Ray Shooting Amidst Convex Polygons in 2D

Abstract

We consider the problem of ray shooting in a two-dimensional scene consisting of m convex polygons with a total of n edges. We present a data structure that requires O(mn log m) space and preprocessing time and that answers a ray shooting query in O(log2 m log2 n) time. If the polygons are pairwise disjoint, the space and preprocessing time can be improved to O((m2 + n)log m) and O((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 only O(n) space, a ray shooting query among a collection of disjoint simple polygons can be answered in time O([m/ √n]1+ε log2 n) time, for any ε > 0. © 1996 Academic Press, Inc.