+ // one can prove that the area of a quadratic spline = 2/3 * the area of
+ // the triangle of its control points!
+ // to do it, first prove it for the spline through (0,0), (1,1), (2,0)
+ // (which is a parabola) and then note that moving the control point
+ // left/right is just shearing and keeps the area of both the spline and
+ // the triangle invariant.
+ //