B-Form Basics.

Abstract : The basic facts about the B(arycentric, -ernstein, -ezier) form of a multivariate polynomial are recorded and, in part, proved. These include: evaluation (de Casteliau's algorithm), differentiation and integration, product, degree raising, change of the underlying simplex, and the behavior on the boundary of the underlying simplex, with application to the construction of smooth pp functions on a given triangulation. Some effort has gone into making the notation fully reflect the symmetries and structure of this form. In particular, the description of this form in terms of difference operators is stressed. Keywords: Piecewise polynomials; Linear interpolation.