Partitioning polygons into tree monotone and y-monotone subpolygons

Authors:
Ralph P. Boland;Jorge Urrutia
Affiliations:
University of Waterloo;Instituto de Mathemáticas, Universidad Nacional Autónoma de México
Venue:
ICCSA'03 Proceedings of the 2003 international conference on Computational science and its applications: PartIII
Year:
2003

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Abstract

A polygon Q is tree monotone if, for some highest or lowest point p on Q and for any point q interior to Q, there is a y-monotone curve from p to q whose interior is interior to Q. We show how to partition an n vertex polygon P in Θ(n) time into tree monotone subpolygons such that any y-monotone curve interior to P intersects at most two of the subpolygons. We then use this partition to further partition P into y-monotone subpolygons such that the number of subpolygons needed to cover any given y-monotone curve interior to P is O(log n). Our algorithm runs in Θ(n) time and space which is an improvement by an O(log n) factor in time and space over the best previous result.