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Is there a standard procedure or algorithm for finding the best fit circular arc to an elliptical arc ?

Where the ellipse arc is:

  1. symmetrical about the minor axis, subtending $[+\theta, -\theta]$ from the centre.
  2. $\theta$ 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.

Klosew
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cumfy
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1 Answers1

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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.

Community
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lemon
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