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arXiv · 2108.07366

The Visibility Center of a Simple Polygon

Anna Lubiw·Anurag Murty Naredla
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Abstract

We introduce the \emph{visibility center} of a set of points inside a polygon -- a point $c_V$ such that the maximum geodesic distance from $c_V$ to see any point in the set is minimized. For a simple polygon of $n$ vertices and a set of $m$ points inside it, we give an $O((n+m) \log {(n+m)})$ time algorithm to find the visibility center. We find the visibility center of \emph{all} points in a simple polygon in $O(n \log n)$ time. Our algorithm reduces the visibility center problem to the problem of finding the geodesic center of a set of half-polygons inside a polygon, which is of independent interest. We give an $O((n+k) \log (n+k))$ time algorithm for this problem, where $k$ is the number of half-polygons.

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Anna Lubiw, Anurag Murty Naredla. 2021-08-16. The Visibility Center of a Simple Polygon. https://arxiv.org/abs/2108.07366

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