The Bernstein - Bézier Form of a Polynomial −

Note: This document is meant to be viewed in color. If you only have a black and white version you can download a colored version at http://www.math.utah.edu/~pa/bform.pdf Introduction. There are many ways to write a polynomial. One particular representation is the Bernstein-Bézier form (or B-form for short) of a polynomial whose use has become extremely wide spread during the past two decades or so. The reason for this well grounded popularity is the fact that the B-form allows to approach algebraic problems (such as evaluation, but in particular, the smooth joining of polynomial pieces) geometrically. One variable. We begin by representing a univariate polynomial in a form that will at first appear cumbersome, but that will lead to a natural generalization in the case of two or more variables.