A standard ellipse with semi-major axis $a$, semi-minor $b$ has a "diameter" of $2a$ in one dimension ($\phi=0$) and $2b$ in the other ($\phi=\pi/2$). Is there a function to find the diameter for an arbitrary angle $\phi$? By "diameter", I mean the distance between two parallel tangents perpendicular to $\phi$. In everyday terms, how wide is the shadow cast by an ellipse when viewed from any angle.
Secondary related question: what's the proper mathematical term for what I mean by "diameter" above; projecting the shadow of the ellipse into 1D and finding the length?