Let P= (p1, p2, …, pn) and Q= (q1, q2, …, qm) be two simple polygons monotonic in directions θs and φ respectively. It is shown that P and Q are separable with a single translation in at least one of the directions: ,. 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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