Computing the Visibility Polygon Using Few Variables

We present several algorithms for computing the visibility polygon of a simple polygon $\ensuremath{\mathcal{P}}$ 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 $O(n\ensuremath{\bar{r}})$ time, where $\ensuremath{\bar{r}}$ denotes the number of reflex vertices of $\ensuremath{\mathcal{P}}$ 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(nlog2r) deterministic time, where r is the number of reflex vertices of $\ensuremath{\mathcal{P}}$ .