Voronoi diagrams on the sphere
نویسندگان
چکیده
منابع مشابه
Voronoi Diagrams on the Sphere
Given a set of compact sites on a sphere, we show that their spherical Voronoi diagram can be computed by computing two planar Voronoi diagrams of suitably transformed sites in the plane. We also show that a planar furthest-site Voronoi diagram can always be obtained as a portion of a nearest-site Voronoi diagram of a set of transformed sites. Two immediate applications are an O(n logn) algorit...
متن کاملVoronoi diagrams on the spher
Given a set of compact sites on a sphere, we show that their spherical Voronoi diagram can be computed by computing two planar Voronoi diagrams of suitably transformed sites in the plane. We also show that a planar furthest-site Voronoi diagram can always be obtained as a portion of a nearest-site Voronoi diagram of a set of transformed sites. Two immediate applications are an O(n logn) algorit...
متن کاملOn the conversion of ordinary voronoi diagrams into laguerre diagrams
We present some geometric relationships between the ordinary Voronoi diagram, and the Voronoi diagram in the Laguerre geometry. We derive from these properties an algorithm for the conversion of ordinary Voronoi diagrams into Voronoi diagrams in the Laguerre geometry.
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In this review, we illustrate the relations between wireless communication and computational geometry. As a concrete example, we consider a fundamental geometric object from each field: SINR diagrams and Voronoi diagrams. We discuss the relations between these representations, which appear in several distinct settings of wireless communication, as well as some algorithmic applications.
متن کاملFurther results on the hyperbolic Voronoi diagrams
In Euclidean geometry, it is well-known that the k-order Voronoi diagram in R can be computed from the vertical projection of the k-level of an arrangement of hyperplanes tangent to a convex potential function in R: the paraboloid. Similarly, we report for the Klein ball model of hyperbolic geometry such a concave potential function: the northern hemisphere. Furthermore, we also show how to bui...
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ژورنال
عنوان ژورنال: Computational Geometry
سال: 2002
ISSN: 0925-7721
DOI: 10.1016/s0925-7721(02)00077-9