Friday, May 27, 2016

Intersection of Ellipses

I was recently pondering about the area of intersection of two ellipses. That is, given two ellipses with known shapes (semi-major and minor axes), centers, and relative or absolute orientation, find the area of intersection.

The general problem turns out to be far more complicated than the simpler problem of area of intersection of two circles.

In particular, as Hughes and Chraibi demonstrate (free preprint, paywalled paper), the number of intersections can be 0, 1, 2, 3, or 4. Eberley also has a nice writeup with derivations (pdf).

Luckily, a software implementation (C++) is available here on GitHub.

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