Approximation of Polyhedral Surface Uniformization

01/27/2013

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by   Yaron Lipman, et al.

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We present a constructive approach for approximating the conformal map (uniformization) of a polyhedral surface to a canonical domain in the plane. The main tool is a characterization of convex spaces of quasiconformal simplicial maps and their approximation properties. As far as we are aware, this is the first algorithm proved to approximate the uniformization of general polyhedral surfaces.