The guts of Circular Interpolation

I am looking for either a website or some literature that explains in
detail what happens inside a CNC controller when executing a circular
interpolation command, either G01 or G02.

It is my understanding that a CNC actually breaks up the arcs into a
set of smaller linear moves so that the cordal deviation with the
line segment and the arc are within the tolerance spec set in the Amp.

These small line segments have a set of coordinates and a velocity.
Which causes both axis of the machine to move. But prior to moving,
it needs to calculate the accelerations and decelerations, distances
to move based on the acceleration values, adjusting the straight line
velocities so that the tool gets to the end of the small sub line
segment at the right time so as to maintain (or try to) velocity
through the entire arc.

Now all of these tiny little calculations take time, and are repeated
many times during a single G02/G03 command. Then all these
calculations have to match up with the servo update clock, and when
things like jerk, acceleration, and velocity on an axis become
limiting factors, things have to slow down.

What I am looking for is how all this is calculated. Does the CNC
controller do all the work, is the servo controller involved with
some of the calculations.

Any info would be appreciated.

Pete Miles