Abstract
In this paper, we study a cell of the subdivision induced by a union of n half lines (or rays) in the plane. We present two results. The first one is a novel proof of the O(n) bound on the number of edges of the boundary of such a cell, which is essentially of methodological interest. The second is an algorithm for constructing the boundary of any cell, which runs in optimal Θ(n log n) time. A byproduct of our results are the notions of skeleton and of skeletal order, which may be of interest in their own right.
This work was partly supported by the CEE ESPRIT Project P-940, by the Ecole Normale Supérieure, Paris, France, and by the NSF grant ECS-84-10902.
This work was done in part while this author was visiting the Ecole Normale Supérieure, Paris, France.
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© 1989 Springer-Verlag Berlin Heidelberg
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Alevizos, P., Boissonnat, JD., Preparata, F.P. (1989). An optimal algorithm for the boundary of a cell in a union of rays. In: Boissonnat, J.D., Laumond, J.P. (eds) Geometry and Robotics. GeoRob 1988. Lecture Notes in Computer Science, vol 391. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51683-2_34
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DOI: https://doi.org/10.1007/3-540-51683-2_34
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