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diff --git a/src/Cech_complex/doc/Intro_cech_complex.h b/src/Cech_complex/doc/Intro_cech_complex.h index e69de29b..f2052763 100644 --- a/src/Cech_complex/doc/Intro_cech_complex.h +++ b/src/Cech_complex/doc/Intro_cech_complex.h @@ -0,0 +1,92 @@ +/* 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): Vincent Rouvreau + * + * Copyright (C) 2018 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_CECH_COMPLEX_INTRO_CECH_COMPLEX_H_ +#define DOC_CECH_COMPLEX_INTRO_CECH_COMPLEX_H_ + +namespace Gudhi { + +namespace cech_complex { + +/** \defgroup cech_complex Cech complex + * + * \author Clément Maria, Pawel Dlotko, Vincent Rouvreau + * + * @{ + * + * \section cechdefinition Cech complex definition + * + * Cech_complex + * <a target="_blank" href="https://en.wikipedia.org/wiki/%C4%8Cech_cohomology">(Wikipedia)</a> is a + * proximity 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. + * + * 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 proximity graph, Cech inserts the proximity graph into the data + * structure, and then expands the simplicial complex when required. + * + * Vertex name correspond to the index of the point in the given range (aka. the point cloud). + * + * \image html "cech_complex_representation.png" "Cech complex proximity 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). + * + * If the Cech_complex interfaces are not detailed enough for your need, please refer to + * <a href="_persistent_cohomology_2cech_persistence_step_by_step_8cpp-example.html"> + * cech_persistence_step_by_step.cpp</a> example, where the graph construction over the Simplex_tree is more detailed. + * + * \section cechpointsdistance Point cloud and distance function + * + * \subsection cechpointscloudexample Example from a point cloud and a distance function + * + * This example builds the proximity 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 Cech_complex/cech_complex_example_from_points.cpp + * + * When launching (Cech maximal distance between 2 points is 7.1, is expanded until dimension 2): + * + * \code $> ./Cech_complex_example_from_points + * \endcode + * + * the program output is: + * + * \include Cech_complex/cech_complex_example_from_points_for_doc.txt + * + */ +/** @} */ // end defgroup cech_complex + +} // namespace cech_complex + +} // namespace Gudhi + +#endif // DOC_CECH_COMPLEX_INTRO_CECH_COMPLEX_H_ |