ABSTRACT
B-patches were introduced by Seidel [8] and shown to agree with multivari ate B-splines on a certain region [6]. The basis functions for the B-patches, referred to as B-bases, are known to be local multivariate generalizations of B-splines. Lineal bases, or L-bases, that is, multivariate polynomial bases formed from products of linear polynomials, were studied by Cavaretta and Micchelli and shown to be dual to B-bases using a multivariate polynomial identity [2]. After briefly reviewing some essential properties of B-bases and L-bases, we establish this duality by generalizing the de Boor-Fix dual func tionals [4] from curves to surfaces. This formula for the dual functionals is then used to demonstrate the duality between certain recurrence diagrams for B-bases and L-bases and to derive the Cavaretta-Micchelli identity. Our work easily generalizes to higher dimensions. Nevertheless, for the sake of simplicity, the results are presented and derived here only for surfaces.
