Re: A question on algebraic circle fitting
- From: Virgil <virgil@xxxxxxxxxxx>
- Date: Mon, 23 Oct 2006 22:20:03 -0600
In article <1161652895.263299.29890@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
anon5874@xxxxxxxxx wrote:
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?
Wouldn't 3 points specify the circle uniquely?
Not if they are colinear.
.
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- A question on algebraic circle fitting
- From: Thomas Mautsch
- Re: A question on algebraic circle fitting
- From: anon5874
- A question on algebraic circle fitting
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