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Constructing conformal maps of triangulated surfaces

2012; Elsevier BV; Volume: 390; Issue: 1 Linguagem: Inglês

10.1016/j.jmaa.2012.01.023

1096-0813

G. Brock Williams,

Advanced Numerical Analysis Techniques

We describe a means of computing the uniformizing conformal map from a triangulated surface whose triangles are realized as Euclidean triangles in R 3 onto a fundamental domain in the unit disc D , plane C , or sphere S 2 . Mapping such triangulated surfaces arises in a number of applications, such as conformal brain flattening. We use the circle packing technique of Bowers, Hurdal, Stephenson, et al., to first create a quasiconformal approximation to the conformal map; then we apply a discrete form of conformal welding to reduce the distortion and converge to the conformal map in the limit.