Z.3 TABLE COORDINATE SYSTEM TRANSFORMATIONS

Any point of the table coordinate system (P Xt , P Yt , P Zt ) (see Figure Z-1) can be expressed in the Isocenter Reference coordinate system (P X , P Y , P Z ) 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, any point of the Isocenter coordinate system (P X , P Y , P Z ) can be expressed in the table coordinate system (P Xt , P Yt , P Zt ) 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 Z-1 Coordinates of a Point ā€œPā€ in the Isocenter and Table coordinate systems