Is there a standard procedure or algorithm for finding the best fit circular arc to an elliptical arc ?
Where the ellipse arc is:
- symmetrical about the minor axis, subtending $[+\theta, -\theta]$ from the centre.
- $\theta$ is between $0$ and $90$ degrees
It seems obvious that the centre of such a circular arc is on the minor axis and I can get good results graphically, but cannot find any analysis of the problem.
I'm not sure whether this will be the best fit but it would certainly be a good fit:
Pick the three points on the ellipse at $-\theta$, $0$, and $+\theta$ and then fit a circle to them as detailed here.
If no one is able to provide an analytical solution for the best fit then I can provide a numerical solution.