Abstract
ElGindy posed the following problem: given a simple polygon P of n vertices and a set S of k points inside P, find the collection of points of P that can see all points of S. This collection of points is called the kernel of S in P. In this paper, we study this problem and show that the kernel of S can be computed in O(n log log n+k log n+k log k) time and O(n+k) space. We also present an O(n log n+k log k) time and O(n+k) space algorithm to determine if there exists a line segment in P that can see all points of S, and if so, to find the shortest one. Several other related problems are also addressed.
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© 1989 Springer-Verlag Berlin Heidelberg
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Ke, Y., O'Rourke, J. (1989). Computing the kernel of a point set in a polygon. In: Dehne, F., Sack, J.R., Santoro, N. (eds) Algorithms and Data Structures. WADS 1989. Lecture Notes in Computer Science, vol 382. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51542-9_12
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DOI: https://doi.org/10.1007/3-540-51542-9_12
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