Dimensions of spline spaces over unconstricted triangulations

One of the puzzlingly hard problems in Computer Aided Geometric Design and Approximation Theory is that of finding the dimension of the spline space of C r piecewise degree n polynomials over a 2D triangulation Ω . We denote such spaces by S n r ( Ω ) . In this note, we restrict Ω to have a special structure, namely to be unconstricted. This will allow for several exact dimension formulas.