eight.base_0.m	eight.base_1.m	eight.base_2.m	eight.base_3.m

Algorithm Description

The algorithm computes the fundamental group generators for closed meshes, which are also the basis for the first homology group.

Input and output

• The input is a closed mesh.
• The output is the fundamental group generators. Each loop is recorded as a set of sharp edges on a mesh.

Command

   homology.exe eight.m eight.base
   The outputs are
   eight.base_0.m eight.base_1.m eight.base_2.m eight.base_3.m

Computational Stability

   The computation is purely combinatorial, it is very stable.

Example

   The input mesh has 7k faces. The computational time is less than 1 seconds on a PC with 3.0 GB of RAM, 3.60 GHz CPU. The data set and the source can be downloaded.