Computing Handle and Tunnel Loops on Surfaces

Nonseparating loops on surfaces generate their first homology group. Among these loops the ones which become trivial in the homology of the bounded space bordered by the surface are called handle loops. The other ones which become trivial in the homology of the unbounded space bordered by the surface are called tunnel loops. The handle and tunnel loops help identifying handles and tunnels for a shape. In this paper we provide a topological analysis leading to an algorithm that can compute loops on surfaces with the distinction whether they are handle or tunnel loops. An implementation of the algorithm shows its effectiveness on practical models.