Further Problems

How to IDENTIFY if two Bezier curve segments belong to one single curve or not?

Please be reminded that Bezier equation can only describe a curve segment instead of the whole curve itself. If two curve segments are connected and belong to a single mother then what would a computer do to solve the intersection points?

Actually, it is pretty easy to deal with two curve segments that belong to two different mothers, however the opposite logical condition is not so simple. I do have found the way to identify the curves of degree 3, and I have proved it in math. But I am still working on the same issue for the curves of degree 4 now. (The curve of degree 2 is a Parabola, it can be identified by its Vertex and Focus point.)

What my believe is, the Identity problem is not just for the purpose to purify the solution of X points. Only if we know how to identify a curve then we may solve the problem of how to best fit a curve form back to its equation, otherwise the so-called Best-Fit curve may not be the real best.