Turn-mill kinematics

I have been working on a turn-mill kinematics component. 
 

I am not able to understand how the G43 and G54 and G92 offsets should be accounted for in the kinematics.
I would like to do polar as well as cylindrical interpolation using these kinematics.
Polar interpolation will be turned on by G12.1 and off by G13.1
Cylindrical interpolation will be turned on by G7.1 and off by G7.2
It also uses the adaptive feed to slow down when the radius (Joint 0 position) is very close to 0 i.e., joint 0 is very close to the centerline of rotation.
Any comments on how to account for the offsets or general comments for this component are welcome and appreciated.
-automata