Reduction of the search space in the edge-tracing algorithm for the voronoi diagram of 3d balls

Authors:
Youngsong Cho;Donguk Kim;Hyun Chan Lee;Joon Young Park;Deok-Soo Kim
Affiliations:
Voronoi Diagram Research Center, Hanyang University, Seoul, Korea;Voronoi Diagram Research Center, Hanyang University, Seoul, Korea;Dept. of Industrial Engineering, Hongik University, Seoul, Korea;Dept. of Industrial and Systems Engineering, Dongguk University, Seoul, Korea;Dept. of Industrial Engineering, Hanyang University, Seoul, Korea
Venue:
ICCSA'06 Proceedings of the 6th international conference on Computational Science and Its Applications - Volume Part I
Year:
2006

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Abstract

Voronoi diagram for 3D balls can be applicable to various fields in science and engineering. The edge-tracing algorithm constructs the Voronoi diagram in O(mn) time in the worst-case where m and n are the numbers of edges and balls, respectively. The computation time of the algorithm is dominated by finding the end vertex of a given edge since all edges in the Voronoi diagram should be traced essentially. In this paper, we define the feasible region which a ball to define the end vertex of a given edge should intersect. Then, balls which do not intersect the feasible region are filtered out before finding an end vertex since they cannot define an end vertex. Therefore, we improve the runtime-performance of the edge-tracing algorithm via the feasible region.