# 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
}
).

[pic]

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

[pic]

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

[pic]

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:

[pic]

[pic]

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