Computing the visibility polygon using few variables

Abstract

We present several algorithms for computing the visibility polygon of a simple polygon from a viewpoint inside the polygon, when the polygon resides in read-only memory and only few working variables can be used. The first algorithm uses a constant number of variables, and outputs the vertices of the visibility polygon in time, where denotes the number of reflex vertices of that are part of the output. The next two algorithms use O(logr) variables, and output the visibility polygon in O(nlogr) randomized expected time or O(nlog 2 r) deterministic time, where r is the number of reflex vertices of . © 2011 Springer-Verlag.