Extremal polygon containment problems

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Given a convex polygonal object P and an environment consisting of polygonal obstacles, we seek a placement for the largest copy of P that does not intersect any of the obstacles, allowing translation, rotation and scaling. We employ the parametric search technique of Megiddo [Me], and the fixed size polygon placement algorithms developed by Leven and Sharir [LS, LS1], to obtain an algorithm that runs in time O(k24(kn) log3 (kn)loglog(kn)). We also present several other efficient algorithms for restricted variants of the extremal polygon containment problem, using the same ideas. These variants include: placement of the largest homothetic copies of one or two convex polygons in another convex polygon and placement of the largest similar copy of a triangle in a convex polygon.

Original languageEnglish
Title of host publicationProceedings of the Annual Symposium on Computational Geometry
PublisherAssociation for Computing Machinery
Number of pages10
ISBN (Print)0897914260
StatePublished - 1 Jun 1991
Event7th Annual Symposium on Computational Geometry, SCG 1991 - North Conway, United States
Duration: 10 Jun 199112 Jun 1991

Publication series

NameProceedings of the Annual Symposium on Computational Geometry


Conference7th Annual Symposium on Computational Geometry, SCG 1991
Country/TerritoryUnited States
CityNorth Conway


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