A mixed hyperbolic/trigonometric non‐stationary subdivision scheme for arbitrary topology meshes

Abstract

In this paper, a new non‐stationary mixed scheme constructed from hyperbolic and trigonometric schemes is presented. It is characterized by a shape parameter that allows 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 the univariate mixed hyperbolic/trigonometric schemes by giving appropriate rules in the neighborhoods of the extraordinary points. This new scheme can generate tangent plane continuous surfaces. Some examples are given to show the performance of these new schemes, such as the reconstruction of 3D models extracted from medical images.