1 files changed, 64 insertions, 39 deletions
diff --git a/src/Alpha_complex/doc/Intro_alpha_complex.h b/src/Alpha_complex/doc/Intro_alpha_complex.h
index 7a375c9f..ab7c4794 100644
--- a/src/Alpha_complex/doc/Intro_alpha_complex.h
+++ b/src/Alpha_complex/doc/Intro_alpha_complex.h
@@ -29,34 +29,34 @@ namespace Gudhi {
 namespace alpha_complex {
 
 /**  \defgroup alpha_complex Alpha complex
- * 
+ *
  * \author    Vincent Rouvreau
  *
  * @{
- * 
+ *
  * \section definition Definition
- * 
+ *
  * Alpha_complex is a <a target="_blank" href="https://en.wikipedia.org/wiki/Simplicial_complex">simplicial complex</a>
  * constructed from the finite cells of a Delaunay Triangulation.
- * 
+ *
  * The filtration value of each simplex is computed as the square of the circumradius of the simplex if the
  * circumsphere is empty (the simplex is then said to be Gabriel), and as the minimum of the filtration
  * values of the codimension 1 cofaces that make it not Gabriel otherwise.
- * 
+ *
  * All simplices that have a filtration value strictly greater than a given alpha squared value are not inserted into
  * the complex.
- * 
+ *
  * \image html "alpha_complex_representation.png" "Alpha-complex representation"
- * 
+ *
  * Alpha_complex is constructing a <a target="_blank"
  * href="http://doc.cgal.org/latest/Triangulation/index.html#Chapter_Triangulations">Delaunay Triangulation</a>
  * \cite cgal:hdj-t-15b from <a target="_blank" href="http://www.cgal.org/">CGAL</a> (the Computational Geometry
  * Algorithms Library \cite cgal:eb-15b) and is able to create a `SimplicialComplexForAlpha`.
- * 
+ *
  * The complex is a template class requiring an Epick_d <a target="_blank"
  * href="http://doc.cgal.org/latest/Kernel_d/index.html#Chapter_dD_Geometry_Kernel">dD Geometry Kernel</a>
  * \cite cgal:s-gkd-15b from CGAL as template parameter.
- * 
+ *
  * \remark
  * - When the simplicial complex is constructed with an infinite value of alpha, the complex is a Delaunay
  * complex.
@@ -65,30 +65,30 @@ namespace alpha_complex {
  * \ref cech_complex can still make sense in higher dimension precisely because you can bound the radii.
  *
  * \section pointsexample Example from points
- * 
+ *
  * This example builds the Delaunay triangulation from the given points in a 2D static kernel, and creates a
  * `Simplex_tree` with it.
- * 
+ *
  * Then, it is asked to display information about the simplicial complex.
- * 
+ *
  * \include Alpha_complex/Alpha_complex_from_points.cpp
- * 
+ *
  * When launching:
- * 
+ *
  * \code $> ./Alpha_complex_example_from_points
  * \endcode
  *
  * the program output is:
- * 
+ *
  * \include Alpha_complex/alphaoffreader_for_doc_60.txt
- * 
+ *
  * \section createcomplexalgorithm Create complex algorithm
- * 
+ *
  * \subsection datastructure Data structure
- * 
+ *
  * In order to create the simplicial complex, first, it is built from the cells of the Delaunay Triangulation.
  * The filtration values are set to NaN, which stands for unknown value.
- * 
+ *
  * In example, :
  * \image html "alpha_complex_doc.png" "Simplicial complex structure construction example"
  *
@@ -106,7 +106,7 @@ namespace alpha_complex {
  * \quad\quad\quad\quad \text{filtration(} \tau \text{) = min( filtration(} \tau \text{), filtration(} \sigma
  * \text{) )}\\
  * \quad\quad\quad \textbf{else}\\
- * \quad\quad\quad\quad \textbf{if } \textbf{if } \tau \text{ is not Gabriel for } \sigma \textbf{ then}\\
+ * \quad\quad\quad\quad \textbf{if } \tau \text{ is not Gabriel for } \sigma \textbf{ then}\\
  * \quad\quad\quad\quad\quad \text{filtration(} \tau \text{) = filtration(} \sigma \text{)}\\
  * \quad\quad\quad\quad \textbf{end if}\\
  * \quad\quad\quad \textbf{end if}\\
@@ -118,53 +118,78 @@ namespace alpha_complex {
  * \f$
  *
  * \subsubsection dimension2 Dimension 2
- * 
+ *
  * From the example above, it means the algorithm looks into each triangle ([0,1,2], [0,2,4], [1,2,3], ...),
  * computes the filtration value of the triangle, and then propagates the filtration value as described
  * here :
  * \image html "alpha_complex_doc_420.png" "Filtration value propagation example"
- * 
+ *
  * \subsubsection dimension1 Dimension 1
- * 
+ *
  * Then, the algorithm looks into each edge ([0,1], [0,2], [1,2], ...),
  * computes the filtration value of the edge (in this case, propagation will have no effect).
- * 
+ *
  * \subsubsection dimension0 Dimension 0
- * 
+ *
  * Finally, the algorithm looks into each vertex ([0], [1], [2], [3], [4], [5] and [6]) and
  * sets the filtration value (0 in case of a vertex - propagation will have no effect).
- * 
+ *
  * \subsubsection nondecreasing Non decreasing filtration values
- * 
+ *
  * As the squared radii computed by CGAL are an approximation, it might happen that these alpha squared values do not
  * quite define a proper filtration (i.e. non-decreasing with respect to inclusion).
  * We fix that up by calling `SimplicialComplexForAlpha::make_filtration_non_decreasing()`.
- * 
+ *
  * \subsubsection pruneabove Prune above given filtration value
- * 
+ *
  * The simplex tree is pruned from the given maximum alpha squared value (cf.
  * `SimplicialComplexForAlpha::prune_above_filtration()`).
  * In the following example, the value is given by the user as argument of the program.
- * 
- * 
+ *
+ *
  * \section offexample Example from OFF file
- * 
+ *
  * This example builds the Delaunay triangulation in a dynamic kernel, and initializes the alpha complex with it.
- * 
- * 
+ *
+ *
  * Then, it is asked to display information about the alpha complex.
- * 
+ *
  * \include Alpha_complex/Alpha_complex_from_off.cpp
- * 
+ *
  * When launching:
- * 
+ *
  * \code $> ./Alpha_complex_example_from_off ../../data/points/alphacomplexdoc.off 32.0
  * \endcode
  *
  * the program output is:
- * 
+ *
  * \include Alpha_complex/alphaoffreader_for_doc_32.txt
- * 
+ *
+ *
+ * \section weighted3dexample 3d specific example
+ *
+ * A specific module for Alpha complex is available in 3d (cf. Alpha_complex_3d) and allows to construct standard,
+ * weighted, periodic or weighted and periodic versions of alpha complexes. Alpha values computation can be
+ * Gudhi::alpha_complex::complexity::FAST, Gudhi::alpha_complex::complexity::SAFE (default value) or
+ * Gudhi::alpha_complex::complexity::EXACT.
+ *
+ * This example builds the CGAL 3d weighted alpha shapes from a small molecule, and initializes the alpha complex with
+ * it. This example is taken from <a href="https://doc.cgal.org/latest/Alpha_shapes_3/index.html#title13">CGAL 3d
+ * weighted alpha shapes</a>.
+ *
+ * Then, it is asked to display information about the alpha complex.
+ *
+ * \include Alpha_complex/Weighted_alpha_complex_3d_from_points.cpp
+ *
+ * When launching:
+ *
+ * \code $> ./Alpha_complex_example_weighted_3d_from_points
+ * \endcode
+ *
+ * the program output is:
+ *
+ * \include Alpha_complex/weightedalpha3dfrompoints_for_doc.txt
+ *
  */
 /** @} */  // end defgroup alpha_complex