Identities for the Univariate and Bivariate Bernstein Basis Functions

Publisher Summary This chapter examines identities for the univariate and bivariate Bernstein basis functions. Bezier curves and surfaces are essential to a wide variety of applications in computer graphics and geometric modeling, and the Bernstein basis functions play a central role in the construction and analysis of these curve and surface schemes. The purpose of this chapter is to assemble in one place those identities involving the univariate and bivariate Bernstein basis functions that help to facilitate the symbolic and numeric manipulation of Bezier curves and surfaces. The chapter presents these identities in a consistent framework and may serve as a compact reference. The formulas are organized into 25 categories. In general, each category begins with the formulas for the univariate bases and then lists the corresponding formulas for the bivariate bases, though in some cases no direct univariate or bivariate analogues exist.