Curves in 3D - 3D Math Primer for Graphics and Game Development - page 713

which was used to draw the parabola, is based on cubic Bezier curves. The
starting and ending x-coordinates for our curve were −0.9683 and 4.2253,
respectively. What were the (x, y) coordinates for all four control points?
11. Returning to the curve in Exercise 3:
(a) Compute the Bezier control points for the segment of the curve from
0.2 to 0.5.
(b) Split this curve into two halves at t = 1/2. What are the Bezier
control points of the curve on each side?
(c) Perform degree elevation on this curve to the quartic case. What are
the five control points?
My curves are not crazy.
— Henri Matisse (1869-1954)