diff options
Diffstat (limited to 'doc/Simplex_tree/Intro_simplex_tree.h')
| -rw-r--r-- | doc/Simplex_tree/Intro_simplex_tree.h | 87 |
1 files changed, 0 insertions, 87 deletions
diff --git a/doc/Simplex_tree/Intro_simplex_tree.h b/doc/Simplex_tree/Intro_simplex_tree.h deleted file mode 100644 index db399489..00000000 --- a/doc/Simplex_tree/Intro_simplex_tree.h +++ /dev/null @@ -1,87 +0,0 @@ -/* 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): ClĂ©ment Maria - * - * Copyright (C) 2014 Inria - * - * 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 - * simplices \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_2example_alpha_shapes_3_simplex_tree_from_off_file_8cpp-example.html"> - * Simplex_tree/example_alpha_shapes_3_simplex_tree_from_off_file.cpp</a> - Simplex tree is computed and displayed - * from a 3D alpha complex (Requires CGAL, GMP and GMPXX to be installed). - * - * \li <a href="_simplex_tree_2graph_expansion_with_blocker_8cpp-example.html"> - * Simplex_tree/graph_expansion_with_blocker.cpp</a> - Simple simplex tree construction from a one-skeleton graph with - * a simple blocker expansion method. - * - * \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. - * - * @} - */ - -} // namespace Gudhi - -#endif // DOC_SIMPLEX_TREE_INTRO_SIMPLEX_TREE_H_ |