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Discrete and Computational Geometry
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A linear-time algorithm for computing the voronoi diagram of a convex polygon

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We present an algorithm for computing certain kinds of three-dimensional convex hulls in linear time. Using this algorithm, we show that the Voronoi diagram of n sites in the plane can be computed in Θ(n) time when these sites form the vertices of a convex polygon in, say, counterclockwise order. This settles an open problem in computational geometry. Our techniques can also be used to obtain linear-time algorithms for computing the furthest-site Voronoi diagram and the medial axis of a convex polygon and for deleting a site from a general planar Voronoi diagram. © 1989 Springer-Verlag New York Inc.

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Discrete and Computational Geometry

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