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A linearized circle packing algorithm. (English) Zbl 1371.65021
Summary: This paper presents a geometric algorithm for approximating radii and centers for a variety of univalent circle packings, including maximal circle packings on the unit disc and the sphere and certain polygonal circle packings in the plane. This method involves an iterative process which alternates between estimates of circle radii and locations of circle centers. The algorithm employs sparse linear systems and in practice achieves a consistent linear convergence rate that is far superior to traditional packing methods. It is deployed in a MATLAB$$^{\circledR}$$ package which is freely available. This paper gives background on circle packing, a description of the linearized algorithm, illustrations of its use, sample performance data, and remaining challenges.
##### MSC:
 65D18 Numerical aspects of computer graphics, image analysis, and computational geometry 52C15 Packing and covering in $$2$$ dimensions (aspects of discrete geometry) 03B40 Combinatory logic and lambda calculus
##### Software:
CirclePack; Knotscape; Matlab
Full Text:
##### References:
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