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Proceedings of CAD'14, 2014, 97-99
Computing Mitered Offset Curves Based on Straight Skeletons

Peter Palfrader, Martin Held, University of Salzburg

Abstract. The straight skeleton of a polygon in 2D was first defined by Aichholzer et al. It is the geometric graph whose edges are the traces of vertices of shrinking mitered offset curves of the polygon. Straight skeletons are a versatile tool in computational geometry and have found applications in diverse fields of industry and science. For example, Tomoeda et al. use straight skeletons to create signs with an illusion of depth, while Sugihara uses (weighted) straight skeletons in the design of pop-up cards. Aichholzer et al apply straight skeletons for roof design and terrain generation. In order to provide a practical tool for mitered offsetting, we converted Aichholzer and Aurenhammer's theoretical description into an implementation that can cope with real-world data. In Palfrader et al, we sketched the theoretical basis of an extension and modification of their algorithm necessary for computing the straight skeleton of a general PSLG within the entire plane, without relying on an implicit assumption of general position of the input. More recently, while implementing our straight-skeleton code Surfer based on the theoretical basis laid out in our prior work, we investigated the peculiarities of a realization of that algorithm on a standard floating-point arithmetic. For instance, we refined the naive (determinant-based) computation of the collapse times in order to make it numerically more reliable.

Keywords. Straight skeleton, mitered offset, beveled offset

DOI: 10.14733/cadconfP.2014.97-99