Computational and structural advantages of circular boundary representation

Abstract

Boundary approximation of planar shapes by circular arcs has quantitive and qualitative advantages compared to using straight-line segments. We demonstrate this by way of three basic and frequent computations on shapes - convex hull, decomposition, and medial axis. In particular, we propose a novel medial axis algorithm that beats existing methods in simplicity and practicality, and at the same time guarantees convergence to the medial axis of the original shape. © Springer-Verlag Berlin Heidelberg 2007.