Heuristics for the Generation of Random Polygons
Proceedings of the 8th Canadian Conference on Computational Geometry
Motorcycle Graphs and Straight Skeletons
Algorithmica
Theoretical and practical results on straight skeletons of planar straight-line graphs
Proceedings of the twenty-seventh annual symposium on Computational geometry
A faster algorithm for computing motorcycle graphs
Proceedings of the twenty-ninth annual symposium on Computational geometry
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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.