Bernstein Polynomial

A Bernstein polynomial, named for the mathematician Sergei Natanovich Bernstein, is a polynomial written as a linear combination of Bernstein basis polynomials, a family studied in the field of numerical analysis. Bernstein first used polynomials of this form in a constructive proof of the Weierstrass approximation theorem, which states that every continuous function on a closed interval can be uniformly approximated by polynomials. With the rise of computer graphics, Bernstein polynomials restricted to the interval from 0 to 1 became central to the definition of Bezier curves, and de Casteljau's algorithm gives a numerically stable way to evaluate a polynomial written in Bernstein form.