MapParallelepiped.hpp

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// Copyright (C) 2019 - 2025.
// Terms register on the GPL-3.0 license.
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// See top level LICENSE file for more details.
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// This file can be used citing references in CITATION.cff file.
 
#ifndef __MapParallelepiped_H
#define __MapParallelepiped_H
 
#include "Eigen/Eigen"
#include "GeometryUtilities.hpp"
 
namespace Gedim
{
class MapParallelepiped
{
  public:
    struct MapParallelepipedData final
    {
        Eigen::Matrix3d Q;
        Eigen::Vector3d b;
        Eigen::Matrix3d QInv;
        double DetQ;
        double DetQInv;
    };
 
    Eigen::MatrixXd ReferenceVertices;
 
  private:
    const Gedim::GeometryUtilities &geometryUtilities;
 
    bool TestMapConfiguration(const Eigen::MatrixXd &vertices,
                              const std::vector<unsigned int> &coordinateSystem,
                              const Eigen::MatrixXd &referencePoints,
                              const unsigned int &secondVertexIndex,
                              const unsigned int &thirdVertexIndex,
                              const unsigned int &fourthVertexIndex,
                              MapParallelepiped::MapParallelepipedData &result) const;
 
  public:
    MapParallelepiped(const Gedim::GeometryUtilities &geometryUtilities);
 
    ~MapParallelepiped()
    {
    }
 
    static Eigen::Matrix3d Q(const Eigen::Vector3d &firstVertex,
                             const Eigen::Vector3d &secondVertex,
                             const Eigen::Vector3d &thirdVertex,
                             const Eigen::Vector3d &fourthVertex)
    {
        Eigen::Matrix3d Q;
        Q.row(0) << secondVertex.x() - firstVertex.x(), thirdVertex.x() - firstVertex.x(),
            fourthVertex.x() - firstVertex.x();
        Q.row(1) << secondVertex.y() - firstVertex.y(), thirdVertex.y() - firstVertex.y(),
            fourthVertex.y() - firstVertex.y();
        Q.row(2) << secondVertex.z() - firstVertex.z(), thirdVertex.z() - firstVertex.z(),
            fourthVertex.z() - firstVertex.z();
 
        return Q;
    }
 
    static inline Eigen::Vector3d b(const Eigen::Vector3d &firstVertex)
    {
        return firstVertex;
    }
 
    MapParallelepipedData Compute(const Eigen::MatrixXd &vertices, const std::vector<unsigned int> &coordinateSystem) const;
 
    static inline Eigen::MatrixXd F(const MapParallelepipedData &mapData, const Eigen::MatrixXd &x)
    {
        return (mapData.Q * x).colwise() + mapData.b;
    }
 
    static inline Eigen::MatrixXd FInv(const MapParallelepipedData &mapData, const Eigen::MatrixXd &x)
    {
        return mapData.QInv * (x.colwise() - mapData.b);
    }
 
    static Eigen::MatrixXd J(const MapParallelepipedData &mapData, const Eigen::MatrixXd &x);
 
    static Eigen::VectorXd DetJ(const MapParallelepipedData &mapData, const Eigen::MatrixXd &x);
};
} // namespace Gedim
 
#endif // __MapParallelepiped_H