polsim

The top figure shows the movement. Tool on top ( dark colour disc).
The bottom figure shows amount of glass remained as dark bars

1/6 D CoC

1/4 D CoC

1/3 D CoC

1/2 D CoC

2/3 D CoC

3/4 D CoC

optimal setting.

As these are simulations, and if some polishing ( grinding ) process is done by human beings, needs to factor in the man-made variations in stroke length and applied pressure along  push- pull travel path. If the polish( grind) by a machine, theoretically, the optimal process to form a sphere surface is 43.3% stroke TOT(see below). The range is around 1/3 stroke + 15% to 25% overshoot ( meaning 38.3% to 45% stroke)

So actually, the past literature of ATM books suggest 1/3 stroke to achieve a sphere, is assumed that the person will overshoot the stroke length. But if overshoot is too much a hole will start to form in the centre.

Reference:

Computer control dwell time algorithm RFITA