A Circle Pattern Algorithm via Combinatorial Ricci Flows

  • Dong-Meng Xi
  • Shi-Yi Lan
  • Dao-Qing DaiEmail author
Part of the Trends in Mathematics book series (TM)


A circle pattern is a configuration of circles with a prescribed combinatoric and prescribed intersection angles. Based on the idea of combinatorial Ricci flows, we present an iterative process which converges exponentially fast to radii of circle patterns in the Euclidean and hyperbolic planes. This provides a new and effective method to find the radii of circle patterns.


Triangulation Circle pattern Ricci flow Discrete Dirichlet problem 

Mathematics Subject Classification (2010)

65N10 65N30 52C15 30G62 



This work is supported in part by NSF of China (11661011, 11631015) and NSF of Guangxi (2016GXNSFAA380099).


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of SciencesGuangxi University for NationalitiesNanningPeople’s Republic of China
  2. 2.Department of MathematicsSun Yat-Sen UniversityGuangzhouPeople’s Republic of China

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