Abstract
Let \(\mathcal{O}\)be some set of orientations, i.e., \(\mathcal{O}\) \(\subseteq\)[0°,360°). In this paper we look at the consequences of defining visibility based on curves that are monotone w.r.t. to the orientations in \(\mathcal{O}\). We call such curves \(\mathcal{O}\)-staircases. Two points p and q in a polygon P are said to \(\mathcal{O}\)-see each other if there exists an \(\mathcal{O}\)-staircase from p to q that is completely contained in P. The \(\mathcal{O}\)-kernel of a polygon P is then the set of all points which \(\mathcal{O}\)-see all other points. We show that the \(\mathcal{O}\)-kernel of a simple polygon can be obtained as the intersection of all θ-kernels, with θ∈\(\mathcal{O}\). With the help of this observation we are able to develop an O(n log |\(\mathcal{O}\)|) algorithm to compute the \(\mathcal{O}\)-kernel in a simple polygon, for finite \(\mathcal{O}\).
This work was supported by the Deutsche Forschungsgemeinschaft under Grant No. Ot 64/5-4 and by Natural Sciences and Engineering Research Council Grant No. A-5692.
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© 1991 Springer-Verlag Berlin Heidelberg
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Schuierer, S., Rawlins, G.J.E., Wood, D. (1991). A Generalization of staircase visibility. In: Bieri, H., Noltemeier, H. (eds) Computational Geometry-Methods, Algorithms and Applications. CG 1991. Lecture Notes in Computer Science, vol 553. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54891-2_21
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DOI: https://doi.org/10.1007/3-540-54891-2_21
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