Xref: utzoo comp.theory:504 comp.sources.wanted:11106 sci.math:10402 sci.math.num-analysis:672 Path: utzoo!attcan!uunet!tut.cis.ohio-state.edu!toto.cis.ohio-state.edu!john_kolen From: john_kolen@toto.cis.ohio-state.edu Newsgroups: comp.theory,comp.sources.wanted,sci.math,sci.math.num-analysis Subject: Re: Smallest circle around n points in space. Keywords: circle, distance, math, algorithms Message-ID: <78402@tut.cis.ohio-state.edu> Date: 23 Mar 90 16:18:02 GMT References: <3078@soleil.oakhill.UUCP> <18376@duke.cs.duke.edu> <5021@hplabsz.HPL.HP.COM> Sender: usenet_news@tut.cis.ohio-state.edu Reply-To: john kolen Followup-To: comp.theory Organization: Ohio State University Computer and Information Science Lines: 22 In article <5021@hplabsz.HPL.HP.COM> sartin@hplabs.hp.com writes: >In article <18376@duke.cs.duke.edu> avr@romeo.cs.duke.edu (A. V. Ramesh) writes: >>2. The bounds of the diameter of this circle are >> distance (P1,P2) < D < sqrt(3) distance(P1,P2) >I don't think that's correct. D could be equal to the distance between >P1 and P2 of all other points are contained within the circle with >center halfway between P1 and P2 and radius distance(P1, P2). D could >be as large as 2 * distance(P1, P2) if there exists P3 with >distance(P1,P2) = distance (P2, P3) = distance(P1, P3)/2 (i.e. P3 on >the line defined by P1, P2 at distance distance(P1, P2) on the opposite >side of P2 from P1). If this was true, then (P1,P3) would be the maximal pair, a contradiction. Given that (P1,P2) is the maximal pair, all points must lie in the intersections of the circles centered at P1 and P2 with radius distance(P1,P2). -- John Kolen (kolen-j@cis.ohio-state.edu)|computer science - n. A field of study Laboratory for AI Research |somewhere between numerology and The Ohio State Univeristy |astrology, lacking the formalism of the Columbus, Ohio 43210 (USA) |former and the popularity of the latter