A circle packing algorithm

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Abstract

A circle packing is a configuration P of circles realizing a specified pattern of tangencies. Radii of packings in the euclidean and hyperbolic planes may be computed using an iterative process suggested by William Thurston. We describe an efficient implementation, discuss its performance, and illustrate recent applications. A central role is played by new and subtle monotonicity results for “flowers” of circles.

Keywords

Circle packing
Conformal geometry
Discrete Dirichlet problem

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The author gratefully acknowledges the support of the National Science Foundation and the Tennessee Science Alliance.