From c882b0478d4b0899005bf6c0e9528a1fc8785cf9 Mon Sep 17 00:00:00 2001
From: vrouvrea <vrouvrea@636b058d-ea47-450e-bf9e-a15bfbe3eedb>
Date: Tue, 16 Oct 2018 08:35:12 +0000
Subject: Toplex definition Remove witness complex graph to compare Toplex_map
 vs Simplex_tree

git-svn-id: svn+ssh://scm.gforge.inria.fr/svnroot/gudhi/branches/toplex_map@3955 636b058d-ea47-450e-bf9e-a15bfbe3eedb

Former-commit-id: 5a1fc1be157b74963faa98b7844b8b47e54a82b6
---
 src/Toplex_map/doc/Intro_Toplex_map.h | 31 ++++++++++++++-----------------
 1 file changed, 14 insertions(+), 17 deletions(-)

(limited to 'src/Toplex_map')

diff --git a/src/Toplex_map/doc/Intro_Toplex_map.h b/src/Toplex_map/doc/Intro_Toplex_map.h
index e3f18b32..93534e0e 100644
--- a/src/Toplex_map/doc/Intro_Toplex_map.h
+++ b/src/Toplex_map/doc/Intro_Toplex_map.h
@@ -2,7 +2,7 @@
  *    (Geometric Understanding in Higher Dimensions) is a generic C++
  *    library for computational topology.
  *
- *    Author:       François Godi
+ *    Author:       François Godi, Vincent Rouvreau
  *
  *    Copyright (C) 2017  INRIA
  *
@@ -32,27 +32,24 @@ namespace Gudhi {
  * @{
  * 
  * \section toplexmapdefinition Definition
- * 
- * Let's consider a simplicial complex, denote by \f$d\f$ its dimension
- * and by \f$k\f$ its number of maximal simplices.
- * Furthermore, denote by \f$\gamma_0\f$ the maximal number of toplices, i.e. maximal simplices,
- * that contain a same vertex.
  *
- * The goal of the Toplex Map is both to represent the complex in optimal
- * O(kd) space and to provide fast standard operations such as : insertion, removal
- * and membership of a simplex, contraction of an edge, collapses. The time needed
- * for these operation is linear or quadratic in \f$\gamma_0\f$ and \f$d\f$.
+ * A Toplex_map is a data structure to represent and store a simplicial complex. A "toplex" is the contraction of
+ * "top-simplex", also known as a maximal simplex. We will call "toplices" a set of "toplex".
  *
- * Toplex map is composed firstly of a raw storage of toplices and secondly of a
- * map which associate any vertex to a set of pointers toward all toplices
- * containing this vertex.
+ * Let's consider a simplicial complex, denote by \f$d\f$ its dimension and by \f$k\f$ its number of maximal simplices.
+ * Furthermore, denote by \f$\gamma_0\f$ the maximal number of toplices, i.e. maximal simplices, that contain a same
+ * vertex.
  *
- * \image html map.png
+ * The goal of the Toplex Map is both to represent the complex in optimal O(kd) space and to provide fast standard
+ * operations such as : insertion, removal, contraction of an edge, collapses and membership of a simplex. The time
+ * needed for these operation is linear or quadratic in \f$\gamma_0\f$ and \f$d\f$.
  *
- * The performances are a lot better than in simplex tree as soon you use maximal simplices and not simplices,
- * here the construction of a strong witness complex of a point set with growing parameter :
+ * Toplex map is composed firstly of a raw storage of toplices and secondly of a map which associate any vertex to a
+ * set of pointers toward all toplices containing this vertex.
+ *
+ * \image html map.png
  *
- * \image html graph.png
+ * The performances are a lot better than the `Simplex_tree` as soon you use maximal simplices and not simplices.
  *
  */
 /** @} */  // end defgroup toplex_map
-- 
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