A non-stationary subdivision scheme for generalizing trigonometric spline surfaces to arbitrary meshes Original Research Article

We present a non-stationary subdivision scheme for generating surfaces from meshes of arbitrary topology. Surfaces generated by this scheme are tensor product bi-quadratic trigonometric spline surfaces except at the extraordinary points. The scheme can be considered as a adaptation of the Doo–Sabin scheme to the non-stationary case. Convergence of the scheme is based on the convergence of a sequence of subdivision matrices to a variant of Doo–Sabin subdivision matrix.