Abstract
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(nlog2 r) deterministic time, where r is the number of reflex vertices of \(\ensuremath{\mathcal{P}}\).
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Barba, L., Korman, M., Langerman, S., Silveira, R.I. (2011). Computing the Visibility Polygon Using Few Variables. In: Asano, T., Nakano, Si., Okamoto, Y., Watanabe, O. (eds) Algorithms and Computation. ISAAC 2011. Lecture Notes in Computer Science, vol 7074. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25591-5_9
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