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diff --git a/doc/Simplex_tree/Intro_simplex_tree.h b/doc/Simplex_tree/Intro_simplex_tree.h new file mode 100644 index 00000000..ddf9ad22 --- /dev/null +++ b/doc/Simplex_tree/Intro_simplex_tree.h @@ -0,0 +1,84 @@ +/* This file is part of the Gudhi Library. The Gudhi library + * (Geometric Understanding in Higher Dimensions) is a generic C++ + * library for computational topology. + * + * Author(s): Clément Maria + * + * Copyright (C) 2014 INRIA Sophia Antipolis-Méditerranée (France) + * + * This program is free software: you can redistribute it and/or modify + * it under the terms of the GNU General Public License as published by + * the Free Software Foundation, either version 3 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU General Public License for more details. + * + * You should have received a copy of the GNU General Public License + * along with this program. If not, see <http://www.gnu.org/licenses/>. + */ + +#ifndef DOC_SIMPLEX_TREE_INTRO_SIMPLEX_TREE_H_ +#define DOC_SIMPLEX_TREE_INTRO_SIMPLEX_TREE_H_ + +// needs namespace for Doxygen to link on classes +namespace Gudhi { + + +/** \defgroup simplex_tree Filtered Complexes + * \author Clément Maria + * + * A simplicial complex \f$\mathbf{K}\f$ on a set of vertices \f$V = \{1, \cdots ,|V|\}\f$ is a collection of + * implices \f$\{\sigma\}\f$, \f$\sigma \subseteq V\f$ such that + * \f$\tau \subseteq \sigma \in \mathbf{K} \rightarrow \tau \in \mathbf{K}\f$. The dimension \f$n=|\sigma|-1\f$ of + * \f$\sigma\f$ is its number of elements minus \f$1\f$. + * + * A filtration of a simplicial complex is a function \f$f:\mathbf{K} \rightarrow \mathbb{R}\f$ satisfying + * \f$f(\tau)\leq f(\sigma)\f$ whenever \f$\tau \subseteq \sigma\f$. 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. + * + * \section filteredcomplexesimplementation Implementations + * \subsection filteredcomplexessimplextree Simplex tree + * 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 \cite boissonnatmariasimplextreealgorithmica + * \image html "Simplex_tree_representation.png" "Simplex tree representation" + * + * \subsubsection filteredcomplexessimplextreeexamples Examples + * + * Here is a list of simplex tree examples : + * \li <a href="_simplex_tree_2simple_simplex_tree_8cpp-example.html"> + * Simplex_tree/simple_simplex_tree.cpp</a> - Simple simplex tree construction and basic function use. + * + * \li <a href="_simplex_tree_2simplex_tree_from_cliques_of_graph_8cpp-example.html"> + * Simplex_tree/simplex_tree_from_cliques_of_graph.cpp</a> - Simplex tree construction from cliques of graph read in + * a file. + * + * Simplex tree construction with \f$\mathbb{Z}/3\mathbb{Z}\f$ coefficients on weighted graph Klein bottle file: + * \code $> ./simplex_tree_from_cliques_of_graph ../../data/points/Klein_bottle_complex.txt 3 \endcode + * \code Insert the 1-skeleton in the simplex tree in 0.000404 s. +max_dim = 3 +Expand the simplex tree in 3.8e-05 s. +Information of the Simplex Tree: +Number of vertices = 10 Number of simplices = 98 \endcode + * + * \li <a href="_simplex_tree_2simplex_tree_from_alpha_shapes_3_8cpp-example.html"> + * Simplex_tree/simplex_tree_from_alpha_shapes_3.cpp</a> - Simplex tree is computed and displayed from a 3D alpha + * complex (Requires CGAL, GMP and GMPXX to be installed) + * + * + * \subsection filteredcomplexeshassecomplex Hasse complex + * 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. + * + * \copyright GNU General Public License v3. + * @{ + */ + +} // namespace Gudhi + +#endif // DOC_SIMPLEX_TREE_INTRO_SIMPLEX_TREE_H_ |