Visual reply to map-related queries-a free space graph approach

Given a map which describes an obstacle-cluttered environment, it is possible to pose a number of different queries. One such query might be whether or not the line-of-sight joining an arbitrary pair of points is obstructed. Another question might be that of finding the shortest path between any pair of points. A third problem might be to describe or collect all points lying within a specified radius of some source-point; here, this type of problem is called a localization query. The solution for a localization query is perhaps best presented graphically, i.e., in visual terms. For the two-dimensional case, a free space graph approach for deriving solutions to visibility and shortest path queries is described. How a simple extension of this method can be used to produce visual replies to localization queries is discussed