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Apollonius tenth problem via radius adjustment and Mobius transformations
- Authors
- Kim, Donguk; Kim, Deok Soo; Sugihara, Kokichi
- Issue Date
- Jan-2006
- Publisher
- ELSEVIER SCI LTD
- Keywords
- apollonius problem; Mobius transformation; apollonius circle; point location problem
- Citation
- COMPUTER-AIDED DESIGN, v.38, no.1, pp.14 - 21
- Indexed
- SCIE
SCOPUS
- Journal Title
- COMPUTER-AIDED DESIGN
- Volume
- 38
- Number
- 1
- Start Page
- 14
- End Page
- 21
- ISSN
- 0010-4485
- Abstract
- The Apollonius Tenth Problem, as defined by Apollonius of Perga circa 200 B.C., has been useful for various applications in addition to its theoretical interest. Even though particular cases have been handled previously, a general framework for the problem has never been reported. Presented in this paper is a theory to handle the Apollonius Tenth Problem by characterizing the spatial relationship among given circles and the desired Apollonius circles. Hence, the given three circles in this paper do not make any assumption regarding on the sizes of circles and the intersection/inclusion relationship among them. The observations made provide an easy-to-code algorithm to compute any desired Apollonius circle which is computationally efficient and robust.
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Related Researcher
- Kim, Deok Soo
- COLLEGE OF ENGINEERING (SCHOOL OF MECHANICAL ENGINEERING)