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VigneronAntoine

Vigneron, Antoine
Geometric Algorithms Lab.
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Maximizing the overlap of two planar convex sets under rigid motions

Author(s)
Ahn, Hee-KapCheong, OtfriedPark, Chong-DaeShin, Chan-SuVigneron, Antoine
Issued Date
2005-06-06
DOI
10.1145/1064092.1064146
URI
https://scholarworks.unist.ac.kr/handle/201301/34493
Fulltext
http://dl.acm.org/citation.cfm?id=1064146
Citation
21st Annual Symposium on Computational Geometry, SCG'05, pp.356 - 363
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.
Publisher
21st Annual Symposium on Computational Geometry, SCG'05

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