Parametrization and smooth approximation of surface triangulations, Michael Floater, CAGD 1997. This paper is a classic for mapping a disk of triangles to the plane, using a linear least-squares solution. The boundary of the mesh is mapped to the boundary of the desired parameterization (usually a square). Each interior vertex tries to map to the centroid of its neighbors. This mapping is guaranteed not to fold, if the boundary is convex. Variations:

The great thing about this paper is that it actually proves that there is no folding.