A fast and simple stretch-minimizing mesh parameterization

We propose a fast and simple method for generating a low-stretch mesh parameterization. Given a triangle mesh, we start from the floater shape preserving parameterization 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-the-art mesh parameterization methods and demonstrate its speed and high efficiency in parameterizing large and geometrically complex models.