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Abstract Simplicial Complex represented with a skeleton/blockers pair. More...
Public Types | |
| typedef SkeletonBlockerDS::Graph_vertex | Graph_vertex |
| The type of stored vertex node, specified by the template SkeletonBlockerDS. | |
| typedef SkeletonBlockerDS::Graph_edge | Graph_edge |
| The type of stored edge node, specified by the template SkeletonBlockerDS. | |
| typedef SkeletonBlockerDS::Vertex_handle | Vertex_handle |
| The type of an handle to a vertex of the complex. | |
| typedef Skeleton_blocker_simplex< Vertex_handle > | Simplex |
| A ordered set of integers that represents a simplex. | |
| typedef Simplex * | Blocker_handle |
| Handle to a blocker of the complex. | |
| typedef boost::graph_traits< Graph >::edge_descriptor | Edge_handle |
| Handle to an edge of the complex. | |
Public Member Functions | |
Vertices operations | |
| Vertex_handle | operator[] (Root_vertex_handle global) const |
| Return a local Vertex_handle of a vertex given a global one. More... | |
| Graph_vertex & | operator[] (Vertex_handle address) |
| Return the vertex node associated to local Vertex_handle. More... | |
| const Graph_vertex & | operator[] (Vertex_handle address) const |
| Return the vertex node associated to local Vertex_handle. More... | |
| Vertex_handle | add_vertex () |
| Adds a vertex to the simplicial complex and returns its Vertex_handle. More... | |
| void | remove_vertex (Vertex_handle address) |
| Remove a vertex from the simplicial complex. More... | |
| bool | contains_vertex (Vertex_handle u) const |
| bool | contains_vertex (Root_vertex_handle u) const |
| bool | contains_vertices (const Simplex &sigma) const |
| virtual boost::optional< Vertex_handle > | get_address (Root_vertex_handle id) const |
| Given an Id return the address of the vertex having this Id in the complex. More... | |
| Root_vertex_handle | get_id (Vertex_handle local) const |
| Vertex_handle | convert_handle_from_another_complex (const Skeleton_blocker_complex &other, Vertex_handle vh_in_other) const |
| Convert an address of a vertex of a complex to the address in the current complex. More... | |
| int | degree (Vertex_handle local) const |
| return the graph degree of a vertex. | |
Edges operations | |
| boost::optional< Edge_handle > | operator[] (const std::pair< Vertex_handle, Vertex_handle > &ab) const |
| return an edge handle if the two vertices forms an edge in the complex | |
| Graph_edge & | operator[] (Edge_handle edge_handle) |
| returns the stored node associated to an edge | |
| const Graph_edge & | operator[] (Edge_handle edge_handle) const |
| returns the stored node associated to an edge | |
| Vertex_handle | first_vertex (Edge_handle edge_handle) const |
| returns the first vertex of an edge More... | |
| Vertex_handle | second_vertex (Edge_handle edge_handle) const |
| returns the first vertex of an edge More... | |
| Simplex | get_vertices (Edge_handle edge_handle) const |
| returns the simplex made with the two vertices of the edge More... | |
| Edge_handle | add_edge (Vertex_handle a, Vertex_handle b) |
| Adds an edge between vertices a and b. More... | |
| void | add_edge (const Simplex &s) |
| Adds all edges of s in the complex. | |
| Edge_handle | add_edge_without_blockers (Vertex_handle a, Vertex_handle b) |
| Adds an edge between vertices a and b without blockers. More... | |
| void | add_edge_without_blockers (Simplex s) |
| Adds all edges of s in the complex without adding blockers. | |
| virtual Edge_handle | remove_edge (Vertex_handle a, Vertex_handle b) |
| Removes an edge from the simplicial complex and all its cofaces. More... | |
| void | remove_edge (Edge_handle edge) |
| Removes edge and its cofaces from the simplicial complex. | |
| void | keep_only_vertices () |
| The complex is reduced to its set of vertices. All the edges and blockers are removed. | |
| bool | contains_edge (Vertex_handle a, Vertex_handle b) const |
| bool | contains_edges (const Simplex &sigma) const |
Print and IO methods | |
| std::string | to_string () const |
| std::string | vertices_to_string () const |
| std::string | edges_to_string () const |
| std::string | blockers_to_string () const |
Simplification operations | |
| enum | simplifiable_status |
| enum | contractible_status |
| bool | is_popable_blocker (Blocker_handle sigma) const |
| void | remove_popable_blockers () |
| void | remove_popable_blockers (Vertex_handle v) |
| void | remove_all_popable_blockers (Vertex_handle v) |
| Removes all the popable blockers of the complex passing through v and delete them. Also remove popable blockers in the neighborhood if they became popable. | |
| void | remove_star (Vertex_handle v) |
| void | remove_star (Vertex_handle a, Vertex_handle b) |
| void | remove_star (Edge_handle e) |
| void | remove_star (const Simplex &sigma) |
| void | add_simplex (const Simplex &sigma) |
| add a simplex and all its faces. More... | |
| simplifiable_status | is_remove_star_homotopy_preserving (const Simplex &simplex) |
| virtual contractible_status | is_contractible () const |
| Test if the complex is reducible using a strategy defined in the class (by default it tests if the complex is a cone) More... | |
Blockers operations | |
| typedef Skeleton_blocker_link_complex< Skeleton_blocker_complex > | Link_complex |
| Blocker_handle | add_blocker (const Simplex &blocker) |
| Adds the simplex to the set of blockers and returns a Blocker_handle toward it if was not present before and 0 otherwise. | |
| void | remove_blocker (const Blocker_handle sigma) |
| Removes the simplex from the set of blockers. More... | |
| void | remove_blockers () |
| Remove all blockers, in other words, it expand the simplicial complex to the smallest flag complex that contains it. | |
| void | delete_blocker (Blocker_handle sigma) |
| bool | contains_blocker (const Blocker_handle s) const |
| bool | contains_blocker (const Simplex &s) const |
| Link_complex | link (Vertex_handle v) const |
| Link_complex | link (Edge_handle edge) const |
| Link_complex | link (const Simplex &simplex) const |
| boost::optional< Simplex > | get_simplex_address (const Root_simplex_handle &s) const |
| Compute the local vertices of 's' in the current complex If one of them is not present in the complex then the return value is uninitialized. | |
| Root_simplex_handle | get_id (const Simplex &local_simplex) const |
| returns a simplex with vertices which are the id of vertices of the argument. | |
| virtual bool | contains (const Simplex &s) const |
| returns true iff the simplex s belongs to the simplicial complex. | |
| bool | empty () const |
| int | num_vertices () const |
| int | num_edges () const |
| int | num_triangles () const |
| size_t | num_simplices () const |
| size_t | num_simplices (int dimension) const |
| size_t | num_blockers () const |
| bool | complete () const |
| int | num_connected_components () const |
| returns the number of connected components in the graph of the 1-skeleton. | |
| bool | is_cone () const |
| Test if the complex is a cone. More... | |
Vertex iterators | |
| typedef Vertex_iterator< Skeleton_blocker_complex > | Complex_vertex_iterator |
| typedef boost::iterator_range< Complex_vertex_iterator > | Complex_vertex_range |
| typedef Neighbors_vertices_iterator< Skeleton_blocker_complex > | Complex_neighbors_vertices_iterator |
| typedef boost::iterator_range< Complex_neighbors_vertices_iterator > | Complex_neighbors_vertices_range |
| Complex_vertex_range | vertex_range () const |
| Returns a Complex_vertex_range over all vertices of the complex. | |
| Complex_neighbors_vertices_range | vertex_range (Vertex_handle v) const |
| Returns a Complex_edge_range over all edges of the simplicial complex that passes through v. | |
Edge iterators | |
| typedef Edge_iterator< Skeleton_blocker_complex > | Complex_edge_iterator |
| typedef boost::iterator_range< Complex_edge_iterator > | Complex_edge_range |
| typedef Edge_around_vertex_iterator< Skeleton_blocker_complex > | Complex_edge_around_vertex_iterator |
| typedef boost::iterator_range< Complex_edge_around_vertex_iterator > | Complex_edge_around_vertex_range |
| Complex_edge_range | edge_range () const |
| Returns a Complex_edge_range over all edges of the simplicial complex. | |
| Complex_edge_around_vertex_range | edge_range (Vertex_handle v) const |
| Returns a Complex_edge_range over all edges of the simplicial complex that passes through 'v'. | |
Triangles iterators | |
| typedef Triangle_around_vertex_iterator< Skeleton_blocker_complex, Superior_link > | Superior_triangle_around_vertex_iterator |
| typedef boost::iterator_range< Triangle_around_vertex_iterator< Skeleton_blocker_complex, Link > > | Complex_triangle_around_vertex_range |
| typedef boost::iterator_range< Triangle_iterator< Skeleton_blocker_complex > > | Complex_triangle_range |
| typedef Triangle_iterator< Skeleton_blocker_complex > | Complex_triangle_iterator |
| Complex_triangle_around_vertex_range | triangle_range (Vertex_handle v) const |
| Range over triangles around a vertex of the simplicial complex. Methods .begin() and .end() return a Triangle_around_vertex_iterator. | |
| Complex_triangle_range | triangle_range () const |
| Range over triangles of the simplicial complex. Methods .begin() and .end() return a Triangle_around_vertex_iterator. | |
Simplices iterators | |
| typedef Simplex_around_vertex_iterator< Skeleton_blocker_complex, Link > | Complex_simplex_around_vertex_iterator |
| typedef boost::iterator_range< Complex_simplex_around_vertex_iterator > | Complex_simplex_around_vertex_range |
| Range over the simplices of the simplicial complex around a vertex. Methods .begin() and .end() return a Complex_simplex_around_vertex_iterator. | |
| typedef Simplex_coboundary_iterator< Skeleton_blocker_complex, Link > | Complex_simplex_coboundary_iterator |
| typedef boost::iterator_range< Complex_simplex_coboundary_iterator > | Complex_coboundary_range |
| Range over the simplices of the coboundary of a simplex. Methods .begin() and .end() return a Complex_simplex_coboundary_iterator. | |
| typedef Simplex_iterator< Skeleton_blocker_complex > | Complex_simplex_iterator |
| typedef boost::iterator_range< Complex_simplex_iterator > | Complex_simplex_range |
| Complex_simplex_around_vertex_range | star_simplex_range (Vertex_handle v) const |
| Returns a Complex_simplex_around_vertex_range over all the simplices around a vertex of the complex. | |
| Complex_coboundary_range | coboundary_range (const Simplex &s) const |
| Returns a Complex_simplex_coboundary_iterator over the simplices of the coboundary of a simplex. | |
| Complex_simplex_range | complex_simplex_range () const |
| Returns a Complex_simplex_range over all the simplices of the complex. | |
Constructors, Destructors | |
| Skeleton_blocker_complex (size_t num_vertices_=0, Visitor *visitor_=NULL) | |
| constructs a simplicial complex with a given number of vertices and a visitor. | |
| template<typename SimpleHandleOutputIterator > | |
| Skeleton_blocker_complex (SimpleHandleOutputIterator simplices_begin, SimpleHandleOutputIterator simplices_end, bool is_flag_complex=false, Visitor *visitor_=NULL) | |
| Constructor with a list of simplices. More... | |
| Skeleton_blocker_complex (const Skeleton_blocker_complex ©) | |
| Skeleton_blocker_complex & | operator= (const Skeleton_blocker_complex ©) |
| bool | operator== (const Skeleton_blocker_complex &other) const |
| bool | operator!= (const Skeleton_blocker_complex &other) const |
| virtual | ~Skeleton_blocker_complex () |
| virtual void | clear () |
| void | set_visitor (Visitor *other_visitor) |
| allows to change the visitor. | |
Blockers iterators | |
| Complex_blocker_around_vertex_range | blocker_range (Vertex_handle v) |
| Returns a range of the blockers of the complex passing through a vertex. | |
| Const_complex_blocker_around_vertex_range | const_blocker_range (Vertex_handle v) const |
| Returns a range of the blockers of the complex passing through a vertex. | |
| Complex_blocker_range | blocker_range () |
| Returns a range of the blockers of the complex. | |
| Const_complex_blocker_range | const_blocker_range () const |
| Returns a range of the blockers of the complex. | |
Edge contraction operations | |
| bool | link_condition (Vertex_handle a, Vertex_handle b, bool ignore_popable_blockers=false) const |
| bool | link_condition (Edge_handle e, bool ignore_popable_blockers=false) const |
| void | contract_edge (Edge_handle edge) |
| void | contract_edge (Vertex_handle a, Vertex_handle b) |
Abstract Simplicial Complex represented with a skeleton/blockers pair.
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Constructor with a list of simplices.
is_flag_complex indicates if the complex is a flag complex or not (to know if blockers have to be computed or not).
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The destructor delete all blockers allocated.
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Adds an edge between vertices a and b.
For instance, the complex contains edge 01 and 12, then calling add_edge with vertex 0 and 2 will create a complex containing the edges 01, 12, 20 but not the triangle 012 (and hence this complex will contains a blocker 012).
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Adds an edge between vertices a and b without blockers.
For instance, the complex contains edge 01 and 12, then calling add_edge with vertex 0 and 2 will create a complex containing the triangle 012.
| void Gudhi::skeleton_blocker::Skeleton_blocker_complex< SkeletonBlockerDS >::add_simplex | ( | const Simplex & | sigma | ) |
add a simplex and all its faces.
the simplex must have dimension greater than one (otherwise use add_vertex or add_edge_without_blockers).
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Adds a vertex to the simplicial complex and returns its Vertex_handle.
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Clears the simplicial complex. After a call to this function, blockers are destroyed. The 1-skeleton and the set of blockers are both empty.
Reimplemented in Gudhi::skeleton_blocker::Skeleton_blocker_sub_complex< ComplexType >.
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Contracts the edge.
| void Gudhi::skeleton_blocker::Skeleton_blocker_complex< SkeletonBlockerDS >::contract_edge | ( | Vertex_handle | a, |
| Vertex_handle | b | ||
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Contracts the edge connecting vertices a and b.
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Convert an address of a vertex of a complex to the address in the current complex.
If the current complex is a sub (or sup) complex of 'other', it converts the address of a vertex v expressed in 'other' to the address of the vertex v in the current one.
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Removes the simplex sigma from the set of blockers and deallocate sigma.
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returns the first vertex of an edge
it assumes that the edge is present in the complex
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Given an Id return the address of the vertex having this Id in the complex.
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return the id of a vertex of address local present in the graph
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returns the simplex made with the two vertices of the edge
it assumes that the edge is present in the complex
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Test if the complex is a cone.
Runs in O(n) where n is the number of vertices.
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Test if the complex is reducible using a strategy defined in the class (by default it tests if the complex is a cone)
Note that NO could be returned if some invariant ensures that the complex is not a point (for instance if the euler characteristic is different from 1). This function will surely have to return MAYBE in some case because the associated problem is undecidable but it in practice, it can often be solved with the help of geometry.
| bool Gudhi::skeleton_blocker::Skeleton_blocker_complex< SkeletonBlockerDS >::is_popable_blocker | ( | Blocker_handle | sigma | ) | const |
Returns true iff the blocker 'sigma' is popable. To define popable, let us call 'L' the complex that consists in the current complex without the blocker 'sigma'. A blocker 'sigma' is then "popable" if the link of 'sigma' in L is reducible.
Returns true if the blocker 'sigma' is popable. To define popable, let us call 'L' the complex that consists in the current complex without the blocker 'sigma'. A blocker 'sigma' is then "popable" if the link of 'sigma' in L is reducible.
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Constructs the link of 'simplex' with points coordinates.
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Constructs the link of 'simplex' with points coordinates.
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Constructs the link of 'simplex' with points coordinates.
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return true if both complexes have the same simplices.
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Return a local Vertex_handle of a vertex given a global one.
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Return the vertex node associated to local Vertex_handle.
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Return the vertex node associated to local Vertex_handle.
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Removes the simplex from the set of blockers.
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Removes an edge from the simplicial complex and all its cofaces.
returns the former Edge_handle representing the edge
| void Gudhi::skeleton_blocker::Skeleton_blocker_complex< SkeletonBlockerDS >::remove_popable_blockers |
Removes all the popable blockers of the complex and delete them.
| void Gudhi::skeleton_blocker::Skeleton_blocker_complex< SkeletonBlockerDS >::remove_popable_blockers | ( | Vertex_handle | v | ) |
Removes all the popable blockers of the complex passing through v and delete them.
| void Gudhi::skeleton_blocker::Skeleton_blocker_complex< SkeletonBlockerDS >::remove_star | ( | const Simplex & | sigma | ) |
Remove the star of the simplex 'sigma' which needs to belong to the complex
| void Gudhi::skeleton_blocker::Skeleton_blocker_complex< SkeletonBlockerDS >::remove_star | ( | Edge_handle | e | ) |
Remove the star of the edge 'e'.
| void Gudhi::skeleton_blocker::Skeleton_blocker_complex< SkeletonBlockerDS >::remove_star | ( | Vertex_handle | a, |
| Vertex_handle | b | ||
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Remove the star of the edge connecting vertices a and b.
| void Gudhi::skeleton_blocker::Skeleton_blocker_complex< SkeletonBlockerDS >::remove_star | ( | Vertex_handle | v | ) |
Remove the star of the vertex 'v'
Remove the star of the vertice 'v'
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Remove a vertex from the simplicial complex.
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returns the first vertex of an edge
it assumes that the edge is present in the complex