Abstract
Let P be a simple polygon of n vertices and let S be a set of N points lying in the interior of P. A geodesic disk GD(p,r) with center p and radius r is the set of points in P that have a geodesic distance ≤ r from p (where the geodesic distance is the length of the shortest polygonal path connection that lies in P). In this paper we present an output sensitive algorithm for finding all N geodesic disks centered at the points of S, for a given value of r. Our algorithm runs in \(O((n+(kn)^{\frac{2}{3}}+k)\log^cn)\) time, for some constant c and output size k. It is the basis of a cluster reporting algorithm where geodesic distances are used.
This research has been partially funded by the Netherlands Organisation for Scientific Research (NWO) under FOCUS/BRICKS grant number 642.065.503.
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Borgelt, M.G., van Kreveld, M., Luo, J. (2007). Geodesic Disks and Clustering in a Simple Polygon. In: Tokuyama, T. (eds) Algorithms and Computation. ISAAC 2007. Lecture Notes in Computer Science, vol 4835. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77120-3_57
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DOI: https://doi.org/10.1007/978-3-540-77120-3_57
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