Re: A question on algebraic circle fitting
- From: "Ray Koopman" <koopman@xxxxxx>
- Date: 24 Oct 2006 00:40:01 -0700
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?
This has been discussed before. See
http://groups-beta.google.com/group/sci.math/msg/392823fc18b9bc17
.
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- A question on algebraic circle fitting
- From: Thomas Mautsch
- A question on algebraic circle fitting
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