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Gudhi::coxeter_triangulation::Coxeter_triangulation< Permutahedral_representation_ > Class Template Reference

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...

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.

## ◆ 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: