A class that stores Coxeter triangulation of type \(\tilde{A}_d\). This triangulation has the greatest simplex quality out of all linear transformations of the Freudenthal-Kuhn triangulation. More...

#include <include/gudhi/Coxeter_triangulation.h>

Public Member Functions
	Coxeter_triangulation (std::size_t dimension)
	Constructor of Coxeter triangulation of a given dimension. More...

Public Member Functions inherited from Gudhi::coxeter_triangulation::Freudenthal_triangulation< Permutahedral_representation_ >
	Freudenthal_triangulation (std::size_t dimension)
	Constructor of the Freudenthal-Kuhn triangulation of a given dimension. More...

	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. More...

	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. More...

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. More...

void	change_offset (const Eigen::VectorXd &offset)
	Change the offset vector to a given value. More...

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. More...

Eigen::VectorXd	cartesian_coordinates (const Vertex_handle &vertex, double scale=1) const
	Returns the Cartesian coordinates of the given vertex. More...

Eigen::VectorXd	barycenter (const Simplex_handle &simplex, double scale=1) const
	Returns the Cartesian coordinates of the barycenter of a given simplex. More...

Additional Inherited Members
Public Types inherited from Gudhi::coxeter_triangulation::Freudenthal_triangulation< Permutahedral_representation_ >
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.

Detailed Description

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

A class that stores Coxeter triangulation of type \(\tilde{A}_d\). This triangulation has the greatest simplex quality out of all linear transformations of the Freudenthal-Kuhn triangulation.

Template Parameters

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

Examples: cell_complex_from_basic_circle_manifold.cpp, manifold_tracing_custom_function.cpp, and manifold_tracing_flat_torus_with_boundary.cpp.

Constructor & Destructor Documentation

◆ Coxeter_triangulation()

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

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

inline

Constructor of Coxeter triangulation of a given dimension.

Parameters

[in] dimension The dimension of the triangulation.

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

include/gudhi/Coxeter_triangulation.h

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ Coxeter_triangulation()