Z.3 Table Coordinate System Transformations
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## Z.3 Table Coordinate System Transformations

Any point of the table coordinate system (PXt, PYt, PZt) (see Figure Z-1) can be expressed in the Isocenter Reference coordinate system (PX, PY, PZ) by applying the following transformation:

Equation Z.3-1.

(PX, PY, PZ)T= (R3 .R2 .R1)T .(PXt, PYt, PZt)T+ (TX, TY, TZ)T

And inversely, any point of the Isocenter coordinate system (PX, PY, PZ) can be expressed in the table coordinate system (PXt, PYt, PZt) by applying the following transformation:

Equation Z.3-2.

(PXt, PYt, PZt)T= (R3 .R2 .R1).((PX, PY, PZ)T- (TX, TY, TZ)T)

Where R1, R2 and R3 are defined as follows:

Equation Z.3-3.

Equation Z.3-4.

Equation Z.3-5.

Figure Z-1. Coordinates of a Point "P" in the Isocenter and Table coordinate systems

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