merge doc

git-svn-id: svn+ssh://scm.gforge.inria.fr/svnroot/gudhi/trunk@377 636b058d-ea47-450e-bf9e-a15bfbe3eedb

Former-commit-id: f50f6eda2f484864be2bf27960a58dbbbaba9793

1 files changed, 25 insertions, 25 deletions

diff --git a/src/Contraction/include/gudhi/Edge_contraction.h b/src/Contraction/include/gudhi/Edge_contraction.h
index 94638415..5dcdbeb2 100644
--- a/src/Contraction/include/gudhi/Edge_contraction.h
+++ b/src/Contraction/include/gudhi/Edge_contraction.h
@@ -44,23 +44,23 @@ namespace contraction{
 \section Introduction
 
 The purpose of this package is to offer a user-friendly interface for edge contraction simplification of huge simplicial complexes.
-It uses the \ref skbl data-structure whose size remains small  during simplification 
-of most used geometrical complexes in topological data analysis such as the Rips or the Delaunay complexes (much lower than the total number of simplices in practice).
+It uses the \ref skbl data-structure whose size remains small  during simplification  
+of  most used geometrical complexes of topological data analysis such as the Rips or the Delaunay complexes. In practice, the 
+size of this data-structure is even uch lower than the total number of simplices.
 
 The edge contraction operation consists in identifying two vertices of a simplicial complex. 
-Several algorithms have been developed in computer graphics that allows to reduce efficiently the size of a
-simplicial complex while preserving its geometry 
-\cite Garland \cite Lindstrom.
-These approaches can be extended to higher-dimensional simplicial complexes. 
+A lot of algorithms have been developed in computer graphics that allows to reduce efficiently the size of 2-dimensional simplicial complexes
+ while preserving its geometry (for instance see \cite Garland \cite Lindstrom).
+These approaches can be extended to higher-dimensional simplicial complexes.
 The main advantage of using the Skeleton-Blocker data structure for edge contraction is that when the number of blockers is small, 
-most operations needed (link computation, edge contraction and so on) have polynomial complexity regarding the size the graph. 
-The simplification can be done without enumerating the set of simplices that is often non tracktable in high-dimension and is then very efficient
+the operations needed for edge contraction algorithms have polynomial complexity regarding the size the graph. 
+Therefore, the simplification can be done without enumerating the set of simplices that is often non tracktable in high-dimension and is then very efficient
 (sub-linear with regards to the number of simplices in practice).
 
-A typical application of this package for homology group computation and is illustrated in the next figure where a Rips is built uppon a set of high-dimensional points and
+A typical application of this package is homology group computation. It is illustrated in the next figure where a Rips complex is built uppon a set of high-dimensional points and
 simplified with edge contractions.
-It has initially a big number of simplices (around 20 millions) but simplifying it to a much reduced form with 15 vertices (and 714 simplices) takes only few seconds on a desktop machine (see the example bellow).
-One can then compute homology group with a simplicial complex of less than one hundred simplices instead of running the homology algorithm on the much bigger initial set of 
+It has initially a big number of simplices (around 20 millions) but simplifying it to a much reduced form with only 15 vertices (and 714 simplices) takes only few seconds on a desktop machine (see the example bellow).
+One can then compute homology group with a simplicial complex having very few simplices instead of running the homology algorithm on the much bigger initial set of 
 simplices which would take much more time and memory.
 
 
@@ -68,7 +68,7 @@ simplices which would take much more time and memory.
 
 \section Design
 
-This class design is policy based and heavily inspired from the similar edge collapse package of CGAL http://doc.cgal.org/latest/Surface_mesh_simplification/index.html (which is restricted to 2D triangulations).
+This class design is policy based and heavily inspired from the similar edge collapse package of CGAL http://doc.cgal.org/latest/Surface_mesh_simplification/index.html (which is however restricted to 2D triangulations).
 
 
 \subsection Policies
@@ -77,7 +77,7 @@ Four policies can be customized in this package:
 
 \li Cost_policy: specify how much cost an edge contraction of a given edge. The edge with lowest cost is iteratively picked and contracted if valid.
 \li Valid_contraction_policy: specify if a given edge contraction is valid. For instance, this policy can check the link condition which ensures that the homotopy type is preserved afer the edge contraction.
-\li Placement_policy: every time an edge is contracted, its points are merge to one point specified by this policy. This may be the middle of the edge of some more sofisticated point such as the minimum of a cost as in 
+\li Placement_policy: every time an edge is contracted, its points are merge to one point specified by this policy. This may be the middle of the edge of some more sophisticated point such as the minimum of a cost as in 
 \cite Garland.
 
 
@@ -86,27 +86,27 @@ Four policies can be customized in this package:
 A visitor which implements the class Contraction_visitor gets called at several key moments
 during the simplification:
 
-\li when the algorithms starts or ends
-\li when an edge is seen for the first time
-\li when an edge is considered for an edge contraction
-\li before and after an edge is contracted
+\li when the algorithms starts or ends,
+\li when an edge is seen for the first time,
+\li when an edge is considered for an edge contraction,
+\li before and after an edge is contracted.
 
 This allows to implements most of edge contraction based algorithm with this 
-package. 
+package without having to change the main simplification source code.
 
 
 \section Performance 
 
 The next figure shows the computation time to reduce a random 2-sphere to a single tetrahedron with 
-this package and with the CGAL equivalent package (to is specific to 2-manifold simplicial complexes).
+this package and with the CGAL equivalent package.
 Despite this package is able to deal with \a arbitrary simplicial complexes (any dimensions, manifold or non manifold),
-it is still \a 65% times faster than CGAL package which is focused on 2-manifold. 
+it is still \a 65% times faster than the CGAL package which is focused on 2-manifold. 
 The main reason is that few blockers appears during the simplification and hence,
 the algorithm only have to deal with the graph and not higher-dimensional simplices
 (in this case triangles). However, we recall that higher-dimensional simplices are \a implicitely 
-stored in the \ref skbl data-structure and hence, if one has to store nodes
-to simplices in an external map if storing information on simplices such 
-as orientation is needed.
+stored in the \ref skbl data-structure. Hence, one has to store
+simplices in an external map if some information needs to be associated with them (information that could be a filtration value or 
+an orientation for instance).
 
 
 \image html "sphere_contraction.png" "Time in seconds to simplify random 2-spheres to a tetrahedron" width=10cm
@@ -114,8 +114,8 @@ as orientation is needed.
 \section Example
 
  
-This example loads points in an off file and build the Rips complex with an user provided parameter. It then simplifies the build Rips complex
-while ensuring that homotopy type is preserved during the contraction (edge are contracted only when the link condition is valid).
+This example loads points from an OFF file and builds the Rips complex with an user provided parameter. It then simplifies the built Rips complex
+while ensuring its homotopy type is preserved during the contraction (edge are contracted only when the link condition is valid).
 
   \code{.cpp}
 #include <boost/timer/timer.hpp>