Separation of two monotone polygons in linear time

Let P = {p1, p2,..., pn} and Q = {q1, q2,..., qm} be two simple polygons monotonic in directions θ and φ, respectively. It is shown that P and Q are separable with a single translation in at least one of the directions: θ + π / 2, φ + π / 2. Furthermore, a direction for carrying out such a translation can be determined in O(m + n) time. This procedure is of use in solving the FIND-PATH problem in robotics.

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