Separate main alpha documentation from class documentation

git-svn-id: svn+ssh://scm.gforge.inria.fr/svnroot/gudhi/branches/alphashapes@635 636b058d-ea47-450e-bf9e-a15bfbe3eedb

Former-commit-id: c1a775a032fc5e5ee6da473b91d07cfc3f1930c6

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diff --git a/src/Alpha_complex/doc/Intro_alpha_complex.h b/src/Alpha_complex/doc/Intro_alpha_complex.h
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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) 2015  INRIA Saclay (France)
+ *
+ *    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/>.
+ */
+
+// needs namespace for Doxygen to link on classes
+namespace Gudhi {
+// needs namespace for Doxygen to link on classes
+namespace alphacomplex {
+
+/**  \defgroup alpha_complex Alpha complex
+ * 
+ * \author    Vincent Rouvreau
+ * 
+ * @{
+ * 
+ * \section definition Definition
+ * 
+ * Alpha_complex is a Simplex_tree constructed from each finite cell of a Delaunay Triangulation.
+ * 
+ * The filtration value of each simplex is computed from the alpha value of the simplex if it is Gabriel or
+ * from the alpha value of the simplex coface that makes the simplex not Gabriel.
+ * 
+ * Please refer to \cite AlphaShapesDefinition for a more complete alpha complex definition.
+ * 
+ * Alpha complex are interesting because it looks like an \ref alpha-shape "Alpha shape" as described in
+ * \cite AlphaShapesIntroduction (an alpha complex concept vulgarization).
+ * 
+ * \section example Example
+ * 
+ * This example loads points from an OFF file, builds the Delaunay triangulation from the points, and finally
+ * initialize the alpha complex with it.
+ * 
+ * Then, it is asked to display information about the alpha complex.
+ * 
+ * \include Alpha_complex_from_off.cpp
+ * 
+ * When launching:
+ * 
+ * \code $> ./alphaoffreader ../../data/points/alphacomplexdoc.off
+ * \endcode
+ *
+ * the program output is:
+ * 
+ * \include alphaoffreader_for_doc.txt
+ * 
+ * \section algorithm Algorithm
+ * 
+ * <b>Data structure</b>
+ * 
+ * In order to build the alpha complex, first, a Simplex tree is build from the cells of a Delaunay Triangulation.
+ * (The filtration value is set to NaN, which stands for unknown value):
+ * \image html "alpha_complex_doc.png" "Simplex tree structure construction example"
+ *
+ * <b>Filtration value computation algorithm</b>
+ *
+ * \f{algorithm}{ 
+ * \caption{Filtration value computation algorithm}\label{alpha}
+ * \begin{algorithmic}
+ * \For{i : dimension $\rightarrow$ 1}
+ *   \ForAll{$\sigma$ of dimension i}
+ *     \If {filtration($\sigma$) is NaN}
+ *       \State filtration($\sigma$) = $\alpha(\sigma)$
+ *     \EndIf
+ *     \ForAll{$\tau$ face of $\sigma$} \Comment{propagate alpha filtration value}
+ *       \If {filtration($\tau$) is not NaN} 
+ *         \State filtration($\tau$) = min (filtration($\tau$), filtration($\sigma$))
+ *       \Else
+ *         \If {$\tau$ is not Gabriel for $\sigma$} 
+ *           \State filtration($\tau$) = filtration($\sigma$)
+ *         \EndIf
+ *       \EndIf
+ *     \EndFor
+ *   \EndFor
+ * \EndFor
+ * \end{algorithmic}
+ * \f}
+ * 
+ * From the example above, it means the algorithm will look into each triangulation ([1,2,3], [2,3,4], [1,3,5], ...),
+ * will compute the filtration value of the triangulation, and then will propagate the filtration value as described
+ * here :
+ * \image html "alpha_complex_doc_135.png" "Filtration value propagation example"
+ * Then, the algorithm will look into each edge ([1,2], [2,3], [1,3], ...),
+ * will compute the filtration value of the edge (in this case, propagation will have no effect).
+ * 
+ * Finally, the algorithm will look into each vertex ([1], [2], [3], [4], [5], [6] and [7]),
+ * will set the filtration value (0 in case of a vertex - propagation will have no effect).
+ * 
+ * \section alpha-shape Alpha shape
+ * 
+ * In the example above, the alpha shape of \f$\alpha_{74} < \alpha < \alpha_{73}\f$ is the alpha complex where the 
+ * \f$\alpha_{74} <\f$ filtration value \f$< \alpha_{73}\f$ as described in \cite AlphaShapesIntroduction
+ * 
+ * \image html "alpha_complex_doc_alpha_shape.png" "Alpha shape example"
+ * \copyright GNU General Public License v3.                         
+ * \verbatim  Contact: gudhi-users@lists.gforge.inria.fr \endverbatim
+ */
+/** @} */  // end defgroup alpha_complex
+
+} // namespace alphacomplex
+
+} // namespace Gudhi