The Theorems on the B-B Polynomials Defined on a Simplex in the Blossoming Form

Abstract

In this paper, an explicit expression of the blossom by the means of the B-form of B-B polynomial defined on a simplex is given. With its help, new but very short and simple blossom proofs of the most important theorems on B-B polynomials are derived, such as the degree elevation formula, the subdivision and the change of the underlying simplex procedure, the control points convergence property, the Marsden's identity.