Re: fitting circle to data

[Primoz PETERLIN]

Hi,

The method with the squares - not the abs() - is easy to solve 
analitically and is known as the Delogne-Kása method. There is more to 
fitting a circle to a set of data points than it looks at first; Nikolai 
Chernov provides an excellent overview of the state of the art:

http://www.math.uab.edu/~chernov/cl/

You can also find some Matlab code there which I believe runs with 
Octave as well.

Best regards,
Primož

address@hidden pravi:
> ARRRGGG!
>
> that should have been
> minimize the sum of the absolute values
>   sum( abs(R^2-(xi-x0)^2-(yi-y))^2) )
>
> since the error is already squared!
>
>
>   
> > From my naive approach:
> >
> > Given a circle or radius, R, with origin at x0 and y0:
> > the error for any data point is:
> > = R^2-(xi-x0)^2-(yi-y))^2
> >
> > now you must minimize the sum of the squares:
> > sum( (R^2-(xi-x0)^2-(yi-y))^2)^2 );
> >
> > Doing it without using sqrt function should preserve your final answers
> > completely in real space, right?
> >
> >
> >     
> > > Hello,
> > >
> > > i need to extract the radius and centre points of a circle fitting a
> > > set of datas. I was trying with this way
> > >
> > > xt = %data
> > > yt = %data
> > >
> > > F = @(x,p) sqrt( p(3).^2 -(x-p(1)).^2)+p(2)
> > > pin = [1;1;1]
> > >
> > > [f, p] = leasqr(xt,yt,pin,f);
> > >
> > > testing it with xt = 2+4*cos(thetas) and yt = 3+4*sin(thetas) works
> > > well,
> > > i get
> > > p =
> > >
> > >    2.0000 + 0.0000i
> > >    3.0000 + 0.0000i
> > >    4.0000 - 0.0000i
> > >
> > > but using the real data i get
> > > p =
> > >
> > >    -2.23630 -  0.62042i
> > >    12.24122 - 64.02140i
> > >     0.34923 + 59.63389i
> > >
> > > and should be aprox. p = [0, 300, 290]
> > >
> > > If i use pin =  [0; 300; 290] get
> > > p =
> > >
> > >     -2.2316 -   1.5828i
> > >     12.2604 - 162.9057i
> > >      0.3318 + 161.1838i
> > >
> > > is that right? how souhld i use this comples result?
> > > Thank you
> > >
> > > PD: here a few xt and yt datas
> > > xt =
> > >
> > >    29.94340
> > >    28.45820
> > >    27.19490
> > >    25.85900
> > >    24.73510
> > >    23.54580
> > >    21.88660
> > >    19.90880
> > >    17.77030
> > >    15.64780
> > >    13.04540
> > >    10.67190
> > >     8.43594
> > >     6.35659
> > >     4.31690
> > >     2.28645
> > >     0.19964
> > >    -1.74150
> > >    -3.66550
> > >    -5.75025
> > >    -7.75397
> > > ...
> > >  yt =
> > >
> > >    13.277
> > >    13.079
> > >    12.952
> > >    12.747
> > >    12.670
> > >    12.638
> > >    12.475
> > >    12.225
> > >    12.059
> > >    11.977
> > >    11.773
> > >    11.676
> > >    11.556
> > >    11.526
> > >    11.454
> > >    11.415
> > >    11.394
> > >    11.449
> > >    11.444
> > >    11.491
> > >    11.556
> > > ...
> > >
> > >
> > >
> > > --
> > > Gastón Araguás
> > > ______________________________________________________
> > > CIII - Centro de Investigación en Informática para la Ingeniería
> > > Univ. Tecnológica Nacional Facultad Regional Córdoba. Argentina
> > >       
> >     
>
>
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