BernsteinPolynomial

Bernstein polynomials are defined as follows:

$$ B_{n, k}(x) = \binom{n}{k} x^k (1 - x)^{n - k} $$

where $\binom{n}{k}$ is the binomial coefficient, $n$ is the degree of the polynomial, and $k$ is the specific term of the polynomial. The variable $x$ must be in the interval $[0,1]$.

A Bernstein polynomial of degree $n$ is a linear combination of these polynomials:

$$ B_n(f)(x) = \sum_{k=0}^{n} f\left(\frac{k}{n}\right)B_{n,k}(x) $$