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Diffstat (limited to 'src/Contraction/include/gudhi')
| -rw-r--r-- | src/Contraction/include/gudhi/Edge_contraction.h | 12 |
1 files changed, 7 insertions, 5 deletions
diff --git a/src/Contraction/include/gudhi/Edge_contraction.h b/src/Contraction/include/gudhi/Edge_contraction.h index b5d85ae4..94638415 100644 --- a/src/Contraction/include/gudhi/Edge_contraction.h +++ b/src/Contraction/include/gudhi/Edge_contraction.h @@ -57,12 +57,14 @@ most operations needed (link computation, edge contraction and so on) have polyn 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 three figure where a Rips is built uppon a set of high-dimensional points. -It has initially a huge number of simplices (todo) but simplifying it to a much reduced form with todo vertices takes only few seconds on a desktop machine. +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 +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 -simplices. +simplices which would take much more time and memory. +\image html "so3.png" "Edge contraction illustration" \section Design @@ -71,7 +73,7 @@ This class design is policy based and heavily inspired from the similar edge col \subsection Policies -Four policies can be customized in this package. +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. @@ -107,7 +109,7 @@ to simplices in an external map if storing information on simplices such as orientation is needed. -\image html "sphere_contraction.png" "Time to simplify random 2-spheres to a tetrahedron" width=10cm +\image html "sphere_contraction.png" "Time in seconds to simplify random 2-spheres to a tetrahedron" width=10cm \section Example |