Remeshing triangulated surfaces with optimal parameterizations

The use of polygonal meshes, especially triangle meshes, is manifold, but a lot of algorithms require the mesh to be structured in a certain way and cannot be applied to an arbitrarily structured mesh. The process of replacing an arbitrarily structured mesh by a structured one is called remeshing and the most important class of structured meshes are triangle meshes with subdivision connectivity. In this paper, we present an algorithm for remeshing triangle meshes with boundary that is based on parameterizing the mesh over a planar domain. We discuss what kind of parameterizations are optimal for the purpose of remeshing and show the advantages of our approach in a series of examples.