Bernstein polynomial

The Bernstein polynomials of $n$ are defined by

$$B_i^n(t)=\left(\genfrac{}{}{0pt}{}{n}{i}\right)t^i{(1-t)}^{n-i}\mathit{\hspace{1em}\hspace{1em}}i=0,1,2,\mathrm{\dots },n$$

where $\left(\genfrac{}{}{0pt}{}{n}{i}\right)$ is the binomial coefficient.

Bernstein polynomials are used extensively in interpolation theory and in computer graphics. They can be computed efficiently using the de Casteljau’s algorithm.