Z.2 Positioner Coordinate System Transformations

Z.2 Positioner Coordinate System Transformations (Current)
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Any point of the Positioner coordinate system (P_Xp, P_Yp, P_Zp) can be expressed in the Isocenter coordinate system (P_X, P_Y, P_Z) by applying the following transformation:

Equation Z.2-1.

(P_X, P_Y, P_Z)^T = (R₂ ^.R₁)^T ^.(R₃ ^T ^.(P_Xp, P_Yp, P_Zp)^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.

(P_Xp, P_Yp, P_Zp)^T= R₃ ^.((R₂ ^.R₁)^.(P_X, P_Y, P_Z)^T)

Where R₁, R₂ and R₃ are defined as follows:

Equation Z.2-3.

Equation Z.2-4.

Equation Z.2-5.