Intersecting Red and Blue Line Segments in Optimal Time and Precision

Authors:
Andrea Mantler;Jack Snoeyink
Affiliations:
-;-
Venue:
JCDCG '00 Revised Papers from the Japanese Conference on Discrete and Computational Geometry
Year:
2000

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Abstract

A common geometric problem in computer graphics and geographic information systems is to compute the arrangement of a set of n segments that can be colored red and blue so that there are no red/red or blue/blue crossings. We give a sweep algorithm that uses the minimum arithmetic precision and runs in optimal O(n log n + k) time and O(n) space to output an arrangement with k vertices, or O(n log n) time to determine k. Our initial implementation in Java can be found at http:\\www.cs.unc.edu\~snoeyink\demos\rbseg.