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.
This research has been partially funded by the International Science & Technology Cooperation Program of China (2010DFA92720), Shenzhen Fundamental Research Project (grant no. JC201005270342A) and by NSF of China under project 60928006.
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Fan, C., Luo, J., Wang, W., Zhu, B. (2012). Voronoi Diagram with Visual Restriction. In: Snoeyink, J., Lu, P., Su, K., Wang, L. (eds) Frontiers in Algorithmics and Algorithmic Aspects in Information and Management. Lecture Notes in Computer Science, vol 7285. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29700-7_4
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DOI: https://doi.org/10.1007/978-3-642-29700-7_4
Publisher Name: Springer, Berlin, Heidelberg
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