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 Skew Azimuth at Rectified Origin parameter defines the azimuth of the central geodesic at the true origin of the projection as described below. This is also the origin of the rectified coordinate system. This parameter is also referred to as the Skew Azimuth in other applications and books on coordinate conversion. In any case, this azimuth is given in degrees east of north. That is, use a value greater than 180 or a negative value for an azimuth that is west of north.
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, Rectified Skew Orthomorphic, Azimuth at Projection Center, supports an azimuth parameter referred to as Geodesic Azimuth at Projection Center. 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 central point of the projection. |
|
PARM2 |
The latitude, in degrees, of the central point of the projection. |
|
PARM3 |
The azimuth of the central great circle, in degrees east of north. |
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SCL_RED |
The scale reduction to be applied. |
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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. |