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...