[Proj] Re: Converting EPSG (Hotine) Oblique Mercator definitions to PROJ lines

[Oscar van Vlijmen]

> From: "Mikael Rittri"
> Date: Thu, 1 Feb 2007 11:43:28 +0100
> Subject: Converting EPSG (Hotine) Oblique Mercator definitions to PROJ lines
> 
> Hello,
> I have thought about the relation between the Hotine Oblique Mercators
> of EPSG and PROJ.4.

What I can contribute to the discussion is a more practical view as in "how
do we calculate it?"

There aren't that many Oblique Mercator projections in actual use. In some
cases omerc is used as an ugly approximation to a projection not to be found
in some applications, like the Swiss grid, Hungarian EOV, Laborde Madagascar
and some others.
Then we have Snyder's technique of providing two points on the centerline
instead of central point and azimuth of the centerline.
The central point/azimuth method is the most common.

In developing my code I started with the libproj code and added merely a
couple of tweaks, found in GCTP (like more overshooting correction with
adj_lon) and a very important one: the alfa_c = 90 deg case. The latter is
not supported in libproj and the EPSG Guidance note 7-2 tells how to deal
with this situation. I'm not impressed by the rest of the omerc code in the
Guidance note however. The alfa_c = 90 case is important for some
approximations done with the aid of omerc.

A relatively simple solution for the 'true' Oblique Mercator projections (as
opposed to approximations): if you encounter an RSO, there are 2 options:
(1) Use omerc with no_offset.
(2) Calculate an adjusted false easting, northing and use the regular omerc
without no_ofs.
For instance, for Michigan Georef Melita gave the adjusted values Ec =
499840.252 m and Nc = 528600.303 m. Or use my values:
x0 = 499840.25238573; y0 = 528600.30337017;