Circle centre from three points on circumference

Neil Main

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Mar 14, 2001, 5:49:50 AM3/14/01

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I need to find the circle centre from three (or more for better
accuracy) points (x,y) on a circumference. Does anyone have a method or
pointers to books or websites? I have tried elementary geometry and
vector algebra books from college days but without success.
Thanks
--
Neil Main
"It's not only a race against the clock but a race against time itself."
Presenter on BBC Wales.

David Byrne

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Mar 14, 2001, 6:58:28 AM3/14/01

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Neil,

Check out Mathlab / Matlab (?)

Many sites have maths functions.

David

in article 7zrZrVAO...@micrometric.co.uk, Neil Main at
Neil...@micrometric.co.uk wrote on 14/3/01 9:49 PM:

Roger Butler

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Mar 14, 2001, 7:14:08 AM3/14/01

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Neil, I've just had a crack at this in Excel, and although it is lightly
tested, I think it works

Suppose your points are (xa,ya) , (xb,yb) and (xc,yc)

Then I think the centre of the circle, (a,b) is :

a=(ya^2+xa^2-yc^2-xc^2-(ya-yc)*(ya^2+xa^2-yb^2-xb^2)/(ya-yb))/2/(xa-xc-(ya-y
c)*(xa-xb)/(ya-yb))
b=(ya^2+xa^2-yb^2-xb^2-2*b*(xa-xb))/(ya-yb)/2

Regards
Rog

Neil Main <Neil...@micrometric.co.uk> wrote in message
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Roger Butler

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Mar 14, 2001, 7:15:40 AM3/14/01

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Oops, typo, b should have been :

b=(ya^2+xa^2-yb^2-xb^2-2*a*(xa-xb))/(ya-yb)/2

Rog

Roger Butler <roger....@marlborough-stirling.com> wrote in message
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Tushar Mehta

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Mar 14, 2001, 1:55:55 PM3/14/01

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I'm not sure if Roger Butler approached the problem the same way I did,
but here's my take on it.

The equation of a circle is (x-a)^2 + (y-b)^2 = r^2, where the center is
at (a,b) and the radius is r.

Given three points on the circumference (x1, y1), (x2, y2), and (x3,
y3), you have three equations in three unknowns.

If you don't want to do this algebraically, here's one numerical
approach.

Designate three cells, say A1, B1, and C1 as being a, b, and r.

Enter the coordinates of the 3 points in a 3x2 range, say A2:B4.

Now, create three equations in three cells, say C2:C4, with the formulas
corr. to the equation of the circle, one for each data point. For
example, one of them should be =(x1-a)^2 + (y1-b)^2 - r^2.

Sum these results in another cell, say C5.

Use Solver to solve for C5=0 by changing a, b, and r. The constraints
should include C2:C4>0 and r>0. Note that a and b can take any values.

Assignment complete.

--
Regards,

Tushar Mehta
www.tushar-mehta.com
--
In <7zrZrVAO...@micrometric.co.uk>, Neil Main
<Neil...@micrometric.co.uk> wrote

Neil Main

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Mar 16, 2001, 10:49:02 AM3/16/01

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In article <q_%r6.10308$tA5.1...@news2.cableinet.net>, Roger Butler
<roger....@marlborough-stirling.com> writes
>Yes, Tushar, I adopted the same approach.
>
>Tushar Mehta <ng_p...@bigfoot.com> wrote in message
>news:MPG.151988ca3...@msnews.microsoft.com...

>> I'm not sure if Roger Butler approached the problem the same way I did,
>> but here's my take on it.
>>

snip

Thanks everyone, done.
--
Neil Main
"Normal people believe that if it ain't broke, don't fix it. Engineers
believe that if it ain't broke, it doesn't have enough features yet."
----- Scott Adams, The Dilbert Principle

Roger Butler

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Mar 15, 2001, 4:32:32 AM3/15/01

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Yes, Tushar, I adopted the same approach.

Rog

Tushar Mehta <ng_p...@bigfoot.com> wrote in message
news:MPG.151988ca3...@msnews.microsoft.com...