A Generalized Cubic Exponential Non-stationary Subdivision Scheme for Arbitrary Topology Meshes

In this paper, a new non-stationary scheme built from generalized cubic exponential spline is presented. It is characterized by two shape parameters that allow the user to modify the shape of the surface obtained from a given initial mesh. Such a non-stationary subdivision scheme is constructed by taking the tensor product of univariate generalized cubic exponential schemes by giving appropriate rules in neighbourhoods of the extraordinary points. This new scheme can generate continuous surfaces in the tangent plane. Some examples are given to show the performance of these of these new schemes.