Nonlinear circle fit with known radius I have data points from a half circle and I already know the approximate radius. I want to find the circle which best fits the points using a fixed radius. How can I do this? If I solve the problem using a typical circle fit algorithm the radius is too unstable due to noise.
 A: I discovered the Hough Circle Transform method and have tested it now. It works really well so I will use it to find the optimal circle center for a given radius.
A: Here is one approach.
First find a line $L$ that passes through two points of your set and has all points on $L$ or to one side.
Then reflect your point set over $L$.  Finally, fit a full circle to the doubled set of points.
You might need a more careful approach, depending on how noisy is your data.
You could check the result against the center of gravity of your points.
I assume your points are from the semicircle boundary (as opposed to points from a half-disk).
Then I calculate that the center of gravity is $2 r/\pi$ to one side of the diameter.
If your fit circle's radius $r$ does not closely match this distance to the c.g.,
then adjustment of $L$ is indicated.
A: I have read about Hough Transfrom, it is good.
If you have like me just a few points (<10) and you are looking for the center of the best fitting circle (with fixed radius) you could:
take a pair of points
use them as the centers of two circles (of fixed radius)
find the apropriate intersection (on the right side)
repeat with all pairs
then the center of the best cicle is the mean point of all intersections.
