Open Access
February 2006 A Sweep-Line Algorithm for the Inclusion Hierarchy among Circles
Deok-Soo Kim, Byunghoon Lee, Kokichi Sugihara
Japan J. Indust. Appl. Math. 23(1): 127-138 (February 2006).


Suppose that there are a number of circles in a plane and some of them may contain several smaller circles. In this case, it is necessary to find the inclusion hierarchy among circles for the various applications such as the simulation of emulsion and diameter estimation for wire bundles. In this paper, we present a plane-sweep algorithm that can identify the inclusion hierarchy among the circles in $O(n\log n)$ time in the worst-case. Also, the proposed algorithm uses the sweep-line method and a red-black tree for the efficient computation.


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Deok-Soo Kim. Byunghoon Lee. Kokichi Sugihara. "A Sweep-Line Algorithm for the Inclusion Hierarchy among Circles." Japan J. Indust. Appl. Math. 23 (1) 127 - 138, February 2006.


Published: February 2006
First available in Project Euclid: 19 June 2006

zbMATH: 1103.68127
MathSciNet: MR2210300

Keywords: computational geometry , interval search , nesting of circles , plane sweep , red-black

Rights: Copyright © 2006 The Japan Society for Industrial and Applied Mathematics

Vol.23 • No. 1 • February 2006
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