Ray Shooting in Polygons Using Geodesic Triangulations

Published: 01 Jan 1991, Last Modified: 15 May 2024ICALP 1991EveryoneRevisionsBibTeXCC BY-SA 4.0
Abstract: Let P be a simple polygon with n vertices. We present a simple decomposition scheme that partitions the interior of P into O(n) so-called geodesic triangles, so that any line segment interior to P crosses at most 2 log n of these triangles. This decomposition can be used to preprocess P in time O(n log n) and storage O(n), so that any ray-shooting query can be answered in time O(log n).The algorithms are fairly simple and easy to implement. We also extend this technique to the case of ray-shooting amidst k polygonal obstacles with a total of n edges, so that a query can be answered in O(√klog n) time.
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