¹Department of Mathematics and Physics, Shijiazhuang Tiedao University, Hebei Shijiazhuang 050043, China
²College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang, Hebei 050016, China

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Abstract—To fill a theory gap of Voronoi diagrams that there have been no reports of extended diagrams in spatial density so far. A new concept of spatial density Voronoi diagram was proposed. An important property was presented and proven. And a construction algorithm was presented. Spatial density can be used to indicate factors related to density such as conveyance and the traffic conditions. Some properties of spatial density Voronoi diagram were also introduced. In accordance with discrete construction method, achieved the construction of spatial density Voronoi diagram. Spatial density Voronoi diagram is a developed Voronoi diagram, and planar ordinary Voronoi diagram can be regarded as its special cases. It both perfected the theory about Voronoi diagrams, and extended the range of applications of Voronoi diagrams.

Index Terms—Voronoi diagram, Voronoi polygon, discrete, construction.

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Cite: Yefei Zhao, Shujuan Liu, Youhui Zhang, "Spatial Density Voronoi Diagram and Construction," Journal of Computers vol. 7, no. 8, pp. 2007-2014, 2012.