An Optimal Algorithm for Computing Visibility in the Plane

Abstract

The authors give an algorithm to compute the visibility polygon from a point among a set of $h$ pairwise-disjoint polygonal obstacles with a total of $n$ vertices. Our algorithm uses $O(n)$ space and runs in optimal time $\Theta(n+h\log h)$, improving the previous upper bound of $O(n\log n)$. A direct consequence of the algorithm is an $O(n+h\log h)$ time algorithm for computing the convex hull of $h$ disjoint simple polygons.