|GeoTIFF Code||CT_ObliqueMercator (3)|
|OGC WKT Name||Oblique_Mercator|
|Supported By||EPSG, GeoTIFF, OGC WKT|
|Name||EPSG #||GeoTIFF ID||Units||Notes|
|Latitude of projection center||1||CenterLat||latitude_of_center||Angular|
|Longitude of projection center||2||CenterLong||longitude_of_center||Angular|
|Azimuth of initial line||3||AzimuthAngle||azimuth||Angular|
|Angle from Rectified to Skew Grid||4||RectifiedGridAngle||recitified_grid_angle||Angular|
|Scale factor on initial line||5||ScaleAtCenter||scale_factor||Unitless|
|Easting at projection center||6||FalseEasting||false_easting||Linear||As far as I know this is just a normal false easting despite the different EPSG name.|
|Northing at projection center||7||FalseNorthing||false_northing||Linear||As far as I know this is just a normal false northing despite the different EPSG name.|
EPSG considers the Oblique Mercator and Hotine Oblique Mercator projections as two very similar but separate methods because there is a subtle difference regarding the point at which the rectification from skew grid to map grid and where the false grid coordinates are applied. It is possible to interchange the two possible points, but to do so requires that the three parameters (skew angle, false grid coordinates) have different values. Conversely, it is important that a set of published parameter values are applied at the correct point. It is the method that determines this. As always, parameters and method must be consistent with each other. This is somewhat analogous to the Lambert Conic Conformal projection where it is possible to inter-relate parameters and appropriate parameter values between the 1- and 2-standard parallel cases. In both cases EPSG publishes a single formula with if statements to accommodate the different methods where necessary. An alternative approach would be to use two independent algorithms in which much code could or would be duplicated. (Note: some folks call the Lambert 1SP case 'Lambert Tangential' which is only true if the scale factor value is unity - which it generally isn't).
More detailed notes on Oblique Mercator and related projection methods can be found in section 1.4.7 of the EPSG Guidance Note # 7.