Create an S curve motion plan and output it over serial on Arduino Uno

I need a Ardunio program written or an existing library modified to output s-curve motion outputs over serial port at specific time interval.

Move to new destination position is requested using a "MoveToPos" function.

Position, velocity and acceleration are outputted at 10ms intervals over serial port so it can be plotted on a PC.

Example of what the plots for an S-curve will look like are attached.

The 10ms "pollSCurve" calculation is done in the main loop using a millis() time check to trigger new calculation, see proposed code example layout.

A new destination "MoveToPos" can be requested part way through a move.

This is not a stepper motor project as the position needs to be updated at fixed time intervals not at fixed steps so the position can be plotted.

Can be written as a library instead of in the main.cpp if preferred.

Example code and layout attached as "main.cpp". This is missing the maths formulas to do the position, velocity and acceleration calculations to plot the graphs as per attached image.

Acceleration and max speed are the settable parameters.

Hardware is an Adruino Uno

https://en.wikipedia.org/wiki/File:Schematic_diagram_of_Jerk,_Acceleration,_and_Speed.svg