Polygonal chain intersection

In order to find all intersections among polygonal chains, this paper presents a procedure consisting of two phases: (1) splitting polygonal chains into a minimal number of monotone chains and (2) finding intersections among the monotone chains. For the first phase, we suggest an optimal algorithm splitting polygonal chains into a minimal number of monotone chains, with an Oðn þ r log rÞ time complexity, where n is the number of line-segments in the polygonal chains and r is the number of C-subchains. For the second phase, we extend Bentley–Ottmann’s sweep-line algorithm and the time complexity is Oððn þ kÞlog mÞ; where k is the number of intersections, and m is the minimal number of monotone chains. r 2002 Elsevier Science Ltd. All rights reserved.