f(t) = a3*t^3 + a2*t^2 + a1*t + a0
f'(t) = 3*a3*t^2 + 2*a2*t + a1
( a3, a2, a1 & a0 are 3D vectors )
L(x)=Integral from 0 to x of Magnitude(f'(t)) which is Sqrt(P(t)) where
P(t) is degree 4 polynomial ...
The only thing I know is this fuction can be expressed using Elliptical
functions ( in relations with elliptical arc length ) ... well this
functions are expressed with integrals ...