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Home/Magazine Archive/February 1977 (Vol. 20, No. 2)/Convex hulls of finite sets of points in two and three.../Abstract

Convex hulls of finite sets of points in two and three dimensions

By F. P. Preparata, S. J. Hong
Communications of the ACM, February 1977, Vol. 20 No. 2, Pages 87-93
10.1145/359423.359430
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The convex hulls of sets of n points in two and three dimensions can be determined with O(n log n) operations. The presented algorithms use the “divide and conquer” technique and recursively apply a merge procedure for two nonintersecting convex hulls. Since any convex hull algorithm requires at least O(n log n) operations, the time complexity of the proposed algorithms is optimal within a multiplicative constant.

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