Path: utzoo!attcan!utgpu!jarvis.csri.toronto.edu!clyde.concordia.ca!uunet!zephyr.ens.tek.com!uw-beaver!ubc-cs!alberta!dvinci!macphed
From: macphed@dvinci.usask.ca (Ian MacPhedran)
Newsgroups: comp.graphics
Subject: Re: smallest sphere enclosing a set of
Message-ID: <1989Dec12.204327.19909@dvinci.usask.ca>
Date: 12 Dec 89 20:43:27 GMT
References: <4893@skinner.nprdc.arpa>
Organization: University of Saskatchewan
Lines: 28

From article <4893@skinner.nprdc.arpa>, by malloy@nprdc.arpa (Sean Malloy):
> In article <658@cditi.UUCP> josh@cditi.UUCP (Josh Muskovitz) writes:
>>In article <207400043@s.cs.uiuc.edu-, mcooper@s.cs.uiuc.edu writes:
>>> [[Suggestion to use largest point to point distance as diameter of
>>> minimum circle.]]
>>  [[Point of exception for equilateral triangle.]]
> Then generalize it. Find the largest distance between any two points.
> Take all the pairs of points with that separation, and average their
> coordinates. This will give you the center of the sphere; the distance
> from that point to any of the equidistant points will give you the
> radius.

You'll have to be more general than this, all isosceles triangles with
equal angles between 45 and 60 degrees will fail, as will several more
general triangles (those with the sum of the two smaller angles greater
than 90 degrees). The case of the equilateral triangle is just a convenient
one.

Ian.

Ian MacPhedran, Engineering Computer Centre, University of Saskatchewan.
2B13 Engineering Building, U. of S. Campus, Saskatoon, Sask., CANADA S7N 0W0
macphed@dvinci.USask.CA  macphedran@sask.USask.CA  macphedran@sask.BITNET

-- 
Ian MacPhedran, Engineering Computer Centre, University of Saskatchewan.
2B13 Engineering Building, U. of S. Campus, Saskatoon, Sask., CANADA S7N 0W0
macphed@dvinci.USask.CA  macphedran@sask.USask.CA  macphedran@sask.BITNET