An algorithm for counting line segments intersections using planar partitions

Abstract

Intersecting a collection of line segments is one of the most fundamental tasks in computer geometry. Bentley and Ottmann [1] proposed an algorithm called Sweep Line Algorithm. The algorithm is quite effective when the number of intersections is relatively small. On the other hand, it is less effective when the number of intersections is large. In this paper, we introduce an algorithm which is effective for both of these cases. Our algorithm divide given line segments into groups using Morton code and l quadtree levels. In our experiments using randomly generated sets of line segments, our algorithm is effective as sweep line algorithm when the number of intersections is small and is effective as brute force algorithm when the number of intersections is large.