I wish to find the asymptote between two cubic Bezier curve segments as shown in the following diagram.



The end of the P segment will always coincide with the start of the Q segment, and the angle P0-Q0-Q3 will always be greater than the angle P0-Q0-Q1; and both of these angles will be between 90 and 180 degrees (I believe this ensures a unique solution).

I am specifically interested in the end-points where the asymptote intersects the two curves (the ends of the orange line in the diagram) and, if possible, I would prefer a simple formula solution, rather than an algorithmic one (such as walking along the curves).

I am in no particular rush as I will be traveling over the next few weeks, but would really appreciate any guidance provided.