# EPSG:9622 DEPRECATED

## Affine orthogonal geometric transformation

### Attributes

Data source: EPSG

Information source: EPSG guidance note #7, http://www.epsg.org

Revision date: 2000-06-10

### Formula

```Note: These formulas have been transcribed from EPSG Guidance Note #7. Users are encouraged to use that document rather than the text which follows as reference because limitations in the transcription will be avoided.

XT = XT0   +   XS .  k . dSX . cos q   +   YS .  k .  dSY  . sin q
YT = YT0   –   XS .  k .  dSX . sin q    +   YS .  k .  dSY  . cos q

where:

XT0 ,YT0  = the coordinates of the origin point of the source coordinate reference system, expressed in the target coordinate reference system;
dSX , dSY  = the length of one unit of the source  axis, expressed in units of the target axis, for the X axes and the Y- axes respectively;
k = point scale factor of the target coordinate reference system in a chosen reference point;
q  = the angle through which the source coordinate reference system axes must be rotated to coincide with the target coordinate refderence system axes (counter-clockwise is positive). Alternatively, the bearing (clockwise positive) of the source coordinate reference system Y-axis measured relative to target coordinate reference system north.```

### Example

```Source coordinate system: imaginary 3D seismic acquisition bin grid.  The two axes are orthogonal, but the unit on the I-axis is 25 metres, whilst the unit on the J-axis is 12.5 metres.
The target projected coordinate system is WGS 84 / UTM Zone 31N and the origin of the bin grid (centre of bin 0,0) is defined at E = 456781.0, N = 5836723.0.  The projected coordinate system point scale factor at the bin grid origin is 0.99984.
The map grid bearing of the I and J axes are 110* and 20* respectively.  Thus the angle through which both the positive I and J axes need to be rotated to coincide with the positive Easting axis and Northing axis respectively is +20 degrees.

Hence:
XT0 ,	=    456 781.0 m
YT0	= 5 836 723.0 m
dSX 	= 25
dSY	= 12.5
k 	= 0.99984
q	= +20 degrees

Forward calculation for centre of bin with coordinates: I = 300, J = 247:

XT = Easting   = XT0   +   XS . k . dSX . cos q   +   YS . k . dSY  . sin q    = 464 855.62 m.

YT = Northing = YT0   –   XS . k . dSX . sin q    +   YS . k . dSY  . cos q  = 5 837 055.90 m

Reverse calculation for this point:
XS = [( XT  – XT0) . cos qY  –  (YT – YT0) . sin qY ] / [k . dSX  . cos (qX – qY)] = 230 bins

YS = [(XT   – XT0) . sin qX   +  (YT – YT0) . cos qX ] / [k . dSY . cos (qX – qY)]  = 162 bins```