Curve from Curvature Function

The curvature function of this curve is
kappa(s) = scale*(2 + cos(s))
The ODE for the velocity v(s) is
v'(s) = kappa(s)*rot(90)*v(s)
The curve c(s) is determined by c'(s)=v(s)

Since the curves are very different in size, they are rescaled at some parameter steps.