A constructive algebraic strategy for interpolatory subdivision schemes induced by bivariate box splines

This paper describes an algebraic construction of bivariate interpolatory subdivision masks induced by three-directional box spline subdivision schemes. Specifically, given a three-directional box spline, we address the problem of defining a corresponding interpolatory subdivision scheme by constructing an appropriate correction mask to convolve with the three-directional box spline mask. The proposed approach is based on the analysis of certain polynomial identities in two variables and leads to interesting new interpolatory bivariate subdivision schemes.