Calculating equidistant points around an ellipse arc

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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 increment 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.