On the degree elevation of Bernstein polynomial representation

摘要

The polynomials determined in the Bernstein (Bézier) basis enjoy considerable popularity in computer-aided design (CAD) applications. The common situation in these applications is, that polynomials given in the basis of degree n have to be represented in the basis of higher degree. The corresponding transformation algorithms are called algorithms for degree elevation of Bernstein polynomial representations. These algorithms are only then of practical importance if they do not require the ill-conditioned conversion between the Bernstein and the power basis. We discuss all the algorithms of this kind known in the literature and compare them to the new ones we establish. Some among the latter are better conditioned and not more expensive than the currently used ones. All these algorithms can be applied componentwise to vector-valued polynomial Bézier representations of curves or surfaces.