update documentation

This commit is contained in:
FrancisGipsa 2019-03-22 13:57:25 +01:00
parent a428595fbd
commit d42a92f898
3 changed files with 2 additions and 4 deletions

View File

@ -6,7 +6,7 @@
/*! /*!
\addtogroup PkgSurfaceMeshTopology \addtogroup PkgSurfaceMeshTopology
\cgalPkgDescriptionBegin{Surface Mesh Topology,PkgSurfaceMeshTopologySummary} \cgalPkgDescriptionBegin{Surface Mesh Topology,PkgSurfaceMeshTopologySummary}
\cgalPkgPicture{sm_topology_logo.svg} \cgalPkgPicture{surface-mesh-topology-logo.png}
\cgalPkgSummaryBegin \cgalPkgSummaryBegin
\cgalPkgAuthor{Guillaume Damiand, Francis Lazarus} \cgalPkgAuthor{Guillaume Damiand, Francis Lazarus}
\cgalPkgDesc{This package provides methods for testing if two (closed) paths on a combinatorial surface are homotopic. The user can choose between free homotopy and homotopy with fixed endpoints. The algorithms are based on a paper by Erickson and Whittlesey \cgalCite{ew-tcsr-13}. If the input surface has size \f$n\f$, the construction of a `Surface_mesh_curve_topology` takes \f$O(n)\f$ time. The homotopy tests are then linear in the size of the input curves.} \cgalPkgDesc{This package provides methods for testing if two (closed) paths on a combinatorial surface are homotopic. The user can choose between free homotopy and homotopy with fixed endpoints. The algorithms are based on a paper by Erickson and Whittlesey \cgalCite{ew-tcsr-13}. If the input surface has size \f$n\f$, the construction of a `Surface_mesh_curve_topology` takes \f$O(n)\f$ time. The homotopy tests are then linear in the size of the input curves.}

Binary file not shown.

After

Width:  |  Height:  |  Size: 12 KiB

View File

@ -1,3 +1 @@
Implementation of topological algorithms on surface meshes. Given two walks in the vertex-edge graph of a combinatorial map, this package provides linear time algorithms to decide if the walks are homotopic, i.e. can be continuously deformed one into the other on the surface of the combinatorial map. Two notions of homotopy are proposed. Homotopy with fixed basepoints applies to non necessarily closed walks and assumes that the common endpoints of the walks stay fix during the deformation. Free homotopy applies only to closed walks and does not impose any restriction on the deformation. Another helpful algorithm is provided to test if a single curve is contractible; it is equivalent to a homotopy test where one of the closed walks is reduced to a point.
TODO: an abstract.