Take this bezier curve
A = -5, 3 (starting point)
C1 = -1,11
C2 = 3, 19
B = 7, -37 (finishing point)
E divides AC1, F divides C1C2, G divides C2B, H divides EF, I divides FG, and P divides HI all in the ratio 1:3
After calulations, P is found to be -2, 8
Then the same coordinates divide the line segments in the ratio t:1-t
P then comes out to be 12t -5, -64t^3 + 24t + 3
Substituting t = 0 and t = 1 into P, it can be seen that P is at A and at B.
Now, my questions are these: (these involve P = 12t -5, -64t^3 + 24t + 3)
1. What values of t determine the points C1 and C2?
2. What is now the value of P if the coordinates divide their respective line segments in half?
Any help would be greatly appreciated
Thanks in advance