Newsgroups: comp.robotics
Path: brunix!cat.cis.Brown.EDU!agate!howland.reston.ans.net!EU.net!uknet!comlab.ox.ac.uk!cameron
From: cameron@comlab.ox.ac.uk (Stephen Cameron)
Subject: Re: Minimum rectangle enclosing a set of 2D points
Message-ID: <1994Jun2.130417.9889@emerald.comlab.ox.ac.uk>
Originator: cameron@emerald.comlab
Organization: Oxford University Computing Laboratory
References: <2sdsgo$mb6@schema.fiu.edu> <2se26j$s5c@search01.news.aol.com>
Date: Thu, 2 Jun 1994 13:04:17 GMT
Lines: 12


In the general case, start by computing the convex hull. Then
there's a proof (can't remember the reference just now) that
the enclosing rectangle of minimum area has (at least) one side
colinear with a side of the hull.  So for an n-sided hull that
gives you n possible rectangles to consider.  If you're smart you
can consider all of these in O(n) time, by by keeping track of the
`far', 'left' and `right' boundaries of the rectangle as you work
your way around the hull.

Stephen Cameron

