Classes | |
struct | Gudhi::Simplex_tree_options_full_featured |
Model of SimplexTreeOptions. More... | |
class | Gudhi::Simplex_tree< SimplexTreeOptions > |
Simplex Tree data structure for representing simplicial complexes. More... | |
A simplicial complex on a set of vertices
is a collection of simplices
,
such that
. The dimension
of
is its number of elements minus
.
A filtration of a simplicial complex is a function satisfying
whenever
. Ordering the simplices by increasing filtration values (breaking ties so as a simplex appears after its subsimplices of same filtration value) provides an indexing scheme.
Implementations: There are two implementation of complexes. The first on is the Simplex_tree data structure. The simplex tree is an efficient and flexible data structure for representing general (filtered) simplicial complexes. The data structure is described in [4]
The second one is the Hasse_complex. The Hasse complex is a data structure representing explicitly all co-dimension 1 incidence relations in a complex. It is consequently faster when accessing the boundary of a simplex, but is less compact and harder to construct from scratch.