منابع مشابه
Hierarchical Data Representations Based on Planar Voronoi Diagrams
Multiresolution representation of high-dimensional scattered data is a fundamental problem in scientific visualization. This paper introduces a data hierarchy of Voronoi diagrams as a versatile solution. Given an arbitrary set of points in the plane, our goal is the construction of an approximation hierarchy using the Voronoi diagram as the essential building block. We have implemented two Voro...
متن کاملTerrain Modeling using Voronoi Hierarchies
We present a new algorithm for terrain modeling based on Voronoi diagrams and Sibson’s interpolant. Starting with a set of scattered data sites in the plane with associated function values defining a height field, our algorithm constructs a top-down hierarchy of smooth approximations. We use the convex hull of given sites as domain for our hierarchical representation. Sibson’s interpolant is us...
متن کاملVoronoi 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 کاملVesicle computers: Approximating Voronoi diagram on Voronoi automata
Irregular arrangements of vesicles filled with excitable and precipitating chemical systems are imitated by Voronoi automata — finite-state machines defined on a planar Voronoi diagram. Every Voronoi cell takes four states: resting, excited, refractory and precipitate. A resting cell excites if it has at least one excited neighbour; the cell precipitates if a ratio of excited cells in its neigh...
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...
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تاریخ انتشار 2002