Xref: utzoo comp.graphics:6073 sci.math:6979 sci.math.num-analysis:25
Path: utzoo!utgpu!watmath!watdragon!violet!wjmartiniii
From: wjmartiniii@violet.waterloo.edu (Bill Martin)
Newsgroups: comp.graphics,sci.math,sci.math.num-analysis
Subject: Re: Need to fit a circle to some points
Summary: Possible counter-example
Keywords: circle algorithm least-squares fit
Message-ID: <14378@watdragon.waterloo.edu>
Date: 8 Jun 89 21:54:35 GMT
References: <573@lehi3b15.csee.Lehigh.EDU> <1088@osf.OSF.ORG>
Sender: daemon@watdragon.waterloo.edu
Reply-To: wjmartiniii@violet.waterloo.edu (Bill Martin)
Organization: U. of Waterloo, Ontario
Lines: 18

In article <1088@osf.OSF.ORG> flowers@osf.org (Ken Flowers) writes:
>In article <573@lehi3b15.csee.Lehigh.EDU> flash@lehi3b15.csee.Lehigh.EDU (Stephen Corbesero) writes:
>>
>>I need an algorithm to fit a set of data points, obtained
>>experimentally, to the best-fit circle.  I have searched through many
>>-- 
>It seems to me that the best fit circle can be simply found by doing
>the following:
>
>    1.  Make the center the average point of all the data points.
>
>    2.  Make the radius the average distance from the center to each
>	data point.
>

With regard to the above approach, consider a large number of points lying
on a line. The given algorithm would choose a point on that line as the center
of the circle.  This is certainly not optimal in general.