i'm addicted to super auto pets now sorry

If you ever played Roller Coaster Tycoon, you will remember the importance of banking the track in order to keep the lateral g-forces within an acceptable limit. In a previous post about my ongoing work on implementing a roller coaster designer and simulator, I mentioned that you can run into problems depending on how you represent bank angle of a track.

A straightforward way to represent bank angle would be create a bank angle function 𝜃(𝑑) along the track, where 𝑑 is the distance travelled, perhaps by defining a couple of key points along the track with specific bank angles and interpolating the bank angle between them.

However, representing bank angle this way will introduce some problems that are not immediately obvious. These problems are a direct consequence of one of my favorite theorems in mathematics, the Hairy Ball Theorem.