On Computing Handle and Tunnel Loops

Tamal K. Dey      Kuiyu Li      Jian Sun

IEEE Proc. Internat. Conf. Cyberworlds 2007. (Journal version is in Computer-Aided Design: doi:10.1016/j.cad.2009.01.001)

Abstract

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.

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