Algorithms for Reporting and Counting Geometric Intersections

An interesting class of "geometric intersection problems" calls for dealing with the pairwise intersections among a set of N objects in the plane, These problems arise in many applications such as printed circuit design, architectural data bases, and computer graphics. Shamos and Hoey have described a number of algorithms for detecting whether any two objects in a planar set intersect. In this paper we extend their work by giving algorithms that count the number of such intersections and algorithms that report all such intersections.