I think you need a prolate cycloid, which is defined by a point outside a circle rolling on a line.
The diameter of your circle -- which would be theoretical and NOT your tool diameter - would be a function of the RPM and the feedrate. In your example, this theoretical circle "rolls" 300mm for 3000 revolutions, i.e. 0.1mm per revolution. Thus, its circumference must be 0.1mm and its diameter 0.1/pi mm.
I believe this is what you are looking for. The x,y position of that point on a stationary rotating tool is a simple sine/cosine function - then add in the relative x-motion of the axis as a function of time. I used a slower RPM because otherwise the graph gets really dense.
cutter motion.pdf 14.8 KB