Re: fitting circle to data

[macy]

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
>
>