Abstract
This paper presents a dynamic algorithm for the construction of the Euclidean Voronoi diagram of a set of convex objects in the plane. We consider first the Voronoi diagram of smooth convex objects forming pseudo-circles set. A pseudo-circles set is a set of bounded objects such that the boundaries of any two objects intersect at most twice. Our algorithm is a randomized dynamic algorithm. It does not use a conflict graph or any sophisticated data structure to perform conflict detection. This feature allows us to handle deletions in a relatively easy way. In the case where objects do not intersect, the randomized complexity of an insertion or deletion can be shown to be respectively O(log2 n) and O(log3 n). Our algorithm can easily be adapted to the case of pseudo-circles sets formed by piecewise smooth convex objects. Finally, given any set of convex objects in the plane, we show how to compute the restriction of the Voronoi diagram in the complement of the objects’ union.
Work partially supported by the IST Programme of the EU as a Shared-cost RTD (FET Open) Project IST-2000-26473 (ECG – Effective Computational Geometry for Curves and Surfaces).
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Karavelas, M.I., Yvinec, M. (2003). The Voronoi Diagram of Planar Convex Objects. In: Di Battista, G., Zwick, U. (eds) Algorithms - ESA 2003. ESA 2003. Lecture Notes in Computer Science, vol 2832. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39658-1_32
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DOI: https://doi.org/10.1007/978-3-540-39658-1_32
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