePoints, reference_element_data));
    }
 
    inline std::vector<Eigen::MatrixXd> ComputeBasisFunctionsDerivativeValues(
        const Polydim::FEM::PCC::FEM_PCC_1D_ReferenceElement_Data &reference_element_data,
        const Polydim::FEM::PCC::FEM_PCC_1D_LocalSpace_Data &local_space,
        const Eigen::MatrixXd &points) const
    {
        const Eigen::MatrixXd referencePoints = FInv(local_space.MapData, points);
 
        Polydim::FEM::PCC::FEM_PCC_1D_ReferenceElement reference_element;
 
        return MapDerivativeValues(local_space, reference_element.EvaluateBasisFunctionDerivatives(referencePoints, reference_element_data));
    }
 
    inline Eigen::MatrixXd InternalDOFsCoordinates(const Polydim::FEM::PCC::FEM_PCC_1D_ReferenceElement_Data &reference_element_data,
                                                   const Polydim::FEM::PCC::FEM_PCC_1D_LocalSpace_Data &local_space) const
    {
        const auto &dof_coordinates = local_space.Dofs;
 
        const unsigned int starting_index = local_space.Dof1DsIndex.at(0);
        const unsigned int num_internal_dofs = reference_element_data.NumDofs1D;
 
        if (num_internal_dofs == 0)
            return Eigen::MatrixXd(0, 0);
 
        const Eigen::MatrixXd edge_dofs_coordinates = dof_coordinates.block(0, starting_index, 3, num_internal_dofs);
 
        return edge_dofs_coordinates;
    }
};
} // namespace PCC
} // namespace FEM
} // namespace Polydim
 
#endif