# FFF.1.2.3.2 Table Movement in the Isocenter Coordinate System

The table coordinate system is defined in section C.8.19.6.13.1.3 of PS 3.3 where the table translation is represented as (T X ,T Y ,T Z ). The table rotation is represented as (At 1 , At 2 , At 3 ).

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Figure FFF.1.2-4At1: Table Horizontal Rotation Angle

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Figure FFF.1.2-5At2: Table Head Tilt Angle

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Figure FFF.1.2-6At3: Table Cradle Tilt Angle

A point (P Xt , P Yt , P Zt ) in the table coordinate system (see Figure FFF.1.2-7) can be expressed as a point (P X , P Y , P Z ) in the Isocenter coordinate system by applying the following transformation:

(P X , P Y , P Z ) T = (R 3 . R 2 . R 1 ) T . (P Xt , P Yt , P Zt ) T + (T X , T Y , T Z ) T

And inversely, a point (P X , P Y , P Z ) in the Isocenter coordinate system can be expressed as a point (P Xt , P Yt , P Zt ) in the table coordinate system by applying the following transformation:

(P Xt , P Yt , P Zt ) T = (R 3 . R 2 . R 1 ) . ( (P X , P Y , P Z ) T - (T X , T Y , T Z ) T )

Where R 1 , R 2 and R 3 are defined as follows:

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Figure FFF.1.2-7Point P in the Table and Isocenter Coordinate Systems