Computing handle and tunnel loops with knot linking

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 gg always has gg handle and gg 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.