We consider the problem of creating a map between two arbitrary triangle meshes.
Whereas previous approaches compose parametrizations over a simpler intermediate
domain, we directly create and optimize a continuous map between the meshes. Map
distortion is measured with a new symmetric metric, and is minimized during
interleaved coarse-to-fine refinement of both meshes. By explicitly favoring low
inter-surface distortion, we obtain maps that naturally align corresponding
shape elements. Typically, the user need only specify a handful of feature
correspondences for initial registration, and even these constraints can be
removed during optimization. Our method robustly satisfies hard constraints if
desired. Inter-surface mapping is shown using geometric and attribute morphs.
Our general framework can also be applied to parametrize surfaces onto
simplicial domains, such as coarse meshes (for semi-regular remeshing), and
octahedron and toroidal domains (for geometry image remeshing). In these
settings, we obtain better parametrizations than with previous specialized
techniques, thanks to our fine-grain optimization.