We present a method for constructing surfaces from irregular control meshes that can be embedded in the plane. This method results from a generalization of B-Splines using the known technology of manifolds. The resulting surface can be built with {GC}^k continuity. The presented approach constructs the surface from a collection of pieces which overlap. This method can be generalized to arbitrary meshes to generate general closed surfaces or surfaces with handles by application of an analogous reasoning locally in a general case.