Seung-Hak Choi

Characterizing and recognizing the visibility graph of a funnel-shaped polygon

A funnel, which is notable for its fundamental role in visibility algorithms, is defined as a polygon that has exactly three convex vertices, two of which are connected by a boundary edge. In this paper we investigate the visibility graph of a funnel which we call an F-graph.We first present two characterizations of an F-graph, one of whose sufficiency proof itself is a linear time Real RAM algorithm for drawing a funnel on the plane that corresponds to an F-graph. We next give a linear-time algorithm for recognizing an F-graph. When the algorithm recognizes an F-graph, it also reports one of the Hamiltonian cycles defining the boundary of its corresponding funnel. This recognition algorithm takes linear time even on a RAM.We finally show that an F-graph is weakly triangulated and therefore perfect, which agrees with the fact that perfect graphs are related to geometric structures.

An optimal algorithm for finding the edge visibility polygon under limited visibility

Abstract Two points in a polygon P are said to be d-visible if the line segment l joining them is contained in P and the length of l is d or less. In applications such as computer graphics and robot vision, the notion of d -visibility is more suitable than the commonly used definition of visibility, which is equivalent to d -visibility with infinite d . We present an O( n ) time algorithm for finding the d -visibility polygon from an edge e in P , where n is the number of vertices in P .