Handle and Tunnel Loops Computation on Surfaces




In this research we focus on detecting and computing loops on surfaces that are topologically and geometrically meaningful. We define handle and tunnel loops on surfaces using homology groups. Intuitively, handle loops can be contracted to a point in the interior of the shape and cannot be contracted to a point in the exterior of the shape. Tunnel loops are similarly defined in a complementary way. See the paper below for precise definitions.

T. K. Dey, K. Li, and J. Sun. On computing handle and tunnel loops. IEEE Proc. NASAGEM 2007, to appear.

We compute handle and tunnel loops for a class of surfaces that are graph retractable (versus surfaces that are "knotted"). The interiors and exteriors of a graph retractable surface retract to inside and outside curve skeletons respectively. They are called core graphs based on which handle and tunnel loops are computed. The curve skeletons are generated by an algorithm described in  Defining and computing curve skeletons with medial geodesic function.

A CAD model that is graph retractable. Two knotted models that are not graph retractable.

We characterize handle and tunnel loops on graph retractable surfaces in terms of their linking with the core graphs.  This characterization gives detection and generation algorithms for the loops. Our algorihtm incorporates geometry into the topological algorihm that enable our software to generate ``very good" handle and tunnel loops (as shown below).

Handle (green) and tunnel (red) loops computed on tested models. The interior and exterior curve skeletons (core graphs) are also shown on the models.

We also apply handle and tunnel loops to feature detection and topological simplifications. For example, handle / tunnel features could be obtanined by sweeping the initial handle / tunnel loops in both directions for some distance. To remove insignificant topologies, one can further cut / fill the corresponding handle / tunnel features. Examples are shown below.

Feature detection and topological simplification.

The HandleTunnel software based on this result is available but we recommend the new HanTun software
based on a follow-up result.