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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… (More)

We use a simple example to introduce a notion of curvature flow in the conformal mapping of polyhedral surfaces. The inquiry was motivated by experiments with discrete conformal maps in the sense of circle packing. We describe the classical theory behind these flows and demonstrate how to modify the Schwarz-Christoffel method to obtain classical numerical… (More)

Recent interest in materials which form microstructures has lead to eeorts to determine the material conngurations computationally. One approach has been to use a bilinear element with a one-point quadrature scheme. Although the computational results using this approximation appear to agree with the theory, it has been conjectured that this approach leads… (More)

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