Simplex Tree data structure for representing simplicial complexes. More...

#include <Simplex_tree.h>

Public Types
typedef FiltrationValue	Filtration_value
	Type for the value of the filtration function. More...

typedef SimplexKey	Simplex_key
	Key associated to each simplex. More...

typedef VertexHandle	Vertex_handle
	Type for the vertex handle. More...

typedef Dictionary::iterator	Simplex_handle
	Handle type to a simplex contained in the simplicial complex represented byt he simplex tree.

Range and iterator types
The naming convention is Container_content_(iterator/range). A Container_content_range is essentially an object on which the methods begin() and end() can be called. They both return an object of type Container_content_iterator, and allow the traversal of the range [ begin();end() ).
typedef boost::transform_iterator < return_first, Dictionary_it >	Complex_vertex_iterator
	Iterator over the vertices of the simplicial complex. More...

typedef boost::iterator_range < Complex_vertex_iterator >	Complex_vertex_range
	Range over the vertices of the simplicial complex.

typedef Simplex_tree_simplex_vertex_iterator < Simplex_tree >	Simplex_vertex_iterator
	Iterator over the vertices of a simplex. More...

typedef boost::iterator_range < Simplex_vertex_iterator >	Simplex_vertex_range
	Range over the vertices of a simplex.

typedef Simplex_tree_boundary_simplex_iterator < Simplex_tree >	Boundary_simplex_iterator
	Iterator over the simplices of the boundary of a simplex. More...

typedef boost::iterator_range < Boundary_simplex_iterator >	Boundary_simplex_range
	Range over the simplices of the boundary of a simplex.

typedef Simplex_tree_complex_simplex_iterator < Simplex_tree >	Complex_simplex_iterator
	Iterator over the simplices of the simplicial complex. More...

typedef boost::iterator_range < Complex_simplex_iterator >	Complex_simplex_range
	Range over the simplices of the simplicial complex.

typedef Simplex_tree_skeleton_simplex_iterator < Simplex_tree >	Skeleton_simplex_iterator
	Iterator over the simplices of the skeleton of the simplicial complex, for a given dimension. More...

typedef boost::iterator_range < Skeleton_simplex_iterator >	Skeleton_simplex_range
	Range over the simplices of the skeleton of the simplicial complex, for a given dimension.

typedef std::vector < Simplex_handle >::iterator	Filtration_simplex_iterator
	Iterator over the simplices of the simplicial complex, ordered by the filtration. More...

typedef boost::iterator_range < Filtration_simplex_iterator >	Filtration_simplex_range
	Range over the simplices of the simplicial complex, ordered by the filtration.

Public Types inherited from FilteredComplex
typedef unspecified	Simplex_handle

typedef unspecified	Simplex_key
	Key associated to each simplex. More...

typedef unspecified	Filtration_value
	Type for the value of the filtration function. More...

typedef unspecified	Indexing_tag
	Specifies the nature of the indexing scheme. More...

typedef unspecified	Boundary_simplex_iterator
	Iterator on the simplices belonging to the boundary of a simplex. More...

typedef unspecified	Boundary_simplex_range
	Range giving access to the simplices in the boundary of a simplex. More...

typedef unspecified	Filtration_simplex_iterator
	Iterator over all simplices of the complex in the order of the indexing scheme. More...

typedef unspecified	Filtration_simplex_range
	Range over the simplices of the complex in the order of the filtration. More...

Public Member Functions
Simplex_key	key (Simplex_handle sh)
	Returns the key associated to a simplex. More...

Simplex_handle	simplex (Simplex_key key)
	Returns the simplex associated to a key. More...

Filtration_value	filtration (Simplex_handle sh)
	Returns the filtration value of a simplex. More...

Filtration_value	filtration ()
	Returns an upper bound of the filtration values of the simplices.

Simplex_handle	null_simplex ()
	Returns a Simplex_handle different from all Simplex_handles associated to the simplices in the simplicial complex. More...

Simplex_key	null_key ()
	Returns a key different for all keys associated to the simplices of the simplicial complex.

Vertex_handle	null_vertex ()
	Returns a Vertex_handle different from all Vertex_handles associated to the vertices of the simplicial complex.

size_t	num_vertices ()
	Returns the number of vertices in the complex.

const unsigned int &	num_simplices () const
	Returns the number of simplices in the complex. More...

int	dimension (Simplex_handle sh)
	Returns the dimension of a simplex. More...

int	dimension ()
	Returns an upper bound on the dimension of the simplicial complex.

bool	has_children (Simplex_handle sh)
	Returns true iff the node in the simplex tree pointed by sh has children.

template<class RandomAccessVertexRange >
Simplex_handle	find (const RandomAccessVertexRange &s)
	Given a range of Vertex_handles, returns the Simplex_handle of the simplex in the simplicial complex containing the corresponding vertices. Return null_simplex() if the simplex is not in the complex. More...

Simplex_handle	find_vertex (Vertex_handle v)
	Returns the Simplex_handle corresponding to the 0-simplex representing the vertex with Vertex_handle v.

template<class RandomAccessVertexRange >
std::pair< Simplex_handle, bool >	insert (RandomAccessVertexRange &simplex, Filtration_value filtration)
	Insert a simplex, represented by a range of Vertex_handles, in the simplicial complex. More...

void	assign_key (Simplex_handle sh, Simplex_key key)
	Assign a value 'key' to the key of the simplex represented by the Simplex_handle 'sh'.

std::pair< Simplex_handle, Simplex_handle >	endpoints (Simplex_handle sh)

Siblings *	self_siblings (Simplex_handle sh)

Siblings *	root ()

void	set_filtration (Filtration_value fil)

void	set_num_simplices (const unsigned int &num_simplices)

void	set_dimension (int dimension)

void	initialize_filtration ()
	Initializes the filtrations, i.e. sort the simplices according to their order in the filtration and initializes all Simplex_keys. More...

template<class OneSkeletonGraph >
void	insert_graph (const OneSkeletonGraph &skel_graph)
	Inserts a 1-skeleton in an empty Simplex_tree. More...

void	expansion (int max_dim)
	Expands the Simplex_tree containing only its one skeleton until dimension max_dim. More...

void	print_hasse (std::ostream &os)
	Write the hasse diagram of the simplicial complex in os. More...

Range and iterator methods
Complex_vertex_range	complex_vertex_range ()
	Returns a range over the vertices of the simplicial complex. More...

Complex_simplex_range	complex_simplex_range ()
	Returns a range over the simplices of the simplicial complex. More...

Skeleton_simplex_range	skeleton_simplex_range (int dim)
	Returns a range over the simplices of the dim-skeleton of the simplicial complex. More...

Filtration_simplex_range	filtration_simplex_range (linear_indexing_tag)
	Returns a range over the simplices of the simplicial complex, in the order of the filtration. More...

Filtration_simplex_range	filtration_simplex_range ()

Simplex_vertex_range	simplex_vertex_range (Simplex_handle sh)
	Returns a range over the vertices of a simplex. More...

Boundary_simplex_range	boundary_simplex_range (Simplex_handle sh)
	Returns a range over the simplices of the boundary of a simplex. More...

Constructor/Destructor
	Simplex_tree ()
	Constructs an empty simplex tree.

	~Simplex_tree ()
	Destructor; deallocates the whole tree structure.

Public Member Functions inherited from FilteredComplex
Simplex_handle	null_simplex ()

size_t	num_simplices ()
	Returns the number of simplices in the complex. More...

int	dimension (Simplex_handle sh)
	Returns the dimension of a simplex.

Filtration_value	filtration (Simplex_handle sh)
	Returns the filtration value of a simplex. More...

Simplex_key	null_key ()
	Returns a key that is different from the keys associated to the simplices.

Simplex_key	key (Simplex_handle sh)
	Returns the key associated to a simplex.

Simplex_handle	simplex (Simplex_key key)
	Returns the simplex associated to a key. More...

void	assign_key (Simplex_handle sh, Simplex_key key)
	Assign a key to a simplex.

Boundary_simplex_range	boundary_simplex_range (Simplex_handle sh)
	Returns a range giving access to all simplices of the boundary of a simplex, i.e. the set of codimension 1 subsimplices of the Simplex. More...

Filtration_simplex_range	filtration_simplex_range ()
	Returns a range over the simplices of the complex in the order of the filtration. More...

Detailed Description

template<typename IndexingTag = linear_indexing_tag, typename FiltrationValue = double, typename SimplexKey = int, typename VertexHandle = int>
class Gudhi::Simplex_tree< IndexingTag, FiltrationValue, SimplexKey, VertexHandle >

Simplex Tree data structure for representing simplicial complexes.

Every simplex $[v_0, \cdots ,v_d]$ admits a canonical orientation induced by the order relation on vertices $v_0 < \cdots < v_d$ .

Details may be found in [4].

Member Typedef Documentation

template<typename IndexingTag = linear_indexing_tag, typename FiltrationValue = double, typename SimplexKey = int, typename VertexHandle = int>

typedef Simplex_tree_boundary_simplex_iterator<Simplex_tree> Gudhi::Simplex_tree< IndexingTag, FiltrationValue, SimplexKey, VertexHandle >::Boundary_simplex_iterator

Iterator over the simplices of the boundary of a simplex.

'value_type' is Simplex_handle.

template<typename IndexingTag = linear_indexing_tag, typename FiltrationValue = double, typename SimplexKey = int, typename VertexHandle = int>

typedef Simplex_tree_complex_simplex_iterator<Simplex_tree> Gudhi::Simplex_tree< IndexingTag, FiltrationValue, SimplexKey, VertexHandle >::Complex_simplex_iterator

Iterator over the simplices of the simplicial complex.

'value_type' is Simplex_handle.

template<typename IndexingTag = linear_indexing_tag, typename FiltrationValue = double, typename SimplexKey = int, typename VertexHandle = int>

typedef boost::transform_iterator<return_first, Dictionary_it> Gudhi::Simplex_tree< IndexingTag, FiltrationValue, SimplexKey, VertexHandle >::Complex_vertex_iterator

Iterator over the vertices of the simplicial complex.

'value_type' is Vertex_handle.

template<typename IndexingTag = linear_indexing_tag, typename FiltrationValue = double, typename SimplexKey = int, typename VertexHandle = int>

typedef std::vector<Simplex_handle>::iterator Gudhi::Simplex_tree< IndexingTag, FiltrationValue, SimplexKey, VertexHandle >::Filtration_simplex_iterator

Iterator over the simplices of the simplicial complex, ordered by the filtration.

'value_type' is Simplex_handle.

template<typename IndexingTag = linear_indexing_tag, typename FiltrationValue = double, typename SimplexKey = int, typename VertexHandle = int>

typedef FiltrationValue Gudhi::Simplex_tree< IndexingTag, FiltrationValue, SimplexKey, VertexHandle >::Filtration_value

Type for the value of the filtration function.

Must be comparable with <.

template<typename IndexingTag = linear_indexing_tag, typename FiltrationValue = double, typename SimplexKey = int, typename VertexHandle = int>

typedef SimplexKey Gudhi::Simplex_tree< IndexingTag, FiltrationValue, SimplexKey, VertexHandle >::Simplex_key

Key associated to each simplex.

Must be a signed integer type.

template<typename IndexingTag = linear_indexing_tag, typename FiltrationValue = double, typename SimplexKey = int, typename VertexHandle = int>

typedef Simplex_tree_simplex_vertex_iterator<Simplex_tree> Gudhi::Simplex_tree< IndexingTag, FiltrationValue, SimplexKey, VertexHandle >::Simplex_vertex_iterator

Iterator over the vertices of a simplex.

'value_type' is Vertex_handle.

template<typename IndexingTag = linear_indexing_tag, typename FiltrationValue = double, typename SimplexKey = int, typename VertexHandle = int>

typedef Simplex_tree_skeleton_simplex_iterator<Simplex_tree> Gudhi::Simplex_tree< IndexingTag, FiltrationValue, SimplexKey, VertexHandle >::Skeleton_simplex_iterator

Iterator over the simplices of the skeleton of the simplicial complex, for a given dimension.

'value_type' is Simplex_handle.

template<typename IndexingTag = linear_indexing_tag, typename FiltrationValue = double, typename SimplexKey = int, typename VertexHandle = int>

typedef VertexHandle Gudhi::Simplex_tree< IndexingTag, FiltrationValue, SimplexKey, VertexHandle >::Vertex_handle

Type for the vertex handle.

Must be a signed integer type. It admits a total order <.

Member Function Documentation

template<typename IndexingTag = linear_indexing_tag, typename FiltrationValue = double, typename SimplexKey = int, typename VertexHandle = int>

Boundary_simplex_range Gudhi::Simplex_tree< IndexingTag, FiltrationValue, SimplexKey, VertexHandle >::boundary_simplex_range ( Simplex_handle sh )

inline

Returns a range over the simplices of the boundary of a simplex.

The boundary of a simplex is the set of codimension $1$ subsimplices of the simplex. If the simplex is $[v_0, \cdots ,v_d]$ , with canonical orientation induced by $v_0 < \cdots < v_d$ , the iterator enumerates the simplices of the boundary in the order: $[v_0,\cdots,\widehat{v_i},\cdots,v_d]$ for $i$ from $0$ to $d$ , where $\widehat{v_i}$ means that the vertex $v_i$ is omitted.

We note that the alternate sum of the simplices given by the iterator gives $(-1)^{\text{dim} \sigma}$ the chains corresponding to the boundary of the simplex.

Parameters

[in] sh Simplex for which the boundary is computed.

template<typename IndexingTag = linear_indexing_tag, typename FiltrationValue = double, typename SimplexKey = int, typename VertexHandle = int>

Complex_simplex_range Gudhi::Simplex_tree< IndexingTag, FiltrationValue, SimplexKey, VertexHandle >::complex_simplex_range ( )

inline

Returns a range over the simplices of the simplicial complex.

In the Simplex_tree, the tree is traverse in a depth-first fashion. Consequently, simplices are ordered according to lexicographic order on the list of Vertex_handles of a simplex, read in increasing < order for Vertex_handles.

template<typename IndexingTag = linear_indexing_tag, typename FiltrationValue = double, typename SimplexKey = int, typename VertexHandle = int>

Complex_vertex_range Gudhi::Simplex_tree< IndexingTag, FiltrationValue, SimplexKey, VertexHandle >::complex_vertex_range ( )

inline

Returns a range over the vertices of the simplicial complex.

The order is increasing according to < on Vertex_handles.

template<typename IndexingTag = linear_indexing_tag, typename FiltrationValue = double, typename SimplexKey = int, typename VertexHandle = int>

int Gudhi::Simplex_tree< IndexingTag, FiltrationValue, SimplexKey, VertexHandle >::dimension ( Simplex_handle sh )

inline

Returns the dimension of a simplex.

Must be different from null_simplex().

template<typename IndexingTag = linear_indexing_tag, typename FiltrationValue = double, typename SimplexKey = int, typename VertexHandle = int>

std::pair<Simplex_handle, Simplex_handle> Gudhi::Simplex_tree< IndexingTag, FiltrationValue, SimplexKey, VertexHandle >::endpoints ( Simplex_handle sh )

inline

Returns the two Simplex_handle corresponding to the endpoints of and edge. sh must point to a 1-dimensional simplex. This is an optimized version of the boundary computation.

template<typename IndexingTag = linear_indexing_tag, typename FiltrationValue = double, typename SimplexKey = int, typename VertexHandle = int>

void Gudhi::Simplex_tree< IndexingTag, FiltrationValue, SimplexKey, VertexHandle >::expansion ( int max_dim )

inline

Expands the Simplex_tree containing only its one skeleton until dimension max_dim.

The expanded simplicial complex until dimension $d$ attached to a graph $G$ is the maximal simplicial complex of dimension at most $d$ admitting the graph $G$ as $1$ -skeleton. The filtration value assigned to a simplex is the maximal filtration value of one of its edges.

The Simplex_tree must contain no simplex of dimension bigger than 1 when calling the method.

template<typename IndexingTag = linear_indexing_tag, typename FiltrationValue = double, typename SimplexKey = int, typename VertexHandle = int>

Filtration_value Gudhi::Simplex_tree< IndexingTag, FiltrationValue, SimplexKey, VertexHandle >::filtration ( Simplex_handle sh )

inline

Returns the filtration value of a simplex.

Called on the null_simplex, returns INFINITY.

template<typename IndexingTag = linear_indexing_tag, typename FiltrationValue = double, typename SimplexKey = int, typename VertexHandle = int>

Filtration_simplex_range Gudhi::Simplex_tree< IndexingTag, FiltrationValue, SimplexKey, VertexHandle >::filtration_simplex_range ( linear_indexing_tag )

inline

Returns a range over the simplices of the simplicial complex, in the order of the filtration.

The filtration is a monotonic function $f: \mathbf{K} \rightarrow \mathbb{R}$ , i.e. if two simplices $\tau$ and $\sigma$ satisfy $\tau \subseteq \sigma$ then $f(\tau) \leq f(\sigma)$ .

The method returns simplices ordered according to increasing filtration values. Ties are resolved by considering inclusion relation (subsimplices appear before their cofaces). If two simplices have same filtration value but are not comparable w.r.t. inclusion, lexicographic order is used.

The filtration must be valid. If the filtration has not been initialized yet, the method initializes it (i.e. order the simplices).

template<typename IndexingTag = linear_indexing_tag, typename FiltrationValue = double, typename SimplexKey = int, typename VertexHandle = int>

template<class RandomAccessVertexRange >

Simplex_handle Gudhi::Simplex_tree< IndexingTag, FiltrationValue, SimplexKey, VertexHandle >::find ( const RandomAccessVertexRange & s )

inline

Given a range of Vertex_handles, returns the Simplex_handle of the simplex in the simplicial complex containing the corresponding vertices. Return null_simplex() if the simplex is not in the complex.

The type RandomAccessVertexRange must be a range for which .begin() and .end() return random access iterators, with value_type Vertex_handle.

template<typename IndexingTag = linear_indexing_tag, typename FiltrationValue = double, typename SimplexKey = int, typename VertexHandle = int>

void Gudhi::Simplex_tree< IndexingTag, FiltrationValue, SimplexKey, VertexHandle >::initialize_filtration ( )

inline

Initializes the filtrations, i.e. sort the simplices according to their order in the filtration and initializes all Simplex_keys.

After calling this method, filtration_simplex_range() becomes valid, and each simplex is assigned a Simplex_key corresponding to its order in the filtration (from 0 to m-1 for a simplicial complex with m simplices).

The use of a depth-first traversal of the simplex tree, provided by complex_simplex_range(), combined with a stable sort is meant to optimize the order of simplices with same filtration value. The heuristic consists in inserting the cofaces of a simplex as soon as possible.

Will be automatically called when calling filtration_simplex_range() if the filtration has never been initialized yet.

template<typename IndexingTag = linear_indexing_tag, typename FiltrationValue = double, typename SimplexKey = int, typename VertexHandle = int>

template<class RandomAccessVertexRange >

std::pair<Simplex_handle, bool> Gudhi::Simplex_tree< IndexingTag, FiltrationValue, SimplexKey, VertexHandle >::insert	(	RandomAccessVertexRange &	simplex,
		Filtration_value	filtration
	)

inline

Insert a simplex, represented by a range of Vertex_handles, in the simplicial complex.

Parameters

[in]	simplex	range of Vertex_handles, representing the vertices of the new simplex
[in]	filtration	the filtration value assigned to the new simplex. The return type is a pair. If the new simplex is inserted successfully (i.e. it was not in the simplicial complex yet) the bool is set to true and the Simplex_handle is the handle assigned to the new simplex. If the insertion fails (the simplex is already there), the bool is set to false. If the insertion fails and the simplex already in the complex has a filtration value strictly bigger than 'filtration', we assign this simplex with the new value 'filtration', and set the Simplex_handle filed of the output pair to the Simplex_handle of the simplex. Otherwise, we set the Simplex_handle part to null_simplex.

All subsimplices do not necessary need to be already in the simplex tree to proceed to an insertion. However, the property of being a simplicial complex will be violated. This allows us to insert a stream of simplices contained in a simplicial complex without considering any order on them.

The filtration value assigned to the new simplex must preserve the monotonicity of the filtration.

The type RandomAccessVertexRange must be a range for which .begin() and .end() return random access iterators, with 'value_type' Vertex_handle.

template<typename IndexingTag = linear_indexing_tag, typename FiltrationValue = double, typename SimplexKey = int, typename VertexHandle = int>

template<class OneSkeletonGraph >

void Gudhi::Simplex_tree< IndexingTag, FiltrationValue, SimplexKey, VertexHandle >::insert_graph ( const OneSkeletonGraph & skel_graph )

inline

Inserts a 1-skeleton in an empty Simplex_tree.

The Simplex_tree must contain no simplex when the method is called.

Inserts all vertices and edges given by a OneSkeletonGraph. OneSkeletonGraph must be a model of boost::AdjacencyGraph, boost::EdgeListGraph and boost::PropertyGraph.

The vertex filtration value is accessible through the property tag vertex_filtration_t. The edge filtration value is accessible through the property tag edge_filtration_t.

boost::graph_traits<OneSkeletonGraph>::vertex_descriptor must be Vertex_handle. boost::graph_traits<OneSkeletonGraph>::directed_category must be undirected_tag.

template<typename IndexingTag = linear_indexing_tag, typename FiltrationValue = double, typename SimplexKey = int, typename VertexHandle = int>

Simplex_key Gudhi::Simplex_tree< IndexingTag, FiltrationValue, SimplexKey, VertexHandle >::key ( Simplex_handle sh )

inline

Returns the key associated to a simplex.

The filtration must be initialized.

template<typename IndexingTag = linear_indexing_tag, typename FiltrationValue = double, typename SimplexKey = int, typename VertexHandle = int>

Simplex_handle Gudhi::Simplex_tree< IndexingTag, FiltrationValue, SimplexKey, VertexHandle >::null_simplex ( )

inline

Returns a Simplex_handle different from all Simplex_handles associated to the simplices in the simplicial complex.

One can call filtration(null_simplex()).

template<typename IndexingTag = linear_indexing_tag, typename FiltrationValue = double, typename SimplexKey = int, typename VertexHandle = int>

const unsigned int& Gudhi::Simplex_tree< IndexingTag, FiltrationValue, SimplexKey, VertexHandle >::num_simplices ( ) const

inline

Returns the number of simplices in the complex.

Does not count the empty simplex.

template<typename IndexingTag = linear_indexing_tag, typename FiltrationValue = double, typename SimplexKey = int, typename VertexHandle = int>

void Gudhi::Simplex_tree< IndexingTag, FiltrationValue, SimplexKey, VertexHandle >::print_hasse ( std::ostream & os )

inline

Write the hasse diagram of the simplicial complex in os.

Each row in the file correspond to a simplex. A line is written: dim idx_1 ... idx_k fil where dim is the dimension of the simplex, idx_1 ... idx_k are the row index (starting from 0) of the simplices of the boundary of the simplex, and fil is its filtration value.

template<typename IndexingTag = linear_indexing_tag, typename FiltrationValue = double, typename SimplexKey = int, typename VertexHandle = int>

Siblings* Gudhi::Simplex_tree< IndexingTag, FiltrationValue, SimplexKey, VertexHandle >::root ( )

inline

Returns a pointer to the root nodes of the simplex tree.

template<typename IndexingTag = linear_indexing_tag, typename FiltrationValue = double, typename SimplexKey = int, typename VertexHandle = int>

Siblings* Gudhi::Simplex_tree< IndexingTag, FiltrationValue, SimplexKey, VertexHandle >::self_siblings ( Simplex_handle sh )

inline

Returns the Siblings containing a simplex.

template<typename IndexingTag = linear_indexing_tag, typename FiltrationValue = double, typename SimplexKey = int, typename VertexHandle = int>

void Gudhi::Simplex_tree< IndexingTag, FiltrationValue, SimplexKey, VertexHandle >::set_dimension ( int dimension )

inline

Set a dimension for the simplicial complex.

template<typename IndexingTag = linear_indexing_tag, typename FiltrationValue = double, typename SimplexKey = int, typename VertexHandle = int>

void Gudhi::Simplex_tree< IndexingTag, FiltrationValue, SimplexKey, VertexHandle >::set_filtration ( Filtration_value fil )

inline

Set an upper bound for the filtration values.

template<typename IndexingTag = linear_indexing_tag, typename FiltrationValue = double, typename SimplexKey = int, typename VertexHandle = int>

void Gudhi::Simplex_tree< IndexingTag, FiltrationValue, SimplexKey, VertexHandle >::set_num_simplices ( const unsigned int & num_simplices )

inline

Set a number of simplices for the simplicial complex.

template<typename IndexingTag = linear_indexing_tag, typename FiltrationValue = double, typename SimplexKey = int, typename VertexHandle = int>

Simplex_handle Gudhi::Simplex_tree< IndexingTag, FiltrationValue, SimplexKey, VertexHandle >::simplex ( Simplex_key key )

inline

Returns the simplex associated to a key.

The filtration must be initialized.

template<typename IndexingTag = linear_indexing_tag, typename FiltrationValue = double, typename SimplexKey = int, typename VertexHandle = int>

Simplex_vertex_range Gudhi::Simplex_tree< IndexingTag, FiltrationValue, SimplexKey, VertexHandle >::simplex_vertex_range ( Simplex_handle sh )

inline

Returns a range over the vertices of a simplex.

The order in which the vertices are visited is the decreasing order for < on Vertex_handles, which is consequenlty equal to $(-1)^{\text{dim} \sigma}$ the canonical orientation on the simplex.

template<typename IndexingTag = linear_indexing_tag, typename FiltrationValue = double, typename SimplexKey = int, typename VertexHandle = int>

Skeleton_simplex_range Gudhi::Simplex_tree< IndexingTag, FiltrationValue, SimplexKey, VertexHandle >::skeleton_simplex_range ( int dim )

inline

Returns a range over the simplices of the dim-skeleton of the simplicial complex.

The $d$ -skeleton of a simplicial complex $\mathbf{K}$ is the simplicial complex containing the simplices of $\mathbf{K}$ of dimension at most $d$ .

Parameters

[in] dim The maximal dimension of the simplices in the skeleton.

The simplices are ordered according to lexicographic order on the list of Vertex_handles of a simplex, read in increasing < order for Vertex_handles.

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

Simplex_tree/include/gudhi/Simplex_tree.h

Public Types

Public Member Functions

Detailed Description

template<typename IndexingTag = linear_indexing_tag, typename FiltrationValue = double, typename SimplexKey = int, typename VertexHandle = int> class Gudhi::Simplex_tree< IndexingTag, FiltrationValue, SimplexKey, VertexHandle >

Member Typedef Documentation

Member Function Documentation

template<typename IndexingTag = linear_indexing_tag, typename FiltrationValue = double, typename SimplexKey = int, typename VertexHandle = int>
class Gudhi::Simplex_tree< IndexingTag, FiltrationValue, SimplexKey, VertexHandle >