# elipsoid surface intersection in $\mathbb{R}^3$

Is there an explicit parametric solution describing the curve result of the intersection of two elipsoid surfaces with abitrary position and orientation in $\mathbb{R}^3$?

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generically you get an elliptic curve, so there is no rational parametrization (you could parametrize it using elliptic functions) – user8268 Mar 20 '12 at 20:08