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/* 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 & Vincent Rouvreau
*
* Copyright (C) 2015 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 and Vincent Rouvreau
*
* @{
*
* \section ripsdefinition Definition
*
* Rips_complex
* <a target="_blank" href="https://en.wikipedia.org/wiki/Vietoris%E2%80%93Rips_complex">(Wikipedia)</a> is a
* <a target="_blank" href="https://en.wikipedia.org/wiki/Simplicial_complex">simplicial complex</a>
* constructed from a one skeleton graph.
*
* The filtration value of each edge is computed from a user-given distance function.
*
* 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 ripspointsexample Example from points
*
* 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
* with other words):
*
* \code $> ./oneskeletonripspoints 12.0
* \endcode
*
* the program output is:
*
* \include Rips_complex/one_skeleton_rips_points_for_doc.txt
*
* \section ripsoffexample Example from OFF file
*
* This example builds the one skeleton graph 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_points_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_
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