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https://doi.org/10.1145/1064092.1064146
Title: | Maximizing the overlap of two planar convex sets under rigid motions | Authors: | Ahn, H.-K. Cheong, O. Park, C.-D. Shin, C.-S. Vigneron, A. |
Keywords: | Approximation algorithm Convex shape Pattern matching Sublinear algorithm |
Issue Date: | 2005 | Citation: | Ahn, H.-K.,Cheong, O.,Park, C.-D.,Shin, C.-S.,Vigneron, A. (2005). Maximizing the overlap of two planar convex sets under rigid motions. Proceedings of the Annual Symposium on Computational Geometry : 356-363. ScholarBank@NUS Repository. https://doi.org/10.1145/1064092.1064146 | Abstract: | Given two compact convex sets P and Q in the plane, we compute an image of P under a rigid motion that approximately maximizes the overlap with Q. More precisely, for any ε > 0, we compute a rigid motion such that the area of overlap is at least 1 -ε times the maximum possible overlap. Our algorithm uses O(l/ε) extreme point and line intersection queries on P and Q, plus O((1/ε2)log(1/ε)) running time. If only translations are allowed, the extra running time reduces to O((1/ε) log(1/ε)). If P and Q are convex polygons with n vertices in total, the total running time is O((1/ε) logn+(1/ε2) log(1/ε)) for rigid motions and O((1/ε) log n + (1/ε) log(1/ε)) for translations. Copyright 2005 ACM. | Source Title: | Proceedings of the Annual Symposium on Computational Geometry | URI: | http://scholarbank.nus.edu.sg/handle/10635/40716 | DOI: | 10.1145/1064092.1064146 |
Appears in Collections: | Staff Publications |
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