Classification and Construction of Bivariate Subdivision Schemes

In this paper, we shall classify all possible stationary subdivision schemes on a triangular or quadrilateral regular mesh. Then we shall propose a general procedure to construct stationary subdivision schemes (subdivision triplets) with certain desired properties. Finally, we shall present some examples of C √ 2, √ 3, and triadic subdivision schemes with small stencils which are of interest in CAGD.