Curves with more than one control point are handled incorrectly

I just discovered that TTF curves with more than one control point actually define chain of quadratic splines between implied midpoints instead of just a cubic or higher order spline. This means the curve (p0, p1, p2, p3) is actually two quadratic splines (p0, p1, (p1 + p2) / 2) and ((p1 + p2) / 2, p2, p3).