Voronoi diagrams for convex polygon-offset distance functions
نویسندگان
چکیده
منابع مشابه
Voronoi Diagrams for Convex Polygon-Offset Distance Functions
In this paper we develop the concept of a convex polygon-offset distance function. Using offset as a notion of distance, we show how to compute the corresponding nearestand furthest-site Voronoi diagrams of point sites in the plane. We provide nearoptimal deterministic O(n(log n + log m) + m)-time algorithms, where n is the number of points and m is the complexity of the underlying polygon, for...
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In this paper we develop the concept of a polygon-ooset distance function and show how to compute the respective nearest-and furthest-site Voronoi diagrams of point sites in the plane. We provide optimal deterministic O(n(log n + log m) + m)-time algorithms, where n is the number of points and m is the complexity of the underlying polygon, for computing compact representations of both diagrams.
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The concept of convex polygon-offset distance function was introduced in 2001 by Barequet, Dickerson, and Goodrich. Using this notion of point-to-point distance, they showed how to compute the corresponding nearestand farthest-site Voronoi diagram for a set of points. In this paper we generalize the polygon-offset distance function to be from a point to any convex object with respect to an m-si...
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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: 2001
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s004540010081