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Re: fitting circle to data
From: |
macy |
Subject: |
Re: fitting circle to data |
Date: |
Mon, 30 Nov 2009 14:35:03 -0800 (PST) |
User-agent: |
SquirrelMail/1.4.13 |
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 IngenierÃa
>> Univ. Tecnológica Nacional Facultad Regional Córdoba. Argentina
>
>