for Computing v"isibility Graphs
Subir Ghosh, David M. Mount · 1987
The visibility graph of a set of nonintersecting polygonal obsta cles in the plane is an undirected graph whose vertices are the vertices of the obstacles and whose edges are pairs of vertices (u, v) such that the open line segment between u and tI does not intersect any of the obstacles. The visibility graph is an impor tant combinatorial structure in computational geometry and is used in applications such as solving visibility problema and com puting shortest paths. An algorithm is presented that computes the visibility graph of a set of obstacles in time 0 (E + n logn), where E is the number of edges in the visibility graph and n is the total number of vertices in all the obstacles.