Circle fit

Fit a circle to a set of measured x,y points.

Description

Revival of a 14 years old code (written in 1991 for MATLAB 2.x).

Given a set of measured x,y pairs that a re supposed to reside on a circle, but with some added noise. A circle to these points, i.e. find xc,yc,R, such that (x-xc)^2+(y-yc)^2=R^2

The method minimizes the sum of squared radial deviations.

• Acknowledgements: This submission has inspired the following:; Ellipse Fit, Circle Fit (Kasa method), Circle Fit (Pratt method), Circle Fit (Taubin method)
• MATLAB release: MATLAB 5.2 (R10)
• Other Files: try_circ_fit.m, ; circfit.m

[Yuri Slobo...]

Can someone please enlighten me where one meets such distributions to be fitted by a circle ?

[Yogesh Mehta]

Yuri,

It can be extremely useful. For example, trying to fit a nyquist plot to an experimentally acquired FRFs... Ideally, nyquist plot is supposed to be a circle, but is not due 'noise'

[Bjorn Hemming]

I have used this function to verify a feature in a Metrology software giving correctly first 4 digits, so it seems OK

[Knut C. Naue]

Nice tool for data covering almost a complete circle. But if data exists describing only an arc, circfit fails identifying the assumed center and radius.

[Hedi Kawano]

http://www.math.niu.edu/~rusin/known-math/99/circlefi tells you that the equation used in this "circle_fit.m" gives an approximate solution.

[Hedi Kawano]

Sorry, it is
http://www.math.niu.edu/~rusin/known-math/99/circlefit
 (last "t" was missing)

[Tomaz Pepelnjak]

Very useful if you need to fit measured points to the circle function and compare it further to reference value.

[Luigi Rosa]

High-quality code, simple and effective

[shmi braun]

Re: Hedi Kawano

  see also
http://www.pitchup.com/matlab/print.aspx?article=168

[Sanjeev Sharma]

I found it to be very effective.

[Hendro Nurhadi]

Just... Excellent.. thanks.
:-)

[Richard Brown]

Note: This code doesn't minimise the sum of squared radial deviations - that is a nonlinear least squares problem

This code minimises sum((x.^2 + y.^2 - R^2).^2)

[Sebastian Laechele]

Works very well!
I don't really know how, but it works! :D
You saved me a bunch of hours there.
Thank you very much!

[Darren Hewett]

 

[Mehmet Alpay]

Works like a charm :-)

[Nikolai Chernov]

This circle fit has been first published by P.Delogne and I.Kasa in the 1970s and is known as "Kasa method" in statistics. It works well when points cover a large part of the circle but is heavily biased when points are restricted to a small arc. Better fits were proposed by Pratt and Taubin.