Hotine Oblique Mercator (Rectified Skew Orthomorphic)

These projections have been deprecated and should not be used. These implementations of the HOM/RSO projection have been replaced by the new Oblique Mercator Azimuth and Oblique Mercator Two Points projection methods. The new projection methods provide the same functionality as these types, but with additional flexibility to support a wider range of Oblique Mercator projections (rectified and unrectified, natural-origin and center-of-projection based, etc.). This older, deprecated method has been maintained for backward compatibility only; it should not be used for new coordinate system definitions.

The Hotine Oblique Mercator (HOM) projection is a cylindrical, conformal map projection. It is similar to the Mercator projection, except that the cylinder is wrapped around the sphere so that it touches the surface along the great circle path chosen for the central line, instead of along the earth's equator.

Scale becomes infinite 90 degrees from the central line and is true along a chosen central line, along two straight lines parallel to the central line, or along a great circle at an oblique angle.

The HOM projection is used for geographic regions that are centered along lines that are neither meridians nor parallels, but that may be taken as great circle routes passing through the region, such as the Alaskan panhandle.

Two cases of the Hotine Oblique Mercator projection are implemented within the Geographic Calculator, differing only in their defining parameters.

The "Hotine Oblique Mercator (2 Points)" projection has the following parameters:

  • False Northing

  • False Easting

  • Latitude of natural origin

  • Scale factor at natural origin

  • Standard longitude 1

  • Standard longitude 2

  • Latitude of 1st standard parallel

  • Latitude of 2nd standard parallel

The Rectified Skew Orthomorphic (RSO) projection is used throughout the world, particularly in Malaysia. The RSO projection is equivalent to a HOM projection except that the defining parameters are different. You can specify a HOM projection by specifying a point and the azimuth defining the central line. This case allows for the entering of parameters for the RSO projection.

The "Hotine Oblique Mercator (1 Point & Azimuth)" projection has the following parameters:

  • False Northing

  • False Easting

  • Latitude of natural origin

  • Longitude of natural origin

  • Azimuth of initial line

  • Angle from Rectified to Skew Grid

  • Scale Factor at natural origin

NOTE 1: The Skew Azimuth parameter is essential for correct rectified to skew coordinate transformation. If you have researched a coordinate system and there is no defined skew angle simply enter the azimuth of the central line as the skew angle. This will provide for an identity rectified to skew transformation.

NOTE 2: There are two variations of the "Hotine Oblique Mercator (1 Point & Azimuth)" projection type. These are mathematically identical in terms of results returned. The only difference is that the second version uses hyperbolic functions in the underlying mathematical computations.