You can generate 1 dimensional profiles in O(1).
For example sinusoidal motion profiling does not need any iterations what so ever; the position, the velocity and the acceleration can be all described with trigonometric functions.
We tried those on our drive system and it worked pretty well, but there might be other methods as well.
For further reading:
https://www.chiefdelphi.com/media/papers/3107
credit to Ether of course
