Computing handle and tunnel loops with knot linking

Authors:
Tamal K. Dey;Kuiyu Li;Jian Sun
Affiliations:
Department of Computer Science and Engineering, The Ohio State University, 2015 Neil Ave, Columbus, OH 43210, USA;Department of Computer Science and Engineering, The Ohio State University, 2015 Neil Ave, Columbus, OH 43210, USA;Department of Computer Science and Engineering, The Ohio State University, 2015 Neil Ave, Columbus, OH 43210, USA
Venue:
Computer-Aided Design
Year:
2009

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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 identify 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.