Spherical parameterization and Remeshing, E. Praun, and H. Hoppe. Siggraph 03. They use a regular polyhedral as the domain and map the mesh to this regular polyhedron, minimizing a measure of conformality plus stretch.

- There is a nice comparison of different methods for generalizing barycentric coordinates to the sphere.
- Take the Jacobian matrix of the mapping (derivative in s and
derivative in t) and find its two singular values. These represent the
largest and smallest stretch. You can create a norm from this by
taking sqrt(a^2+b^2). This simplifies to a constant value, weighted by
the area of the triangle.
Minimize inverse stretch, i.e. the difference between the min and max stretch. This measure doesn't work well for long, thin triangles, so they split those.

They use progressive meshes to do a coarse to fine parameterization.

They unfold the n-gon into n squares.