git-svn-id: svn+ssh://scm.gforge.inria.fr/svnroot/gudhi/branches/Nerve_GIC@2411 636b058d-ea47-450e-bf9e-a15bfbe3eedb

Former-commit-id: 92552c44d0a2369735bd29495c3504f53010a06c

4 files changed, 40 insertions, 4 deletions

diff --git a/src/Nerve_GIC/doc/COPYRIGHT b/src/Nerve_GIC/doc/COPYRIGHT
new file mode 100644
index 00000000..0c36a526
--- /dev/null
+++ b/src/Nerve_GIC/doc/COPYRIGHT
@@ -0,0 +1,19 @@
+The files of this directory are part of the Gudhi Library. The Gudhi library
+(Geometric Understanding in Higher Dimensions) is a generic C++ library for
+computational topology.
+
+Author(s):       Mathieu Carrière
+
+Copyright (C) 2017  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/>.
diff --git a/src/Nerve_GIC/doc/Intro_graph_induced_complex.h b/src/Nerve_GIC/doc/Intro_graph_induced_complex.h
index 8c31b262..f30d51a4 100644
--- a/src/Nerve_GIC/doc/Intro_graph_induced_complex.h
+++ b/src/Nerve_GIC/doc/Intro_graph_induced_complex.h
@@ -33,23 +33,31 @@ namespace graph_induced_complex {
  * 
  * @{
  * 
+ * \section covers Covers
+ *
+ * Nerves and Graph Induced Complexes require a cover C of the input point cloud P,
+ * that is a set of subsets of P whose union is P itself.
+ * Very often, this cover is obtained from the preimage of a family of intervals covering
+ * the image of some scalar-valued function f defined on P. This family is parameterized
+ * by its resolution, which can be either the number or the length of the intervals,
+ * and its gain, which is the overlap percentage between consecutive intervals (ordered by their first values).
+ *
  * \section nerves Nerves
  *
  * \subsection nervedefinition Nerve definition
  *
- * Assume you are given a cover C of your point cloud P, that is a set of subsets of P
- * whose union is P itself. Then, the Nerve of this cover
+ * Assume you are given a cover C of your point cloud P. Then, the Nerve of this cover
  * is the simplicial complex that has one k-simplex per k-fold intersection of cover elements.
  * See also <a target="_blank" href="https://en.wikipedia.org/wiki/Nerve_of_a_covering"> Wikipedia </a>.
  *
+ * \image html "nerve.png" "Nerve of a double torus"
+ *
  * \subsection nerveexample Example
  *
  * This example builds the Nerve of a point cloud sampled on a 3D human shape (human.off).
  * The cover C comes from the preimages of intervals (10 intervals with gain 0.3)
  * covering the height function (coordinate 2),
  * which are then refined into their connected components using the triangulation of the .OFF file.
- * All intervals have the resolution (either the length or the number of the intervals)
- * and gain (overlap percentage).
  *
  * \include Nerve_GIC/Nerve.cpp
  *
@@ -62,6 +70,13 @@ namespace graph_induced_complex {
  *
  * \include Nerve_GIC/Nerve.txt
  *
+ * The first three lines are requirements for visualization with Kepler-Mapper.
+ * The fourth line contains the number of vertices nv and edges ne of the Nerve.
+ * The next nv lines represent the vertices. Each line contains the vertex ID,
+ * the number of data points it contains, and their average color function value.
+ * Finally, the next ne lines represent the edges, characterized by the ID of their vertices.
+ *
+ *
  * \section gic Graph Induced Complexes (GIC)
  *
  * \subsection gicdefinition GIC definition
@@ -73,6 +88,8 @@ namespace graph_induced_complex {
  * See <a target="_blank" href="https://arxiv.org/abs/1304.0662"> this article </a>
  * for more details.
  *
+ * \image html "gic_complex.png" "GIC of a point cloud."
+ *
  * \subsection gicexample Example
  *
  * This example builds the GIC of a point cloud sampled on a 3D human shape (human.off).
diff --git a/src/Nerve_GIC/doc/gic_complex.png b/src/Nerve_GIC/doc/gic_complex.png
new file mode 100644
index 00000000..fb4b20ad
--- /dev/null
+++ b/src/Nerve_GIC/doc/gic_complex.png
diff --git a/src/Nerve_GIC/doc/nerve.png b/src/Nerve_GIC/doc/nerve.png
new file mode 100644
index 00000000..b66da4a4
--- /dev/null
+++ b/src/Nerve_GIC/doc/nerve.png