ArXiv | 2021
The Visibility Center of a Simple Polygon
Abstract
We introduce the visibility center of a set of points inside a polygon – a point cV such that the maximum geodesic distance from cV 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 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. 2012 ACM Subject Classification Theory of computation → Computational geometry