Maximum-Area Rectangles in a Simple Polygon

10/19/2019
by   Yujin Choi, et al.
0

We study the problem of finding maximum-area rectangles contained in a polygon in the plane. There has been a fair amount of work for this problem when the rectangles have to be axis-aligned or when the polygon is convex. We consider this problem in a simple polygon with n vertices, possibly with holes, and with no restriction on the orientation of the rectangles. We present an algorithm that computes a maximum-area rectangle in O(n^3log n) time using O(kn^2) space, where k is the number of reflex vertices of P. 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 contained in a convex polygon with n vertices in O(n^3) time using O(n) space.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
07/24/2020

Largest triangles in a polygon

We study the problem of finding maximum-area triangles that can be inscr...
research
07/01/2023

Maximum Overlap Area of Several Convex Polygons Under Translations

Let k ≥ 2 be a constant. Given any k convex polygons in the plane with a...
research
01/08/2023

Maximum overlap area of a convex polyhedron and a convex polygon under translation

Let P be a convex polyhedron and Q be a convex polygon with n vertices i...
research
11/01/2017

Finding all Maximal Area Parallelograms in a Convex Polygon

We consider the problem of finding the maximum area parallelogram (MAP) ...
research
05/23/2018

Maximal and maximum transitive relation contained in a given binary relation

We study the problem of finding a maximal transitive relation contained ...
research
05/30/2019

Largest Inscribed Rectangles in Geometric Convex Sets

We consider the problem of finding inscribed boxes and axis-aligned insc...
research
07/14/2020

A Practical Algorithm with Performance Guarantees for the Art Gallery Problem

Given a closed simple polygon P, we say two points p,q see each other if...

Please sign up or login with your details

Forgot password? Click here to reset