NDLI: Theoretical and practical results on straight skeletons of planar straight-line graphs

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Theoretical and practical results on straight skeletons of planar straight-line graphs

Content Provider	ACM Digital Library
Author	Huber, Stefan Held, Martin
Abstract	We study straight skeletons and make both theoretical and practical contributions which support new approaches to the computation of straight skeletons of arbitrary planar straight-line graphs (PSLGs). We start with an adequate extension of the concept of motorcycle graphs to PSLGs, with motorcycles starting at the reflex vertices of a PSLG, which allows us to generalize well-known results on the relation between the straight skeleton and the motorcycle graph to arbitrary PSLGs: the edges of the motorcycle graph cover a specific subset of the edges of the straight skeleton, and they form the basis of 3D slabs such that the projection of the lower envelope of those slabs to the plane forms the straight skeleton. As an immediate application we sketch how to use a graphics hardware for computing (approximate) straight skeletons of PSLGs. Further, we present and analyze a novel wavefront-type algorithm which bridges the current gap between the theory and practice of straight-skeleton computations. Our algorithm handles arbitrary PSLGs, is easy to implement, and is fast enough to handle complex data: it can be expected to run in O(n log n) time in practice for an n-vertex PSLG; its worst-case complexity is $O(n^{2}$ log n). Extensive experimental results confirm an average runtime of 20 n log n µs on a standard PC for virtually all of our 13500 datasets of different characteristics. As also confirmed by our experiments, this constitutes an average gain in performance by a multiplicative factor of n, or at least one to two orders of magnitude, relative to the speed of the implementation provided by CGAL for closed polygons.
Starting Page	171
Ending Page	178
Page Count	8
File Format	PDF
ISBN	9781450306829
DOI	10.1145/1998196.1998223
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2011-06-13
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Motorcycle graph Wavefront propagation Experiments Implementation Straight skeleton
Content Type	Text
Resource Type	Article

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