Robust arithmetic for multivariate Bernstein-form polynomials

Abstract

There are several ways to represent, to handle and to display curved surfaces in computer-aided geometric design that involve the use of polynomials. This paper deals with polynomials in the Bernstein form. Other work has shown that these polynomials are more numerically stable and robust than power-form polynomials. However, these advantages are lost if conversions to and from the customary power form are made. To avoid this, algebraic manipulations have to be done in the Bernstein basis. Farouki and Rajan (R.T. Farouki, V.T. Rajan, Algorithms for polynomials in Bernstein form, Computer Aided Geometric Design 5 (1988) 1–26) present methods for doing arithmetic on univariate Bernstein-basis polynomials. This paper extends all polynomial arithmetic operations to multivariate Bernstein-form polynomials.