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I would like to create an animation of an object using an elliptical path. I realize there may be an infinite number of possible ellipses given three points, but so long as I can find one that will allow me to animate along that path, I’m fine.
If it helps, the points are (0,0) (500,0) and (1000,1000). So the second point is halfway between the other two.
@ruakh is correct, a circle is the most simple, straightforward approach to this. Here are some equations that can help you:
http://paulbourke.net/geometry/circlesphere/