Smooth Acceleration Formula or Software?

I have a Digital to Analog circuit which I hope to upgrade to a
proportional controller with software to do S-Curve Acceleration or
Smooth Acceleration / Deceleration. I know this is related to
Calculus but it's been years. I remember someone here once suggested a
site which had free government sponsored software for CNC. Anyone
remember that site or any other source for this information?

Thanks,
Kirk W. Fraser