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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):       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_