Voronoi diagram with visual restriction

Authors:
Chenglin Fan;Jun Luo;Wencheng Wang;Binhai Zhu
Affiliations:
Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, China;Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, China,Top Key Discipline of Computer Software and Theory, Zhejiang Provincial Colleges, Zhejiang Normal University, China;Institute of Software, Chinese Academy of Sciences, China;Top Key Discipline of Computer Software and Theory, Zhejiang Provincial Colleges, Zhejiang Normal University, China,Department of Computer Science, Montana State University, Bozeman, MT
Venue:
FAW-AAIM'12 Proceedings of the 6th international Frontiers in Algorithmics, and Proceedings of the 8th international conference on Algorithmic Aspects in Information and Management
Year:
2012

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Abstract

In a normal Voronoi diagram, each site is able to see all the points in the plane. In this paper, we study the case such that each site is only able to see a visually restricted region in the plane and construct the so-called Visual Restriction Voronoi Diagram (VRVD). We show that the visual restriction Voronoi cell of each site is not necessary convex and it could consist of many disjoint regions. We prove that the combinatorial complexity of the VRVD on n sites is Θ(n 2). Then we give an O (n 2logn ) time and O (n 2) space algorithm to construct VRVD.