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- W2108536469 abstract "The farthest line-segment Voronoi diagram illustrates properties surprisingly different from its counterpart for points: Voronoi regions may be disconnected and they are not characterized by convex-hull properties. In this paper we introduce the farthest hull and its Gaussian map as a closed polygonal curve that characterizes the regions of the farthest line-segment Voronoi diagram, and derive tighter bounds on the (linear) size of this diagram. With the purpose of unifying construction algorithms for farthest-point and farthest line-segment Voronoi diagrams, we adapt standard techniques to construct a convex hull and compute the farthest hull in O(n log n) or output sensitive O(n log h) time, where n is the number of line-segments and h is the number of faces in the corresponding farthest Voronoi diagram. As a result, the farthest line-segment Voronoi diagram can be constructed in output sensitive O(n log h) time. Our algorithms are given in the Euclidean plane but they hold also in the general L p metric, 1 ≤ p ≤ ∞." @default.
- W2108536469 created "2016-06-24" @default.
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- W2108536469 date "2013-12-01" @default.
- W2108536469 modified "2023-09-24" @default.
- W2108536469 title "ON THE FARTHEST LINE-SEGMENT VORONOI DIAGRAM" @default.
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- W2108536469 doi "https://doi.org/10.1142/s0218195913600121" @default.
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