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As an extension to this question on equiangular fisheye distortion, how can I calculate equidistant points around an ellipse (or 1/4 segment of) given it's aspect ratio?

When it's circular, I can use a simple angle around the central point, but as the aspect ratio gets smaller, the length of the arc gets shorter and the angles are no longer equidistant.


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The problem you have is that the arclength of an ellipse is a so-called elliptic integral, which is nonelementary (but easily computed numerically, see this related question), and is not easily inverted. Are you fine with a numerical solution? –  J. M. Jul 19 '12 at 8:00
Oh, no wonder I couldn't figure it out on my own... :) What do you mean by a numerical solution? (as opposed to a formula?) –  Deanna Jul 19 '12 at 8:09
See also math.stackexchange.com/questions/55986/…. –  joriki Jul 19 '12 at 8:25
Yes, I am saying that you will have to resort to numerical methods to do what you want. If you're interested, I can sketch up an algorithm for you in an answer... –  J. M. Jul 19 '12 at 10:51
If you can, that'd be useful. Thanks. –  Deanna Jul 19 '12 at 11:13

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