Let $E_1$ and $E_2$ be two ellipses with centers $c_1$ and $c_2$ and semi-major axis $m_1$ and $m_2$, respectively. How could I determine a minimum $dist(c_1,c_2)$ to guarantee that two ellipses not touch (or intersect) themselves?
It could be only an approximation. I was thinking of just summing $m_1+m_2$ and if $dist(c_1,c_2)>m_1+m_2$ but I'm not sure if it guarantees that the two ellipses will not touch in any occasion (the ellipses can be rotated with any orientation).
Thanks!
Yes, $\operatorname{dist}(c_1,c_2)>m_1+m_2$ is sufficient.
$E_1$ is fully contained in a circle around $c_1$ with radius $m_1$ and likewise $E_2$ in a circle around $c_2$ with radius $m_2$. Since these two circles don't overlp, the ellipses they contain can never overlap, no matter how you rotate them.