Xref: utzoo comp.theory:498 comp.sources.wanted:11095 sci.math:10396 sci.math.num-analysis:668 Path: utzoo!utgpu!news-server.csri.toronto.edu!cs.utexas.edu!mailrus!hellgate.utah.edu!helios.ee.lbl.gov!pasteur!ucbvax!hplabs!hplabsz!sartin From: sartin@hplabsz.HPL.HP.COM (Rob Sartin) 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: <5021@hplabsz.HPL.HP.COM> Date: 23 Mar 90 02:27:42 GMT References: <3078@soleil.oakhill.UUCP> <18376@duke.cs.duke.edu> Reply-To: sartin@hplabs.hp.com Organization: Hewlett-Packard, Software Technology Lab Lines: 28 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) > > where P1 and P2 are the pair of points that are separated by a distance >larger than any other given pair of points. (i.e. maximum apart) 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). So: distance(P1, P2) <= D <= 2 * distance(P1, P2) where P1 and P2 are the points with greatest separation. I'm not sure how this observation helps in the solution of the problem. I haven't even thought about that. Rob Sartin uucp: hplabs!sartin "Some may say that I have gone astray. internet: sartin@hplabs.hp.com How would they know? They never follow."