An efficient method for computing the feasible region with translational containment between two convex polygons

A convex polygon containment problem is studied: whether a given convex polygon P can be translated to fit inside another fixed convex polygon Q. An O(pq log q) time algorithm is presented for solving such a problem, where p and q are the numbers of vertices of P and Q. In addition, by utilizing the existence algorithm, it takes O(pq log q) time to find the set of all placements of P that fit inside Q.