Approximation of functions on subdivision surfaces

On subdivision surfaces it is natural to approximate functions with the nodal functions, i.e. the functions with control net δ_i. Approximation properties of these functions were studied for Loop subdivision by Greg Arden in his thesis. The approach is, however, specific to Loop subdivision. The focus of the project is to generalize Arden's result to other schemes using the notion of local linear independence. Additionally using other charts to obtain faster convergence is investigated.