Calculating Distance of a Point from an Ellipse Border

I’m thinking about using oriented ellipses to represent curves (dents/bumps etc.) in my physics engine, and have a few questions about working with them:

  1. What methods are there to finding the minimum distance between a point and an ellipse? I need methods of varying cost (in terms of # of calculations) for different parts of my engine.

  2. How do you test the distance between two ellipses? I figure you could combine the two methods above by transforming both ellipses in a way that makes one a circle, then test the distance from the center of the circle ellipse to the regular ellipse’s edge, and finally compare that distance to the radius of the circle ellipse.

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