Local parameterization
Only three types of patches:      is
üconical if it has 1 boundary;
ücylindrical if it has 2 boundary components;
übody type otherwise.
to be cut
G. Patanè, M. Spagnuolo, B. Falcidieno. Para-Graph: Graph-based Parameterization of Triangle Meshes with Arbitrary Genus. Computer Graphics Forum, 23-4, pp. 783-797, 2004.