A Faster Algorithm for Computing Straight Skeletons
We present a new algorithm for computing the straight skeleton of a polygon. For a polygon with n vertices, among which r are reflex vertices, we give a deterministic algorithm that reduces the straight skeleton computation to a motorcycle graph computation in O(n (log n) log r) time. It improves on...
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| Language: | en |
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2014
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| Online Access: | Mencel, L. A. (2014). A Faster Algorithm for Computing Straight Skeletons. KAUST Research Repository. https://doi.org/10.25781/KAUST-O3U19 http://hdl.handle.net/10754/316713 |
| Summary: | We present a new algorithm for computing the straight skeleton of a polygon. For a polygon with n vertices, among which r are reflex vertices, we give a deterministic algorithm that reduces the straight skeleton computation to a motorcycle graph computation in O(n (log n) log r) time. It improves on the previously best known algorithm for this reduction, which is randomised, and runs in expected O(n √(h+1) log² n) time for a polygon with h holes. Using known motorcycle graph algorithms, our result yields improved time bounds for computing straight skeletons. In particular, we can compute the straight skeleton of a non-degenerate polygon in O(n (log n) log r + r^(4/3 + ε)) time for any ε > 0. On degenerate input, our time bound increases to O(n (log n) log r + r^(17/11 + ε)) |
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