Voronoi Diagram with Visual Restriction

  • Chenglin Fan
  • Jun Luo
  • Wencheng Wang
  • Binhai Zhu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7285)


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.


Voronoi Diagram Boundary Line Convex Polygon Combinatorial Complexity Left Endpoint 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Chenglin Fan
    • 1
  • Jun Luo
    • 1
    • 3
  • Wencheng Wang
    • 2
  • Binhai Zhu
    • 3
    • 4
  1. 1.Shenzhen Institutes of Advanced TechnologyChinese Academy of SciencesChina
  2. 2.Institute of SoftwareChinese Academy of SciencesChina
  3. 3.Top Key Discipline of Computer Software and Theory, Zhejiang Provincial CollegesZhejiang Normal UniversityChina
  4. 4.Department of Computer ScienceMontana State UniversityBozemanUSA

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