Approximation of Polyhedral Surface Uniformization

2013/01/27 by Yaron Lipman, Lipman, Yaron
Computer Science · Mathematics · #Computational Geometry (cs.CG) #FOS: Computer and information sciences #FOS: Mathematics #Graphics (cs.GR) #Numerical Analysis (math.NA) #cs.CG #cs.GR #cs.NA #math.NA

paper · pdf · doi:10.48550/arxiv.1301.6336

arxiv created 2013/01/27 · arxiv updated 2013/01/29

Abstract

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.

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