title: Elliptical Arc Length
body: <p>Given a point <code>P</code> on a 'canonical' ellipse defined by axes <code>a, b</code>, and an arc length <code>s</code>, how can I find a point <code>Q</code>, also on the ellipse, that is <code>s</code> clockwise along the elliptical curve from <code>P</code> — such that if I were to start at <code>P</code> and 'walk along' the elliptical curve for a distance of <code>s</code>, I would reach <code>Q</code> — programatically and without breaking the computational bank?</p>
  
  <p>I have heard that this can be computed through some sort of elliptical integration, but I need to do this a bunch, and quickly. What I'm looking for is <strong>an easy to use, computationally inexpensive, and fairly accurate approximation method.</strong> Or at least a method that is one or two of those things. I will be implementing this in python.</p>
  
  <p><strong>Edit:</strong> alternatively, I might be forced to create a lookup table of position values around ellipses (I might only need in the 10s of dissimilar ellipses). How should I do this, and what method can I use to fill it?</p>