DICOM PS3.17 2025a - Explanatory Information
Z.3 Table Coordinate System Transformations (Current)
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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. 


Coordinates of a Point "P" in the Isocenter and Table coordinate systems

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


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DICOM PS3.17 2025a - Explanatory Information