Many applications such as topology repair, model editing, surface parameterization, and feature recognition benefit from computing loops on surfaces that wrap around their 'handles' and 'tunnels'. Computing such loops while optimizing their geometric lengths is difficult. On the other hand, computing such loops without considering geometry is easy but may not be very useful. In this paper we strike a balance by computing topologically correct loops that are also geometrically relevant. Our algorithm is a novel application of the concepts from topological persistence introduced recently in computational topology. The usability of the computed loops is demonstrated with some examples in feature identification and topology simplification. 

[Paper] [Project Page] [HanTun Software] [Video]

Many applications seek to identify features like handles and tunnels in a shape bordered by a surface embedded in three dimensions. To this end we define handle and tunnel loops on surfaces which can help identifying these features. We show that a closed surface of genus g always has g handle and g tunnel loops induced by the embedding. For a class of shapes that retract to graphs, we characterize these loops by a linking condition with these graphs. These characterizations lead to algorithms for detection and generation of these loops. We provide an implementation with applications to feature detection and topology simplification to show the effectiveness of the method.

[Paper] [Project Page] [HandleTunnel Software] [Slides at NASAGEM2007]