A moving mesh approach to stretch-minimizing mesh parameterization

We propose to use a moving mesh approach, a popular grid adaption technique in computational mechanics, for fast generating low-stretch mesh parameterizations. Given a triangle mesh approximating a surface, we construct an initial parameterization of the mesh and then improve the parameterization gradually. At each improvement step, we optimize the parameterization generated at the previous step by minimizing a weighted quadratic energy where the weights are chosen in order to minimize the parameterization stretch. This optimization procedure does not generate triangle flips if the boundary of the parameter domain is a convex polygon. Moreover already the first optimization step produces a high-quality mesh parameterization. We compare our parameterization procedure with several state-of-art mesh parameterization methods and demonstrate its speed and high efficiency in parameterizing large and geometrically complex models.