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| relative neighborhood graph ： ウィキペディア英語版 |
relative neighborhood graph
In computational geometry, the relative neighborhood graph (RNG) is an undirected graph defined on a set of points in the Euclidean plane by connecting two points ''p'' and ''q'' by an edge whenever there does not exist a third point ''r'' that is closer to both ''p'' and ''q'' than they are to each other. This graph was proposed by Godfried Toussaint in 1980 as a way of defining a structure from a set of points that would match human perceptions of the shape of the set.〔.〕〔.〕
==Algorithms==
showed how to construct the relative neighborhood graph efficiently in O(''n'' log ''n'') time.〔.〕 It can be computed in O (''n'') expected time, for random set of points distributed uniformly in the unit square.〔.〕 The relative neighborhood graph can be computed in linear time from the Delaunay triangulation of the point set.〔.〕〔.〕
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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