An Output-Sensitive Algorithm for Computing Visibility Graphs

Abstract

The visibility graph of a set of nonintersecting polygonal obstacles in the plane is an undirected graph whose vertex set consists of the vertices of the obstacles and whose edges are pairs of vertices $(u,v)$ such that the open line segment between u and v does not intersect any of the obstacles. The visibility graph is an important combinatorial structure in computational geometry and is used in applications such as solving visibility problems and computing shortest paths. This paper presents an algorithm that computes the visibility graph of a set of obstacles in time $O(E + n\log n)$, where E is the number of edges in the visibility graph and n is the total number of vertices in all the obstacles.