Voronoi diagram with visual restriction

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 necessarily convex and it could consist of many disjoint regions. We prove that the combinatorial complexity of the VRVD on n   sites is Θ(n2)Θ(n2), and then show that the VRVD can be constructed in O(n2)O(n2) time and O(n2)O(n2) space. Besides that, we also give another algorithm with an extra log n factor of running time to compute VRVD, which is easy to implement in practice.