Separating Two Simple Polygons, by a Sequence of Translations (Classic Reprint) - Softcover

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Excerpt from Separating Two Simple Polygons, by a Sequence of Translations

Let P and Q be two disjoint simple polygons having m and n sides respectively. We present an algorithm which determines whether Q can be moved by a sequence of translations to a position sufficiently far from P without colliding with P, and which produces such a motion if it exists. Our algorithm runs in time O(mn a(mn) log m log n) where a(k) is the extremely slowly growing inverse Ackermann's function. Since. In the worst ease O(mn) translations may be necessary to separate Q from P, our algorithm is close to optimal.

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