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diff --git a/src/Rips_complex/doc/Intro_rips_complex.h b/src/Rips_complex/doc/Intro_rips_complex.h new file mode 100644 index 00000000..64fd34bc --- /dev/null +++ b/src/Rips_complex/doc/Intro_rips_complex.h @@ -0,0 +1,152 @@ +/* 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, Pawel Dlotko, Vincent Rouvreau + * + * Copyright (C) 2016 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_RIPS_COMPLEX_INTRO_RIPS_COMPLEX_H_ +#define DOC_RIPS_COMPLEX_INTRO_RIPS_COMPLEX_H_ + +namespace Gudhi { + +namespace rips_complex { + +/** \defgroup rips_complex Rips complex + * + * \author Clément Maria, Pawel Dlotko, Vincent Rouvreau + * + * @{ + * + * \section ripsdefinition Rips complex definition + * + * Rips_complex + * <a target="_blank" href="https://en.wikipedia.org/wiki/Vietoris%E2%80%93Rips_complex">(Wikipedia)</a> is a + * one skeleton graph that allows to construct a + * <a target="_blank" href="https://en.wikipedia.org/wiki/Simplicial_complex">simplicial complex</a> + * from it. + * The input can be a point cloud with a given distance function, or a distance matrix. + * + * The filtration value of each edge is computed from a user-given distance function, or directly from the distance + * matrix. + * + * All edges that have a filtration value strictly greater than a given threshold value are not inserted into + * the complex. + * + * When creating a simplicial complex from this one skeleton graph, rips inserts the one skeleton graph into the data + * structure, and then expands the simplicial when required. + * + * \image html "rips_complex_representation.png" "Rips-complex one skeleton graph representation" + * + * On this example, as edges (4,5), (4,6) and (5,6) are in the complex, simplex (4,5,6) is added with the filtration + * value set with \f$max(filtration(4,5), filtration(4,6), filtration(5,6))\f$. + * And so on for simplex (0,1,2,3). + * + * \section ripspointsdistance Point cloud and distance function + * + * \subsection ripspointscloudexample Example from a point cloud and a distance function + * + * This example builds the one skeleton graph from the given points, threshold value, and distance function. + * Then it creates a `Simplex_tree` with it. + * + * Then, it is asked to display information about the simplicial complex. + * + * \include Rips_complex/example_one_skeleton_rips_from_points.cpp + * + * When launching (rips maximal distance between 2 points is 12.0, is expanded until dimension 1 - one skeleton graph + * in other words): + * + * \code $> ./oneskeletonripspoints + * \endcode + * + * the program output is: + * + * \include Rips_complex/one_skeleton_rips_for_doc.txt + * + * \subsection ripsoffexample Example from OFF file + * + * This example builds the Rips_complex from the given points in an OFF file, threshold value, and distance + * function. + * Then it creates a `Simplex_tree` with it. + * + * + * Then, it is asked to display information about the rips complex. + * + * \include Rips_complex/example_rips_complex_from_off_file.cpp + * + * When launching: + * + * \code $> ./ripsoffreader ../../data/points/alphacomplexdoc.off 12.0 3 + * \endcode + * + * the program output is: + * + * \include Rips_complex/full_skeleton_rips_for_doc.txt + * + * + * + * \section ripsdistancematrix Distance matrix + * + * \subsection ripsdistancematrixexample Example from a distance matrix + * + * This example builds the one skeleton graph from the given distance matrix and threshold value. + * Then it creates a `Simplex_tree` with it. + * + * Then, it is asked to display information about the simplicial complex. + * + * \include Rips_complex/example_one_skeleton_rips_from_distance_matrix.cpp + * + * When launching (rips maximal distance between 2 points is 1.0, is expanded until dimension 1 - one skeleton graph + * with other words): + * + * \code $> ./oneskeletonripsdistance + * \endcode + * + * the program output is: + * + * \include Rips_complex/one_skeleton_rips_for_doc.txt + * + * \subsection ripscsvdistanceexample Example from a distance matrix read in a csv file + * + * This example builds the one skeleton graph from the given distance matrix read in a csv file and threshold value. + * Then it creates a `Simplex_tree` with it. + * + * + * Then, it is asked to display information about the rips complex. + * + * \include Rips_complex/example_rips_complex_from_csv_distance_matrix_file.cpp + * + * When launching: + * + * \code $> ./ripscsvdistancereader ../../data/distance_matrix/full_square_distance_matrix.csv 1.0 3 + * \endcode + * + * the program output is: + * + * \include Rips_complex/full_skeleton_rips_for_doc.txt + * + * \copyright GNU General Public License v3. + * \verbatim Contact: gudhi-users@lists.gforge.inria.fr \endverbatim + */ +/** @} */ // end defgroup rips_complex + +} // namespace rips_complex + +} // namespace Gudhi + +#endif // DOC_RIPS_COMPLEX_INTRO_RIPS_COMPLEX_H_ |