Computing the Full Visibility Graph of a Set of Line Segments

Let S be a collection of n non-intersecting line segments in the plane in general position. Two segments u and v are deened as visible if a line segment could be drawn from some point of u to some point of v that intersects no other segment in S. The full visibility graph associated with S is denoted as G(S), and deened to be the graph whose n vertices correspond to the line segments of S and whose edge set represents the visibility relation between pairs of segments. A worst case optimal O(n 2) time and space algorithm for computing G(S) is presented.