A class that stores any affine transformation of the Freudenthal-Kuhn triangulation. More...

#include <include/gudhi/Freudenthal_triangulation.h>

Public Types
using	Simplex_handle = Permutahedral_representation_
	Type of the simplices in the triangulation.
using	Vertex_handle = typename Permutahedral_representation_::Vertex
	Type of the vertices in the triangulation.

Public Member Functions
	Freudenthal_triangulation (std::size_t dimension)
	Constructor of the Freudenthal-Kuhn triangulation of a given dimension.
	Freudenthal_triangulation (std::size_t dimension, const Matrix &matrix)
	Constructor of the Freudenthal-Kuhn triangulation of a given dimension under a linear transformation by a given matrix.
	Freudenthal_triangulation (unsigned dimension, const Matrix &matrix, const Vector &offset)
	Constructor of the Freudenthal-Kuhn triangulation of a given dimension under an affine transformation by a given matrix and a translation vector.
unsigned	dimension () const
	Dimension of the triangulation.
const Matrix &	matrix () const
	Matrix that defines the linear transformation of the triangulation.
const Vector &	offset () const
	Vector that defines the offset of the triangulation.
void	change_matrix (const Eigen::MatrixXd &matrix)
	Change the linear transformation matrix to a given value.
void	change_offset (const Eigen::VectorXd &offset)
	Change the offset vector to a given value.
template<class Point_d>
Simplex_handle	locate_point (const Point_d &point, double scale=1) const
	Returns the permutahedral representation of the simplex in the triangulation that contains a given query point.
Eigen::VectorXd	cartesian_coordinates (const Vertex_handle &vertex, double scale=1) const
	Returns the Cartesian coordinates of the given vertex.
Eigen::VectorXd	barycenter (const Simplex_handle &simplex, double scale=1) const
	Returns the Cartesian coordinates of the barycenter of a given simplex.

Detailed Description

template<class Permutahedral_representation_ = Permutahedral_representation<std::vector<int>, std::vector<std::vector<std::size_t> > >>
class Gudhi::coxeter_triangulation::Freudenthal_triangulation< Permutahedral_representation_ >

A class that stores any affine transformation of the Freudenthal-Kuhn triangulation.

The data structure is a record that consists of a matrix that represents the linear transformation of the Freudenthal-Kuhn triangulation and a vector that represents the offset.

Template Parameters

Permutahedral_representation_ Type of a simplex given by a permutahedral representation. Needs to be a model of SimplexInCoxeterTriangulation.

Constructor & Destructor Documentation

◆ Freudenthal_triangulation() [1/3]

template<class Permutahedral_representation_ = Permutahedral_representation<std::vector<int>, std::vector<std::vector<std::size_t> > >>

Gudhi::coxeter_triangulation::Freudenthal_triangulation< Permutahedral_representation_ >::Freudenthal_triangulation ( std::size_t dimension )

inline

Constructor of the Freudenthal-Kuhn triangulation of a given dimension.

Parameters

[in] dimension The dimension of the triangulation.

◆ Freudenthal_triangulation() [2/3]

template<class Permutahedral_representation_ = Permutahedral_representation<std::vector<int>, std::vector<std::vector<std::size_t> > >>

Gudhi::coxeter_triangulation::Freudenthal_triangulation< Permutahedral_representation_ >::Freudenthal_triangulation	(	std::size_t	dimension,
		const Matrix &	matrix )

inline

Constructor of the Freudenthal-Kuhn triangulation of a given dimension under a linear transformation by a given matrix.

Parameters

[in]	dimension	The dimension of the triangulation.
[in]	matrix	The matrix that defines the linear transformation. Needs to be invertible.

◆ Freudenthal_triangulation() [3/3]

template<class Permutahedral_representation_ = Permutahedral_representation<std::vector<int>, std::vector<std::vector<std::size_t> > >>

Gudhi::coxeter_triangulation::Freudenthal_triangulation< Permutahedral_representation_ >::Freudenthal_triangulation	(	unsigned	dimension,
		const Matrix &	matrix,
		const Vector &	offset )

inline

Constructor of the Freudenthal-Kuhn triangulation of a given dimension under an affine transformation by a given matrix and a translation vector.

Parameters

[in]	dimension	The dimension of the triangulation.
[in]	matrix	The matrix that defines the linear transformation. Needs to be invertible.
[in]	offset	The offset vector.

Exceptions

std::invalid_argument In debug mode, if offset size is different from dimension.

Member Function Documentation

◆ barycenter()

template<class Permutahedral_representation_ = Permutahedral_representation<std::vector<int>, std::vector<std::vector<std::size_t> > >>

Eigen::VectorXd Gudhi::coxeter_triangulation::Freudenthal_triangulation< Permutahedral_representation_ >::barycenter	(	const Simplex_handle &	simplex,
		double	scale = 1 ) const

inline

Returns the Cartesian coordinates of the barycenter of a given simplex.

Using the additional parameter scale, the search can be done in a triangulation that shares the origin, but is scaled by a given factor. This parameter can be useful to simulate the computation of Cartesian coordinates of the barycenter of a simplex in a subdivided triangulation.

Parameters

[in]	simplex	The query simplex.
[in]	scale	The scale of the triangulation.

◆ cartesian_coordinates()

template<class Permutahedral_representation_ = Permutahedral_representation<std::vector<int>, std::vector<std::vector<std::size_t> > >>

Eigen::VectorXd Gudhi::coxeter_triangulation::Freudenthal_triangulation< Permutahedral_representation_ >::cartesian_coordinates	(	const Vertex_handle &	vertex,
		double	scale = 1 ) const

inline

Returns the Cartesian coordinates of the given vertex.

Using the additional parameter scale, the search can be done in a triangulation that shares the origin, but is scaled by a given factor. This parameter can be useful to simulate the computation of Cartesian coordinates of a vertex in a subdivided triangulation.

Parameters

[in]	vertex	The query vertex.
[in]	scale	The scale of the triangulation.

◆ change_matrix()

template<class Permutahedral_representation_ = Permutahedral_representation<std::vector<int>, std::vector<std::vector<std::size_t> > >>

void Gudhi::coxeter_triangulation::Freudenthal_triangulation< Permutahedral_representation_ >::change_matrix ( const Eigen::MatrixXd & matrix )

inline

Change the linear transformation matrix to a given value.

Parameters

[in] matrix New value of the linear transformation matrix.

Examples: manifold_tracing_flat_torus_with_boundary.cpp.

◆ change_offset()

template<class Permutahedral_representation_ = Permutahedral_representation<std::vector<int>, std::vector<std::vector<std::size_t> > >>

void Gudhi::coxeter_triangulation::Freudenthal_triangulation< Permutahedral_representation_ >::change_offset ( const Eigen::VectorXd & offset )

inline

Change the offset vector to a given value.

Parameters

[in] offset New value of the offset vector.

Examples: cell_complex_from_basic_circle_manifold.cpp, and manifold_tracing_flat_torus_with_boundary.cpp.

◆ locate_point()

template<class Permutahedral_representation_ = Permutahedral_representation<std::vector<int>, std::vector<std::vector<std::size_t> > >>

template<class Point_d>

Simplex_handle Gudhi::coxeter_triangulation::Freudenthal_triangulation< Permutahedral_representation_ >::locate_point	(	const Point_d &	point,
		double	scale = 1 ) const

inline

Returns the permutahedral representation of the simplex in the triangulation that contains a given query point.

Using the additional parameter scale, the search can be done in a triangulation that shares the origin, but is scaled by a given factor. This parameter can be useful to simulate the point location in a subdivided triangulation. The returned simplex is always minimal by inclusion.

Template Parameters

Point_d A class that represents a point in d-dimensional Euclidean space. The coordinates should be random-accessible. Needs to provide the method size().

Parameters

[in]	point	The query point.
[in]	scale	The scale of the triangulation.

Exceptions

std::invalid_argument In debug mode, if point dimension is different from triangulation one.

The documentation for this class was generated from the following file:

include/gudhi/Freudenthal_triangulation.h

Public Types

Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ Freudenthal_triangulation() [1/3]

◆ Freudenthal_triangulation() [2/3]

◆ Freudenthal_triangulation() [3/3]

Member Function Documentation

◆ barycenter()

◆ cartesian_coordinates()

◆ change_matrix()

◆ change_offset()

◆ locate_point()