Proceedings of the twenty-eighth annual symposium on Computational geometry
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Given any ε0 and any planar region Ω bounded by a simple n-gon P we construct a (1+ε)-quasiconformal map between Ω and the unit disk in time C(ε)n. One can take $C(\epsilon)=C+C\log \frac{1}{\epsilon}\log \log \frac{1}{\epsilon}$.