I was working on integrating this into a stepper motor utility, when I realized that perhaps some people might be interested into the secret world of Quadradic curves.
The funny thing is: many of you have probably have probably drawn them as string art when you were kids, without knowing it.
Part way down, there’s a Quadradic Curve Plotter that looks like:
This math is beyond me, but that detail is not stopping me from programming it. I pasted the results into a spreadsheet. Now, if I can move this into the positive err-domain and get everything running on faster longs and ints, so that the lowly Arduino can do it quickly with all of its 16mhz/8-bit ferocity. : )