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From: toms@ncifcrf.gov (Tom Schneider)
Newsgroups: comp.graphics,sci.math,sci.math.num-analysis
Subject: Re: Need to fit a circle to some points
Keywords: circle algorithm least-squares fit
Message-ID: <938@fcs280s.ncifcrf.gov>
Date: 2 Jun 89 00:54:48 GMT
References: <573@lehi3b15.csee.Lehigh.EDU> <1088@osf.OSF.ORG>
Reply-To: toms@ncifcrf.gov (Tom Schneider)
Organization: NCI Supercomputer Center, Frederick, MD
Lines: 29

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
>>book son least squares anaylsis, but can only find simple cases.  I
>>started to do the math, but it became rather involved very quickly.
>>
>>Stephen Corbesero                              flash@lehi3b15.UUCP
>>VLSI Design Automation Lab                     flash@lehi3b15.CSEE.Lehigh.EDU
>>Computer Science And Electrical Engineering,   usgcorb@vax1.CC.Lehigh.EDU
>>Lehigh University, Bethlehem, PA 18015
>  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.

That was my first thought also.  But suppose that all of the data points
lie on one side of the circle, or are confined to a small angular region.
Then this method will fail because it will place the center much to close
to the circle.  If Stephen knows that the points are pretty well spread
around then this method should be pretty good, but it wouldn't be as good
as a true least squares fit.  Seems to me that should be possible, where
one is determining the minimum square radial distance from each point
to the circle along radii.  (Also an MIT grad, but in biology!)
  Tom Schneider
  National Cancer Institute
  Laboratory of Mathematical Biology
  Frederick, Maryland  21701-1013
  toms@ncifcrf.gov