Given two intersecting polygons and a direction vector, how can one find the distance that one (and only one) of the polygons needs to be translated in the given direction in order to eliminate the intersection?
I.e. let $p1$, $p2$ be polygons such that $p1 \cap p2 \ne \emptyset$; let $v$ be a vector. Find a scalar $s$ such that $( p1 + vs ) \cap p2 = \emptyset$.
I have attempted several strategies so far, but neither seems to be general enough. Since an intuitive solution is evident when looking at an image, I'm sure there must be a general procedure, but so far have been unable to find one, and all references to similar problems are mired in the concreteness of their specific domains (i.e. GIS, gaming programming, etc).