I learned a lot about Bezier curves when I was playing a lot of No Limits, a roller coaster designer/simulator. It used beziers for defining the track, and it was always difficult to get a smooth track because you needed the radius of the curve to be the same on both sides of every control point. Otherwise, there'd be a noticeable "bump" as the change in change of direction (not a typo) was sudden.

Also, the math of quadratic beziers made it so even if you did get the handles of each control point the right length to avoid a bump, you could get a "pumping" effect as the radius of curvature changed from wide to narrow and back to wide, though you could avoid this by avoiding trying to create circles in your track design.

No Limits 2 eventually came out which uses a different type of curve which was far easier to make smooth. It also included a way to define the track by graphing out the ride's G-forces and banking changes, and it would plot the control points for you. It was an absolute game changer for making smooth track.