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Circle packing: Experiments in discrete analytic function theory. (English) Zbl 0853.52019

Summary: Circle packings are configurations of circles with specified patterns of tangency, and lend themselves naturally to computer experimentation and visualization. Maps between them display, with surprising faithfulness, many of the geometric properties associated with classical analytic functions. This paper introduces the fundamentals of an emerging “discrete analytic function theory” and investigates connections with the classical theory. It then describes several experiments, ranging from investigation of a conjectured discrete Koebe \({1\over 4}\) theorem to a multigrid method for computing discrete approximations of classical analytic functions. These experiments were performed using CirclePack, a software package described in the paper and available free of charge.

MSC:

52C15 Packing and covering in \(2\) dimensions (aspects of discrete geometry)
30C20 Conformal mappings of special domains
30C30 Schwarz-Christoffel-type mappings
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