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Gudhi::coxeter_triangulation::Permutahedral_representation< Vertex_, Ordered_set_partition_ > Class Template Reference

A class that stores the permutahedral representation of a simplex in a Coxeter triangulation or a Freudenthal-Kuhn triangulation. More...

#include <include/gudhi/Permutahedral_representation.h>

## Public Types

typedef Vertex_ Vertex
Type of the vertex.

typedef Ordered_set_partition_ OrderedSetPartition
Type of the ordered partition.

## Public Member Functions

Permutahedral_representation (const Vertex &vertex, const OrderedSetPartition &partition)
Permutahedral_representation constructor from a vertex and an ordered set partition. More...

Permutahedral_representation ()
Constructor for an empty permutahedral representation that does not correspond to any simplex.

std::size_t dimension () const
Dimension of the simplex.

Vertexvertex ()
Lexicographically-minimal vertex.

const Vertexvertex () const
Lexicographically-minimal vertex.

OrderedSetPartitionpartition ()
Ordered set partition.

const OrderedSetPartitionpartition () const
Identifying vertex.

bool operator== (const Permutahedral_representation &other) const
Equality operator. Returns true if an only if both vertex and the ordered set partition coincide.

bool operator!= (const Permutahedral_representation &other) const
Inequality operator. Returns true if an only if either vertex or the ordered set partition are different.

Vertex_range vertex_range () const
Returns a range of vertices of the simplex. The type of vertices is Vertex.

Face_range face_range (std::size_t value_dim) const
Returns a range of permutahedral representations of faces of the simplex. More...

Face_range facet_range () const
Returns a range of permutahedral representations of facets of the simplex. The dimension of the simplex must be strictly positive.

Coface_range coface_range (std::size_t value_dim) const
Returns a range of permutahedral representations of cofaces of the simplex. More...

Coface_range cofacet_range () const
Returns a range of permutahedral representations of cofacets of the simplex. The dimension of the simplex must be strictly different from the ambient dimension (the size of the vertex).

bool is_face_of (const Permutahedral_representation &other) const
Returns true, if the simplex is a face of other simplex. More...

## Detailed Description

template<class Vertex_, class Ordered_set_partition_>
class Gudhi::coxeter_triangulation::Permutahedral_representation< Vertex_, Ordered_set_partition_ >

A class that stores the permutahedral representation of a simplex in a Coxeter triangulation or a Freudenthal-Kuhn triangulation.

The data structure is a record consisting of a range that represents the vertex and a range that represents the ordered set partition, both of which identify the simplex in the triangulation.

Template Parameters
 Vertex_ needs to be a random-access range. Ordered_set_partition_ needs to be a a random-access range that consists of random-access ranges.

## ◆ Permutahedral_representation()

template<class Vertex_ , class Ordered_set_partition_ >
 Gudhi::coxeter_triangulation::Permutahedral_representation< Vertex_, Ordered_set_partition_ >::Permutahedral_representation ( const Vertex & vertex, const OrderedSetPartition & partition )
inline

Permutahedral_representation constructor from a vertex and an ordered set partition.

Parameters
 [in] vertex Vertex. [in] partition Ordered set partition.

If the size of vertex is d, the ranges in partition must consist of the integers 0,...,d without repetition or collision between the ranges.

## ◆ coface_range()

template<class Vertex_ , class Ordered_set_partition_ >
 Coface_range Gudhi::coxeter_triangulation::Permutahedral_representation< Vertex_, Ordered_set_partition_ >::coface_range ( std::size_t value_dim ) const
inline

Returns a range of permutahedral representations of cofaces of the simplex.

Parameters
 [in] value_dim The dimension of the cofaces. Must be between the dimension of the simplex and the ambient dimension (the size of the vertex).

## ◆ face_range()

template<class Vertex_ , class Ordered_set_partition_ >
 Face_range Gudhi::coxeter_triangulation::Permutahedral_representation< Vertex_, Ordered_set_partition_ >::face_range ( std::size_t value_dim ) const
inline

Returns a range of permutahedral representations of faces of the simplex.

Parameters
 [in] value_dim The dimension of the faces. Must be between 0 and the dimension of the simplex.

## ◆ is_face_of()

template<class Vertex_ , class Ordered_set_partition_ >
 bool Gudhi::coxeter_triangulation::Permutahedral_representation< Vertex_, Ordered_set_partition_ >::is_face_of ( const Permutahedral_representation< Vertex_, Ordered_set_partition_ > & other ) const
inline

Returns true, if the simplex is a face of other simplex.

Parameters
 [in] other A simplex that is potential a coface of the current simplex.

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