Just thought I would throw out some old stuff to chew on. As a toolmaker from the 70's before there were cnc's there were nc's which basically ran from paper tape and did the moves without the use of a computer (just plain old ttl logic). Our shop had a Lagun mill with a 2 axis stepper that could do lines (G01) and arcs (G02 & G03). The arcs were limited to a quadrant. So to do a whole circle took four steps if starting on a axis or five steps if not. Since most of the guys in the shop were old school and did not want to learn something new I was the one who used it.
Started my own shop and the guy I worked for turned the mill into a manual one and gave me the steppers and the control box. I did adapt it to a mill and got it working but the control was getting flaky. Did a little poking around inside and basically it was using rate multiplier chips to do the linear and circular moves. From that I programmed my commode 64 to mimick the same idea but in assembly.
At the time Bridgeport had older 3 axis machines (nc using ttl circuits) which moved the knee instead of the quill for the z axis and the newer cnc ones which did move the quill. Funny thing is that Bridgeport still used the ttl hardware for the newer cnc ones. The computer would just do fancy stuff like scaling and rotation and etc. but the driving of the steppers was still using the old ttl logic just being fed by the computer rather than by the paper tape.
Pretty much the idea used was that everything is moving at a "rate". A 2 axis move is only a right triangle with the x and y being the cosine and sine which are fixed whereas in a circular move the rate of change for the cosine is the sine and vice versa. With rate multipliers and some control logic this was how it was done in the controller that I was given.