Maximum-area and maximum-perimeter rectangles in polygons
SCIE
SCOPUS
- Title
- Maximum-area and maximum-perimeter rectangles in polygons
- Authors
- Choi, Yujin; Lee, Seungjun; Ahn, Hee-Kap
- Date Issued
- 2021-03
- Publisher
- Elsevier BV
- Abstract
- 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.
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/106643
- DOI
- 10.1016/j.comgeo.2020.101710
- ISSN
- 0925-7721
- Article Type
- Article
- Citation
- Computational Geometry: Theory and Applications, vol. 94, 2021-03
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