**Project Description:**

We propose an efficient parallel algorithm for
computing the global conformal parameterization of a simply-connected open or
closed surface embedded in R3. The method is specially designed for large-scale
problems, of which surface meshes contain a large number of vertices. The main
idea is based on the observation that a global conformal parameterization can be
retrieved from local parameterizations of arbitrary patches using the welding
maps. A numerical algorithm for the global conformal parameterization of a
high-resolution surface mesh can then be developed by conformally glueing the
local conformal parameterizations of various patches. Each local conformal
parameterization can be computed in parallel. Hence, our proposed algorithm is
parallelizable. The procedure conformal glueing can be efficiently carried out
through a partial zipper algorithm, which involves only the boundary vertices.
Extensive experiments on different simply-connected open and closed surface
meshes demonstrate the efficacy of our proposed method.

**Publication:**

- Y. Leung Liu, X.F. Gu, L.M. Lui, A Parallel Algorithm for Global Conformal Parameterization using Welding Maps, to be submitted (2018)