Approximate $n$ grade Bézier through cubic and/or quadratic Bézier curves

Question

I'm trying to draw a $6$ grade (start point, $4$ control points, end point) Bézier curve but the API offers me only cubic and quadratic curves methods.

Is there a way to split or approximate the $6$ (or $n$) grade curve only through cubic or quadratic curve(s) ?

Answer 1

This is called "degree reduction" and there's quite a lot of literature on it. The short answer is that there isn't an exact reduction, so you have to approximate; the approximation you choose depends on what you care about most.

I suggest you start with a good bibliography on Bézier curves.