I don’t think that’s the right assessment about the abrupt changes in color. What I think those instead reveal is areas of the parameter space where there is a

I don’t think that’s the right assessment about the abrupt changes in color. What I think those instead reveal is areas of the parameter space where there is a collapse of a degree of freedom: if your curve is close to a parabola, then you can make many different cubic curves which are close approximations, and it doesn’t much matter which among them you choose. Raph’s optimizer picks opposite choices for which arm should be the short one when you go across that boundary, but if you smoothed the map out so there were no creases I don’t think you’d get significantly worse results. (I’d be interested to see him try this ;)