1 Feb 11:43 2007

### Converting EPSG (Hotine) Oblique Mercator definitions to PROJ lines

Mikael Rittri <Mikael.Rittri <at> carmenta.se>

2007-02-01 10:43:28 GMT

2007-02-01 10:43:28 GMT

Hello, I have thought about the relation between the Hotine Oblique Mercators of EPSG and PROJ.4. I'll explain my current understanding in the form of two design questions. (This concerns only Hotine Oblique Mercator == Rectified Skew Orthomorphic; not Swiss/Hungarian Oblique Mercator or Laborde Oblique Mercator.) 1) Where is the point located, whose projected coordinates are x_0, y_0 (false easting, false northing)? This question has two possible answers. a) At the projection center (which has the central longitude and the central latitude, and is on the central line). EPSG calls this choice "Oblique Mercator", with coordinate operation method code 9815, and the x_0 and y_0 are called EC and NC (Easting at projection center, Northing at projection center). In PROJ.4, this corresponds to +proj=omerc, without using +no_uoff. b) At the so-called natural origin, which is the nearest intersection of the central line and the aposphere equator. (It is enough to know that this will be pretty near the ordinary equator of the earth.) This answer was apparently preferred by Hotine, as it simplifies the formulas a little, and the countries he mapped were near the equator anyway. EPSG calls this choice "Hotine Oblique Mercator", with coordinate operation method code 9812,(Continue reading)