Constriction Computation using Surface Curvature

Abstract

This paper provides a curvature-based algorithm to compute locally shortest geodesics on closed triangulated surfaces. These curves, which are called "constrictions", are useful for shape segmentation. The key idea of the algorithm is that constrictions are almost plane curves; it first finds well-located simple, plane, closed curves, and then slides them along the surface until a shortest geodesic is reached. An initial curve is defined as a connected component of the intersection between the surface and a plane going through an initial vertex. Initial vertices and planes are determined using approximations of surface curvature.