Voronoi Diagrams and Convex Hulls of Random Moving Points
نویسندگان
چکیده
منابع مشابه
Voronoi Diagrams of Moving Points
Consider a set of n points in d-dimensional Euclidean space, d 2, each of which is continuously moving along a given individual trajectory. At each instant in time, the points deene a Voronoi diagram. As the points move, the Voronoi diagram changes continuously, but at certain critical instants in time, topological events occur that cause a change in the Voronoi diagram. In this paper, we prese...
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Suppose we are given n moving postmen described by their motion equations p i (t) = s i + v i t; i = 1; : : : ; n, where s i 2 I R 2 is the position of the i'th postman at time t = 0, and v i 2 I R 2 is his velocity. The problem we address is how to preprocess the postmen data so as to be able to eeciently answer two types of nearest-neighbor queries. The rst one asks who is the nearest postman...
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We describe a kinetic data structure for maintaining a compact Voronoi-like diagram of convex polygons moving around in the plane. We use a compact diagram for the polygons, dual to the Voronoi, first presented in [MKS96]. A key feature of this diagram is that its size is only a function of the number of polygons and not of their complexity. We demonstrate a local certifying property of that di...
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The combinatorial complexities of (1) the Voronoi diagram of moving points in 2D and (2) the Voronoi diagram of lines in 3D, both under the Euclidean metric, continues to challenge geometers because of the open gap between the (n2) lower bound and the O(n3+ε) upper bound. Each of these two combinatorial problems has a closely related problem involving Minkowski sums: (1′) the complexity of a Mi...
متن کاملOn the Average Complexity of 3D-Voronoi Diagrams of Random Points on Convex Polytopes
It is well known that the complexity, i.e. the number of vertices, edges and faces, of the 3-dimensional Voronoi diagram of n points can be as bad as (n2). It is also known that if the points are chosen Independently Identically Distributed uniformly from a 3-dimensional region such as a cube or sphere, then the expected complexity falls to O(n). In this paper we introduce the problem of analyz...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2000
ISSN: 0179-5376
DOI: 10.1007/pl00009505