Need to figure out polynomials and splines. I'm limiting myself to
uniform splines atm. Let's start with the Bernstein polynomials, which
come from the binomial expansion of
$$
1
= [x + (1 - x)]^n
= \sum_{k=0}^n \binom{n}{k}x^n(1-x)^{n-k}
= \sum_{k=0}^n b_{k,n}(x)
.
$$
A polynomial written in terms of the basis $b_{k,n}$ is a Bezier
curve, and its coefficients are called control points.