3 files changed, 73 insertions, 1 deletions
diff --git a/src/common/doc/main_page.h b/src/common/doc/main_page.h
index b3e9ea03..30d4e71b 100644
--- a/src/common/doc/main_page.h
+++ b/src/common/doc/main_page.h
@@ -42,6 +42,22 @@
     </td>
  </tr>
 </table>
+ \subsection CechComplexDataStructure Čech complex
+ \image html "cech_complex_representation.png" "Čech complex representation"
+<table border="0">
+  <tr>
+    <td width="25%">
+      <b>Author:</b> Vincent Rouvreau<br>
+      <b>Introduced in:</b> GUDHI 2.2.0<br>
+      <b>Copyright:</b> GPL v3<br>
+    </td>
+    <td width="75%">
+    The Čech complex is a simplicial complex constructed from a proximity graph.<br>
+    The set of all simplices is filtered by the radius of their minimal enclosing ball.<br>
+    <b>User manual:</b> \ref cech_complex - <b>Reference manual:</b> Gudhi::cech_complex::Cech_complex
+    </td>
+ </tr>
+</table>
  \subsection CubicalComplexDataStructure Cubical complex
  \image html "Cubical_complex_representation.png" "Cubical complex representation"
 <table border="0">
@@ -57,6 +73,7 @@
     <b>User manual:</b> \ref cubical_complex - <b>Reference manual:</b> Gudhi::cubical_complex::Bitmap_cubical_complex
     </td>
  </tr>
+</table>
  \subsection RipsComplexDataStructure Rips complex
  \image html "rips_complex_representation.png" "Rips complex representation"
 <table border="0">
@@ -75,7 +92,6 @@
     </td>
  </tr>
 </table>
-</table>
  \subsection SimplexTreeDataStructure Simplex tree
  \image html "Simplex_tree_representation.png" "Simplex tree representation"
 <table border="0">
diff --git a/src/common/include/gudhi/distance_functions.h b/src/common/include/gudhi/distance_functions.h
index f7baed6f..4dfba1bf 100644
--- a/src/common/include/gudhi/distance_functions.h
+++ b/src/common/include/gudhi/distance_functions.h
@@ -25,7 +25,10 @@
 
 #include <gudhi/Debug_utils.h>
 
+#include <gudhi/Miniball.hpp>
+
 #include <boost/range/metafunctions.hpp>
+#include <boost/range/size.hpp>
 
 #include <cmath>  // for std::sqrt
 #include <type_traits>  // for std::decay
@@ -68,6 +71,53 @@ class Euclidean_distance {
   }
 };
 
+/** @brief Compute the radius of the minimal enclosing ball between Points given by a range of coordinates.
+ * The points are assumed to have the same dimension. */
+class Minimal_enclosing_ball_radius {
+ public:
+  /** \brief Minimal_enclosing_ball_radius from two points.
+   *
+   * @param[in] point_1 First point.
+   * @param[in] point_2 second point.
+   * @return The minimal enclosing ball radius for the two points (aka. Euclidean distance / 2.).
+   *
+   * \tparam Point must be a range of Cartesian coordinates.
+   *
+   */
+  template< typename Point >
+  typename std::iterator_traits<typename boost::range_iterator<Point>::type>::value_type
+  operator()(const Point& point_1, const Point& point_2) const {
+    return Euclidean_distance()(point_1, point_2) / 2.;
+  }
+  /** \brief Minimal_enclosing_ball_radius from a point cloud.
+   *
+   * @param[in] point_cloud The points.
+   * @return The minimal enclosing ball radius for the points.
+   *
+   * \tparam Point_cloud must be a range of points with Cartesian coordinates.
+   * Point_cloud is a range over a range of Coordinate.
+   *
+   */
+  template< typename Point_cloud,
+            typename Point_iterator = typename boost::range_const_iterator<Point_cloud>::type,
+            typename Point= typename std::iterator_traits<Point_iterator>::value_type,
+            typename Coordinate_iterator = typename boost::range_const_iterator<Point>::type,
+            typename Coordinate = typename std::iterator_traits<Coordinate_iterator>::value_type>
+  Coordinate
+  operator()(const Point_cloud& point_cloud) const {
+    using Min_sphere = Miniball::Miniball<Miniball::CoordAccessor<Point_iterator, Coordinate_iterator>>;
+
+    Min_sphere ms(boost::size(*point_cloud.begin()), point_cloud.begin(),point_cloud.end());
+#ifdef DEBUG_TRACES
+    std::cout << "Minimal_enclosing_ball_radius = " << std::sqrt(ms.squared_radius()) << " | nb points = "
+              << boost::size(point_cloud) << " | dimension = "
+              << boost::size(*point_cloud.begin()) << std::endl;
+#endif  // DEBUG_TRACES
+
+    return std::sqrt(ms.squared_radius());
+  }
+};
+
 }  // namespace Gudhi
 
 #endif  // DISTANCE_FUNCTIONS_H_
diff --git a/src/common/include/gudhi/graph_simplicial_complex.h b/src/common/include/gudhi/graph_simplicial_complex.h
index 6ab7b0b4..49fe56cc 100644
--- a/src/common/include/gudhi/graph_simplicial_complex.h
+++ b/src/common/include/gudhi/graph_simplicial_complex.h
@@ -42,6 +42,12 @@ struct vertex_filtration_t {
   typedef boost::vertex_property_tag kind;
 };
 
+/** \brief Proximity_graph contains the vertices and edges with their filtration values in order to store the result
+ * of `Gudhi::compute_proximity_graph` function.
+ *
+ * \tparam SimplicialComplexForProximityGraph furnishes `Filtration_value` type definition.
+ *
+ */
 template <typename SimplicialComplexForProximityGraph>
 using Proximity_graph = typename boost::adjacency_list < boost::vecS, boost::vecS, boost::undirectedS
 , boost::property < vertex_filtration_t, typename SimplicialComplexForProximityGraph::Filtration_value >