This is one of many variations of a class of projections that is often referred to as Oblique Mercator. The formulas developed by Hotine are commonly used, but formulas have also been developed by Rosenmund and Laborde. Snyder has also published a variation of Hotine's formulas. All of these formulations produce similar, but not precisely identical, results. Thus, it is not uncommon to qualify the general Oblique Mercator with some indication of the formulation used.
This is the formulation/variation of the Oblique Mercator which most widely used (Alaska excepted). This variation requires three parameters: The Central Point Latitude and Central Point Longitude parameters define the approximate center of the region to be mapped, and the Geodesic Azimuth at Projection Center parameter defines the azimuth of the central geodesic at the central point in degrees east of north. (This is the point given by the first two parameters.)
The true origin of this projection is at the point where "the central geodesic intersects the equator of the 'aposphere,' and is, thus, a rather academic location" (Snyder, p70). Thus, neither the Origin Latitude or Origin Longitude parameter are used. This also makes this projection rather difficult for use when defining a new custom coordinate system. See Rectified Skew Orthomorphic, Origin at Center.
Note that another variation of this projection, named Rectified Skew Orthomorphic, Skew Azimuth at Rectified Origin, supports an azimuth parameter referred to as Skew Azimuth at Projection Origin. It might seem to the casual cartographer that these would be the same; but on an ellipsoid, these numbers are different by a small (but significant) amount.
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Parameter Name |
Description |
|---|---|
|
PARM1 |
Longitude, in degrees, of the center point of the projection. |
|
PARM2 |
Latitude, in degrees, of the center point of the projection |
|
PARM3 |
The azimuth of the central great circle, in degrees east of north. |
|
SCL_RED |
The scale reduction to be applied. |
|
X_OFF |
The false easting to be applied to all X coordinates, usually selected to cause all X coordinates within the coordinate system to be positive values of reasonable size. |
|
Y_OFF |
The false northing to be applied to all Y coordinates. |