Elsevier

Journal of Algorithms

Volume 21, Issue 3, November 1996, Pages 508-519
Journal of Algorithms

Regular Article
Ray Shooting Amidst Convex Polygons in 2D

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Abstract

We consider the problem of ray shooting in a two-dimensional scene consisting ofmconvex polygons with a total ofnedges. We present a data structure that requiresO(mn log m) space and preprocessing time and that answers a ray shooting query inO(log2 m log2 n) time. If the polygons are pairwise disjoint, the space and preprocessing time can be improved toO((m2+n)log m) andO((m2+n log n)log m), respectively. Our algorithm also works for a collection of disjoint simple polygons. We also show that if we allow onlyO(n) space, a ray shooting query among a collection of disjoint simple polygons can be answered in timeO(⌈m/[formula]⌉1+ε log2 n) time, for any ε>0.

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Work on this paper by Pankaj Agarwal has been supported by National Science Foundation Grant CCR-91-06514. Work by Micha Sharir has been supported by National Science Foundation Grant CCR-91-22103, and by grants from the U.S.–Israeli Binational Science Foundation, the G.I.F.—the German–Israeli Foundation for Scientific Research and Development, and the Fund for Basic Research administered by the Israeli Academy of Sciences.