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)

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)