Originally Posted by

**sthomas**
Ok, so I want to see if I can pin down exactly what Blender is doing. Let's just consider x animating over time for now. Blender allows for manipulation of a curve P(s) = [t(s), x(s)], where P is a cubic Bezier curve, and hence t(s) and x(s) are cubic polynomials of s, i.e. t(s) = a*s^3 + b*s^2 + c*s + d. However we're not concerned with looking up values of x given s, we want to find values of x given t. So somehow Blender must be able to take a t value and find the corresponding x.