Constructing conformal maps of triangulated surfaces

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Abstract

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.

Original languageEnglish
Pages (from-to)113-120
Number of pages8
JournalJournal of Mathematical Analysis and Applications
Volume390
Issue number1
DOIs
StatePublished - Jun 1 2012

Keywords

  • Circle packing
  • Conformal maps
  • Conformal welding

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