Computer-Aided Design and Applications (ISSN 1686-4360) is an independent, international peer-reviewed technical journal dedicated to the applications of computer-aided design and manufacturing.
Volume 8 Number 1 Pages 87-97
Curve Skeletons of Planar Domains
Abstract. Curve skeletons are 1D entities that capture the essential topology and geometry of a shape in a simple and very compact form, and have found a multitude of applications in engineering and science. The concept itself is ill-defined, which is why the many existing definitions are ad-hoc and employ heuristic algorithms revolving around the (unique) medial axis. We propose a framework for computing curve skeletons for arbitrary planar domains that relies on a modified medial axis, and is based on R-functions that can be thought of as continuous forms of the Boolean logic functions. Furthermore, we propose one particular definition of such a curve skeleton that preserves the homotopy of the domain, is stable in the presence of noise and is well-suited to downstream applications. The framework can be implemented in any commercial geometric kernel for planar domains, and has attractive computational properties. Furthermore, the mathematical concepts are extendable to medial surfaces and curve skeletons in 3D domains.
Keywords: distance functions, medial axis, curve skeletons.
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