General formula for the mask of (2n + 4)-point symmetric subdivision scheme

In this work, we present explicitly a general formula for the mask of (2n + 4)-point symmetric subdivision scheme with two parameters which reproduces all polynomials of degree • 2n + 1. Villiers, Goosen and Herbst [9] derived Deslauriers-Dubuc (DD) masks as being the unique symmetric masks of minimal support that reproduce polynomials of a certain predetermined degree. In this work, the minimalsupport condition is relaxed, so that longer masks are produced. These masks are not necessarily interpolatory, but reproduce polynomials of the same degree as the shorter DD masks. The main idea of relaxing the minimal support condition leads to a generalization of the DD masks that includes various other well known subdivision schemes.