Smooth Convergence of Subdivision and Degree Elevation for Bezier Tensor Product Surfaces

Bezier subdivision and degree elevation algorithms generate piecewise bilinear approximations of Bezier tensor product surfaces that converge to the original Bezier tensor product surfaces. In this paper, by the uniform parameterization of control meshes and the definition of discrete partial derivatives of piecewise bilinear functions, we prove that discrete partial derivatives of arbitrary order of these control meshes can converge to the corresponding continuous partial derivatives of the original Bezier surface.