Hughes Hoppe has done a variety of research that depends on finding interesting parameterizations of meshes. His papers aren't exactly lightweight on the math, but you may find some ideas there:

http://research.microsoft.com/en-us/um/people/hoppe/

http://research.microsoft.com/en-us/um/people/hoppe/proj/vfd...

http://research.microsoft.com/en-us/um/people/hoppe/proj/lap...

I seem to remember there's some good stuff from Pixar on contouring which might be helpful.

http://graphics.pixar.com/library/Contours/paper.pdf

if you check out the CGAL library, they have code that solves surface parameterization problems. the least squares conformal mapping is pretty nice for creating uv maps.

http://doc.cgal.org/latest/Surface_mesh_parameterization/gro...

http://doc.cgal.org/latest/Surface_mesh_parameterization/Sur...