If the four points of a cubic Bézier curve are known, how do you derive algebraically the universal equations of that curve (which is, one equation for $x$ and the other for $y$)? Let's say I have:
- $A: (x_0,y_0)$, start point,
- $B: (x_1,y_1)$, control point,
- $C: (x_2,y_2)$, control point,
- $D: (x_3, y_3)$, end point.
I have attempted deriving the formula using vectors, however it did not quite work out. I have, however, been able to successfully derive the universal equations for a quadratic Bézier curve.
Any help or hints would be greatly appreciated.