Awesome visualizations. The part that I was expecting to see but didn't: how can you move at a constant speed? For the original purpose of positioning objects along a path, it doesn't matter. But when moving, you can see it's moving much more slowly at the beginning and end (mostly determined by the radius). What if I want it to travel at a constant rate? Or even apply an easing function to the speed? I'm sure there'…
For constant speed you need a so-called “Euclidean parameterization” where the t value is proportional to s, the Euclidean distance traveled (and thus no matter the value of t, if you add some dt it always works out to the same ds). This is super commonly needed when animating motion along all sorts of curves, as you might guess. Unfortunately, there’s usually no closed-form solution for it, so we have to do it numer…
Generally this idea is called motion profiling: https://www.motioncontroltips.com/what-is-a-motion-profile/