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Abstract

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.