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Discrete & Computational Geometry

, Volume 44, Issue 2, pp 330–428 | Cite as

Conformal Mapping in Linear Time

  • Christopher J. Bishop
Article

Abstract

Given any ε>0 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 \(C(\epsilon)=C+C\log \frac{1}{\epsilon}\log \log \frac{1}{\epsilon}\).

Keywords

Numerical conformal mappings Schwarz–Christoffel formula Hyperbolic 3-manifolds Sullivan’s theorem Convex hulls Quasiconformal mappings Quasisymmetric mappings Medial axis CRDT algorithm 

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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Mathematics DepartmentSUNY at Stony BrookStony BrookUSA

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