Computing the Visibility Polygon Using Few Variables

We present several algorithms for computing the visibility polygon of a simple polygon P 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 O(nr̄) time, where r̄ denotes the number of reflex vertices of P that are part of the output. The next two algorithms use O(log r) variables, and output the visibility polygon in O(n log r) randomized expected time or O(n log r) deterministic time, where r is the number of reflex vertices of P.