I wish to find the asymptote between two cubic Bezier curve segments as shown in the following diagram.
![bezier-asymptote.png](./download/file.php?id=4927&sid=00326c4ad3b46935a2a6af0614623d09)
- bezier-asymptote.png (5.3 KiB) Viewed 2931 times
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.