By Bézout's theorem, we know that two cubic Bézier curves can intersect at 9 points (not counting self-intersections). Is there any way to compute the end points and control points of two cubic Bézier curves that intersect at 9 points? I have a graphical description of such a configuration from the Graphic Gems IV book:
but I wonder if there is some way to use Mathematica or other CAS to solve this algebraically or numerically. Thanks!