Constructing conformal maps of triangulated surfaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:390

Article

Williams, G. Brock

关键词: Circle packing;    Conformal maps;    Conformal welding;   

DOI  :  10.1016/j.jmaa.2012.01.023

来源: Elsevier

【 摘 要 】

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. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free