Re: A question on algebraic circle fitting
- From: Han de Bruijn <Han.deBruijn@xxxxxxxxxxxxxx>
- Date: Tue, 24 Oct 2006 13:57:47 +0200
Thomas Mautsch wrote:
Given a finite number of points in the plane, (x1,y1), (x2,y2), ..., (xn,yn), the "algebraic way" to fit a circle to these points is to minimize the sum
sum( (xi^2 + yi^2 + 2 D xi + 2 E yi + F)^2 , i = 1..n )
over the variables D,E,F.
Is it correct that the resulting minimizers will satisfy the condition
D^2 + E^2 >= F ?
Under what conditions will minimizers D,E,F exist? - A necessary condition is that not all points (xi,yi) lie on a common line in case n >= 3. Is this condition also sufficient, or what other conditions are there?
http://huizen.dto.tudelft.nl/deBruijn/programs/delphi.htm#BFC
Read the paragraph "Method by RI" (: Robert Israel). Yes, it is correct
that the resulting minimizers will satisfy the condition D^2 + E^2 >= F
as far as I can see.
Han de Bruijn
.
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