Hallo everybody,
I have the following problem regarding shortest paths in $R^2$.
Suppose you are given two points $p$ and $q$ and two unit disks, as in the picture. I am looking for a path from $p$ to $q$ through a point $c_1$ in the first disk and $c_2$ in the second disk such that the sum $\overline{p c_1}+\overline{c_1 c_2}+\overline{c_2 q}$ is minimum.
I know how to find a path if there is only one disk, via reflection properties of ellipses. However, the case for two disks eludes me. I was hoping that you could have some suggestions, or some pointers to something to read.
Thanks in advance for your answers.