Cubic Bezier reverse GetPoint equation: float for Vector <=> Vector for float

Question

Is it possible to get float t back given the resulting value and the four points? If so, how?

public static Vector3 GetPoint (Vector3 p0, Vector3 p1, Vector3 p2,         


        

Answer 1

Solving the following cubic polynomial should reveal your original t:

(p3 - (3 * p2) + (3 * p1) - p0) * t^3
+ ((3 * p2) - (6 * p1) + (3 * p0)) * t^2
+ ((3 * p1) - (3 * p0)) * t
+ p0
= 0

I put it in standard form so you could easily get the roots from the coefficients.