#include <Inertia_Utilities.hpp>

Public Member Functions
void	InertiaMapping2D (const Gedim::GeometryUtilities &geometryUtilities, const Eigen::MatrixXd &vertices, const Eigen::Vector3d &centroid, const double &diameter, const std::vector< Eigen::Matrix3d > &triangulation_vertices, Polydim::Utilities::Inertia_Data &inertia_data) const
	Compute the inertia mapping of a polygon (2D).

void	InertiaMapping3D (const Gedim::GeometryUtilities &geometryUtilities, const Eigen::MatrixXd &vertices, const Eigen::Vector3d &centroid, const double &diameter, const std::vector< Eigen::MatrixXd > &tetrahedrons_vertices, Polydim::Utilities::Inertia_Data &inertia_data) const
	Compute the inertia mapping of a polyhedron (3D).

Member Function Documentation

◆ InertiaMapping2D()

void Polydim::Utilities::Inertia_Utilities::InertiaMapping2D	(	const Gedim::GeometryUtilities &	geometryUtilities,
		const Eigen::MatrixXd &	vertices,
		const Eigen::Vector3d &	centroid,
		const double &	diameter,
		const std::vector< Eigen::Matrix3d > &	triangulation_vertices,
		Polydim::Utilities::Inertia_Data &	inertia_data
	)		const

Compute the inertia mapping of a polygon (2D).

Constructs the affine map that sends the polygon onto an isotropic reference configuration aligned with its principal axes of inertia. The element is first rescaled by its diameter and translated to the centroid; the polygon mass (second-moment) matrix is then assembled from the triangulation and diagonalized (self-adjoint eigensolver), and its eigenpairs define a whitening transform that normalizes and aligns the principal directions; a final diameter rescaling is applied. The resulting map, its inverse, translation, Jacobian magnitude and orientation sign are stored in inertia_data.

Parameters

	geometryUtilities	GeDiM helper providing polygon mass and diameter.
	vertices	Polygon vertices (one per column).
	centroid	Polygon centroid.
	diameter	Polygon diameter \(h_E\) (initial rescaling factor).
	triangulation_vertices	Sub-triangulation of the polygon (per-triangle vertices), used to compute the mass matrix.
[out]	inertia_data	Resulting affine-map data (see Inertia_Data).

Exceptions

std::runtime_error if the inertia (mass) matrix is singular.

◆ InertiaMapping3D()

void Polydim::Utilities::Inertia_Utilities::InertiaMapping3D	(	const Gedim::GeometryUtilities &	geometryUtilities,
		const Eigen::MatrixXd &	vertices,
		const Eigen::Vector3d &	centroid,
		const double &	diameter,
		const std::vector< Eigen::MatrixXd > &	tetrahedrons_vertices,
		Polydim::Utilities::Inertia_Data &	inertia_data
	)		const

Compute the inertia mapping of a polyhedron (3D).

Three-dimensional counterpart of InertiaMapping2D(): builds the affine map that aligns the polyhedron with its principal axes of inertia and normalizes it to an isotropic reference configuration, starting from a tetrahedral decomposition used to assemble the mass (second-moment) matrix. The map, its inverse, translation, Jacobian magnitude and orientation sign are stored in inertia_data.