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A sweep-line algorithm for the inclusion hierarchy among circles
- Authors
- Kim, Deok Soo; Lee, Byunghoon; Sugihara, Kokichi
- Issue Date
- Feb-2006
- Publisher
- Kinokuniya Co., Ltd.
- Keywords
- nesting of circles; plane sweep; red-black; interval search; computational geometry
- Citation
- Japan Journal of Industrial and Applied Mathematics, v.23, no.1, pp 127 - 138
- Pages
- 12
- Indexed
- SCIE
SCOPUS
- Journal Title
- Japan Journal of Industrial and Applied Mathematics
- Volume
- 23
- Number
- 1
- Start Page
- 127
- End Page
- 138
- ISSN
- 0916-7005
1868-937X
- Abstract
- 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 0(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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