A bit more detail for those curious.
If you picture some reflective tape on a rotating shaft and then a digital optical pickup on the shaft and collect the data with a standard digital signal analyser that includes anti-alias filtering you will get a signal much like this.
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Note the signal overshoot due to the filtering.
In my case the equipment is usually large industrial equipment that changes speed slowly. In the case of a paper machine winder, because of the fragile paper web, the acceleration rate of change (jerk) occurs over a few seconds and the speed profile looks like the following figure, where the winder speed was reduced in the middle, probably due to a paper issue. with a close up view as this.
If you look closely, you will see that the different splines tried have differing capability of following the acceleration change.
Another use case in the automotive industry would be following a car engine rotational speed as the transmission is shifting. In the ideal world, knot placement would automatically occur around the gear shift, or acceleration change, or high jerk. But the spline would smooth out the jitter in the signal. In practice, so far I have used uniformly spaced splines, though have thought about more clever knot placement.
I have done some testing where a variable speed AC drive was used for a speed sweep. In this case, it was more like a stepped speed sweep rather than a uniformly varying speed sweep. Again an ideal situation for placing knots at the locations of speed change. But again that will be much more complex than uniformly distributed knots.