Point Visibility Computing in Polygons with Holes

In this paper, we have discussed how to query the visibility polygon of an arbitrary point v in a polygon P with n vertices and h holes, denoted by VP(P;v). We first decompose P into O(h) simple polygons, and then decompose the interior and exterior of each simple polygon into visibility cells and create data structures. In the running phase, our algorithm can report VP(P;v) in O(jVP(P;v)j + h + log 2 m + hlog(n=h)) time, where m is the size of the simple polygon that contains v and m < n, with O(n 2 ) space and O(n 2 logn) preprocessing time.