You don't want a train to suddenly experience a sideways force as it enters a curve. So the 2nd derivative of the position, acceleration, should not instantly go from 0 to a constant, instead, it should grow smoothly, like pictured in TFA. So you want a non-zero 3rd derivative, and possibly even a non-zero 4th derivative.

Cubic splines of course give you a nice 3rd derivative. In fact, you can't make a perfect circle using cubic splines, because of that. Draw your device's shape in Illustrator or Inkscape, and you likely make it Apple-like :)

https://news.ycombinator.com/item?id=32005421