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CLC number: TP391

On-line Access: 2012-08-02

Received: 2012-01-13

Revision Accepted: 2012-06-21

Crosschecked: 2012-07-06

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Journal of Zhejiang University SCIENCE C 2012 Vol.13 No.8 P.559-564

http://doi.org/10.1631/jzus.C1200010


A note on circle packing


Author(s):  Young Joon Ahn, Christoph M. Hoffmann, Paul Rosen

Affiliation(s):  Department of Mathematics Education, Chosun University, Gwangju 501-759, Korea; more

Corresponding email(s):   ahn@chosun.ac.kr, cmh@cs.purdue.edu, prosen@sci.utah.edu

Key Words:  Circle packing, Algorithm performance, Parallel computation, Graphics processing unit (GPU)


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Young Joon Ahn, Christoph M. Hoffmann, Paul Rosen. A note on circle packing[J]. Journal of Zhejiang University Science C, 2012, 13(8): 559-564.

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Abstract: 
The problem of packing circles into a domain of prescribed topology is considered. The circles need not have equal radii. The Collins-Stephenson algorithm computes such a circle packing. This algorithm is parallelized in two different ways and its performance is reported for a triangular, planar domain test case. The implementation uses the highly parallel graphics processing unit (GPU) on commodity hardware. The speedups so achieved are discussed based on a number of experiments.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

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[7]Hoffmann, C.M., Joan-Arinyo, R., 2002. Parametric Modeling. In: Farin, G., Hoschek, J., Kim, M.S. (Eds.), Handbook of Computer Aided Geometric Design. Elsevier North Holland, Amsterdam.

[8]Kharevych, L., Springborn, B., Schroder, P., 2005. Discrete Conformal Mappings via Circle Patterns. ACM SIGGRAPH Courses, p.6.

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[10]Liu, J., Xue, S., Liu, Z., Xu, D., 2009. An improved energy landscape paving algorithm for the problem of packing circles into a larger containing circle. Comput. Ind. Eng., 57(3):1144-1149.

[11]Lopez, C.O., Beasley, J.E., 2011. A heuristic for the circle packing problem with a variety of containers. Eur. J. Oper. Res., 214(3):512-525.

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[14]Stephenson, K., 2005. Introduction to Circle Packing: the Theory of Discrete Analytic Functions. Cambridge University Press, New York.

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[16]Willams, G.B., 2001. Approximation of quasisymmetries using circle packings. Discr. Comput. Geom., 25:103-124.

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