Covering a simple polygon by monotone directions

Authors:
Hee-Kap Ahn;Peter Brass;Christian Knauer;Hyeon-Suk Na;Chan-Su Shin
Affiliations:
Department of Computer Science and Engineering, POSTECH, Republic of Korea;Department of Computer Science, City College, New York, USA;Institute of Computer Science, Free University Berlin, Germany;School of Computing, Soongsil University, Seoul, Republic of Korea;School of Electrical and Information Engineering, Hankuk University of Foreign Studies, Republic of Korea
Venue:
Computational Geometry: Theory and Applications
Year:
2010

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Abstract

In this paper we study the problem of finding a set of k directions for a given simple polygon P, such that for each point p@?P there is at least one direction in which the line through p intersects the polygon only once. For k=1, this is the classical problem of finding directions in which the polygon is monotone, and all such directions can be found in linear time for a simple n-gon. For k1, this problem becomes much harder; we give an O(n^5log^2n)-time algorithm for k=2, and O(n^3^k^+^1logn)-time algorithm for fixed k=3.