Abstract
Presented in this paper is an algorithm to compute the exact Voronoi diagram of circle set from the Voronoi diagram of point set. In particular, the topology aspect of the algorithm is presented here. The circles are located in a two dimensional Euclidean space, the radii of circles are not necessarily equal, and the circles are allowed to intersect. Even though the time complexity is O(n 2), the algorithm turns out to be fast and robust. The algorithm uses the topology of the point set Voronoi diagram as an initial solution, and finds the correct topology of the Voronoi diagram of circle set from its point set counterpart. Hence, the algorithm is as stable as point set Voronoi diagram algorithm.
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Kim, DS., Kim, D., Sugihara, K. (2000). Voronoi Diagram of a Circle Set Constructed from Voronoi Diagram of a Point Set. In: Goos, G., Hartmanis, J., van Leeuwen, J., Lee, D.T., Teng, SH. (eds) Algorithms and Computation. ISAAC 2000. Lecture Notes in Computer Science, vol 1969. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-40996-3_37
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DOI: https://doi.org/10.1007/3-540-40996-3_37
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