Circle Packing

Definition of Circle Packing in Wikipedia

In geometry, circle packing is the study of the arrangement of circles (of equal or varying sizes) on a given surface such that no overlapping occurs and so that all circles touch another. The associated “packing density”, η, of an arrangement is the proportion of the surface covered by the circles. Generalisations can be made to higher dimensions – this is called sphere packing, which usually deals only with identical spheres.

Some Grasshopper Definition:

Spiraling Circle Packing by Tobias Schwinn
Circle packing definition by Daniel Piker
adaptive circle packing from ufo originally developed by steven janssen

But I still want to know the secrets  behind them, maybe the following things will help:

Minimal surfaces from circle patterns: Geometry from combinatorics(pdf)
A circle packing algorithm(pdf)
http://mathworld.wolfram.com/CirclePacking.html
http://www.math.utk.edu/~kens/
http://en.wikipedia.org/wiki/Circle_packing_theorem

Books in Amazon DE:
1. Introduction to Circle Packing: The Theory of Discrete Analytic Functions
2. New Approaches to Circle Packing in a Square: With Program Codes (Springer Optimization and Its Applications)

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