The polynomials defined by B_(i, n)(t) = (n i) t^i (1 - t)^(n - i), where (n k) is a binomial coefficient. The Bernstein polynomials of degree n form a basis for the power polynomials of degree n.

Bernstein expansion | Bézier curve | spline

BernsteinBasis

Sergei Natanovich Bernstein