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authorsalinasd <salinasd@636b058d-ea47-450e-bf9e-a15bfbe3eedb>2014-12-17 16:37:27 +0000
committersalinasd <salinasd@636b058d-ea47-450e-bf9e-a15bfbe3eedb>2014-12-17 16:37:27 +0000
commit0ef4de65595354c0bad3a9f19d314a5de7d29d92 (patch)
tree9830a4c2d11581981ec5067e2d97a2ae2f69da67 /src/Skeleton_blocker/include
parent9097b9ef34b7b15b0313ab9b7f057c0b4b4f5eb6 (diff)
merge doc
git-svn-id: svn+ssh://scm.gforge.inria.fr/svnroot/gudhi/trunk@377 636b058d-ea47-450e-bf9e-a15bfbe3eedb Former-commit-id: f50f6eda2f484864be2bf27960a58dbbbaba9793
Diffstat (limited to 'src/Skeleton_blocker/include')
-rw-r--r--src/Skeleton_blocker/include/gudhi/Skeleton_blocker.h17
1 files changed, 8 insertions, 9 deletions
diff --git a/src/Skeleton_blocker/include/gudhi/Skeleton_blocker.h b/src/Skeleton_blocker/include/gudhi/Skeleton_blocker.h
index e67323e5..77f59e35 100644
--- a/src/Skeleton_blocker/include/gudhi/Skeleton_blocker.h
+++ b/src/Skeleton_blocker/include/gudhi/Skeleton_blocker.h
@@ -41,10 +41,9 @@ namespace skbl{
\author David Salinas
\section Introduction
-The Skeleton-Blocker data-structure had been introduced in the two papers
-\cite socg_blockers_2011,\cite blockers2012.
-It proposes a light encoding for simplicial complexes by storing only an *implicit* representation of its
-simplices.
+The Skeleton-Blocker data-structure proposes a light encoding for simplicial complexes by storing only an *implicit* representation of its
+simplices
+\cite socg_blockers_2011,\cite blockers2012.
Intuitively, it just stores the 1-skeleton of a simplicial complex with a graph and the set of its "missing faces" that
is very small in practice (see next section for a formal definition).
This data-structure handles all simplicial complexes operations such as
@@ -60,7 +59,7 @@ An abstract simplex is a finite non-empty set and its dimension is its number of
Whenever \f$\tau \subset \sigma\f$ and \f$\tau \neq \emptyset \f$, \f$ \tau \f$ is called a face of
\f$ \sigma\f$ and \f$ \sigma\f$ is called a coface of \f$ \tau \f$ . Furthermore,
when \f$ \tau \neq \sigma\f$ we say that \f$ \tau\f$ is a proper-face of \f$ \sigma\f$.
-An abstract simplicial complex is a set of simplices that contains all the faces of their simplices.
+An abstract simplicial complex is a set of simplices that contains all the faces of its simplices.
The 1-skeleton of a simplicial complex (or its graph) consists of its elements of dimension lower than 2.
*\image html "ds_representation.png" "Skeleton-blocker representation" width=20cm
@@ -81,8 +80,8 @@ In practice, the set of blockers of a simplicial complex
remains also small when simplifying a Rips complex with edge contractions
but also for most of the simplicial complexes used in topological data-analysis such as Delaunay, Cech or Witness complexes.
For instance, the numbers of blockers is depicted for random 3-dimensional spheres embedded into \f$R^4\f$
-in next figure. Storing the graph and blockers of such simplicial complex is much compact in this case than storing
-its simplices.
+in next figure. Storing the graph and blockers of such simplicial complexes is much compact in this case than storing
+their simplices.
*\image html "blockers_curve.png" "Number of blockers of random triangulations of 3-spheres" width=10cm
@@ -94,7 +93,7 @@ its simplices.
\subsection Overview
-Four classes are implemented for simplicial complex in this representation namely (most user will just need to use Skeleton_blocker_geometric_complex)
+Four classes are implemented for simplicial complex in this representation namely (most user will just need to use Skeleton_blocker_geometric_complex):
\li Skeleton_blocker_complex : a simplicial complex with basic operations such as vertex/edge/simplex enumeration and construction
\li Skeleton_blocker_link_complex : the link of a simplex in a parent complex. It is represented as a sub complex
@@ -181,7 +180,7 @@ The Euler Characteristic is 1
\subsection Acknowledgements
The author wishes to thank Dominique Attali and André Lieutier for
-their collaboration to write the two initial papers about this data-structure
+their collaboration to write the two initial papers (cite socg_blockers_2011,\cite blockers2012) about this data-structure
and also Dominique for leaving him use a prototype.