Z.2 Positioner Coordinate System Transformations

Any point of the Positioner coordinate system (PXp, PYp, PZp) can be expressed in the Isocenter coordinate system (PX, PY, PZ) by applying the following transformation:

Equation Z.2-1. 

(PX, PY, PZ)T = (R2 .R1)T .(R3 T .(PXp, PYp, PZp)T)

And inversely, any point of the Isocenter coordinate system (P X , P Y , P Z ) can be expressed in the Positioner coordinate system (P Xp , P Yp , P Zp ) by applying the following transformation:

Equation Z.2-2. 

(PXp, PYp, PZp)T= R3 .((R2 .R1).(PX, PY, PZ)T)

Where R1, R2 and R3 are defined as follows:

Equation Z.2-3. 


Equation Z.2-4. 


Equation Z.2-5.