Abstract
We study the computation of the straight skeleton of a planar straight-line graph (PSLG) by means of the triangulation-based wavefront propagation proposed by Aichholzer and Aurenhammer in 1998, and provide both theoretical and practical insights. As our main theoretical contribution we explain the algorithmic extensions and modifications 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, and when using a finite-precision arithmetic. We implemented this extended algorithm in C and report on extensive experiments. Our main practical contribution is (1) strong experimental evidence that the number of flip events that occur in the kinetic triangulation of real-world data is linear in the number n of input vertices, (2) that our implementation, Surfer, runs in \(\ensuremath\mathcal{O}(n \log n)\) time on average, and (3) that it clearly is the fastest straight-skeleton code currently available.
The authors would like to thank Willi Mann for valuable discussions and comments. Work supported by Austrian FWF Grant L367-N15.
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Palfrader, P., Held, M., Huber, S. (2012). On Computing Straight Skeletons by Means of Kinetic Triangulations. In: Epstein, L., Ferragina, P. (eds) Algorithms – ESA 2012. ESA 2012. Lecture Notes in Computer Science, vol 7501. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33090-2_66
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DOI: https://doi.org/10.1007/978-3-642-33090-2_66
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