I have Bézier curve as shown by the wikipedia gif here:
I would like to create a new curve that is a segment of the old one. For example, in this gif (from the same article):
.. if I wanted B to be the starting point of the new curve, but for the curve to follow the same path, how could I find the new control point?
I can see that the answer is very straightforward and easily solvable, but my mind still hasn't caught up with the logic behind the equation for the quadratic Bézier curve:
so I'm having trouble thinking it out. I would greatly appreciate any hints/advice that would help push me in the right direction.