منابع مشابه
Constructing Levels in Arrangements and Higher Order Voronoi Diagrams 1 Constructing Levels in Arrangements and Higher Order Voronoi Diagrams
We give simple randomized incremental algorithms for computing the k-level in an arrangement of n hyperplanes in two-and three-dimensional space. The expected running time of our algorithms is O(nk + nn(n) log n) for the planar case, and O(nk 2 + n log 3 n) for the three-dimensional case. Both bounds are optimal unless k is very small. The algorithm generalizes to computing the k-level in an ar...
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We review recent progress in the study of arrangements of surfaces in higher dimensions. This progress involves new and nearly tight bounds on the complexity of lower envelopes, single cells, zones, and other substructures in such arrangements, and the design of eecient algorithms (near optimal in the worst case) for constructing and manipulating these structures. We then present applications o...
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Given a family of k disjoint connected polygonal sites in general position and of total complexity n, we consider the farthest-site Voronoi diagram of these sites, where the distance to a site is the distance to a closest point on it. We show that the complexity of this diagram is O(n), and give an O(n log n) time algorithm to compute it. We also prove a number of structural properties of this ...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 1986
ISSN: 0179-5376,1432-0444
DOI: 10.1007/bf02187681