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首页> 外文期刊>Computational geometry: Theory and applications >Maximum-area and maximum-perimeter rectangles in polygons
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Maximum-area and maximum-perimeter rectangles in polygons

机译：多边形中的最大区域和最大周长矩形

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摘要

We study the problem of finding maximum-area and maximum-perimeter rectangles that are inscribed in polygons in the plane. There has been a fair amount of work on this problem when the rectangles have to be axis-aligned or when the polygons are convex. We consider this problem in polygons with n vertices that are not necessarily convex, possibly with holes, and with no restriction on the orientation of the rectangles. We present an algorithm that computes a maximum-area rectangle and a maximum-perimeter rectangle in O (n(3) log n) time using O (kn(2) + n) space, where k is the number of reflex vertices of the polygon. Our algorithm can report all maximum-area rectangles in the same time using O (n(3)) space. We also present a simple algorithm that finds a maximum-area rectangle inscribed in a convex polygon with n vertices in O (n(3)) time using O(n) space. (c) 2020 Elsevier B.V. All rights reserved.
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