Finding minimal convex nested polygons

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Abstract

We consider the problem of finding a polygon nested between two given convex polygons that has a minimal number of vertices. Our main result is an O(n log k) algorithm for solving the problem, where n is the total number of vertices of the given polygons, and k is the number of vertices of a minimal nested polygon. We also present an O(n) sub-optimal algorithm, and a simple O(nk) optimal algorithm.

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A preliminary version of this paper appeared in the first Annual Symposium on Computational Geometry, 1985, pp. 296–303, Baltimore, MD 21218.

Author's present address: Dept. of Computer Science, Princeton University, Princeton, NJ 08544.

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Author's present address: Department of Computer Science, Smith College, Northampton, MA 01063.