Goodness of Fit Metric for Circle Fits

All,

I have been trying to fit circles, portions of circles and arcs to my
data. Now I am in need of a metric for the goodness of fit. (Maybe
R-squared? correlation?).

The equation of the circle I use is
y.^2 + x.^2 + p1.*y + p2.*x + p3 = 0;

I have been using a number of methods to fit the data (circfit being
one of them and some other scripts that I have written). Now I need to
evaluate the performance of these methods. The question is primarily,
given parameters (p1, p2 p3) and x, how do I generate 'y_fit'?

I tried
angles = acos((x - centre_x)/radius);
y_fit = centre_y + radius*sin(angles);

And then compute the correlation between y & y_fit. However I am not
convinced that this is the best solution. If you can provide me some
insights/alternative methods, I would much appreciate it.

Regards
Vijit

.

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