[Proj] Coordinate transformation from meters to longitude/latitude

[Oscar van Vlijmen]

> From: "Yuriy Rusinov"
> Date: Tue, 23 Jan 2007 17:45:29 +0300
> Subject: [Proj] Coordinate transformation from meters to longitude/latitude

> I want to transform some cartesian coordinates from its own projection
> invproj +proj=tmerc +lat_0=0 +lon_0=38.99999952571766 +k=1.000000 +x_0=0
> +y_0=0 +ellps=WGS84 +units=m +no_defs
> 7.41094e+06 6.16614e+06
> Results are 
> 135d51'17.113"W 234d40'40.974"N
> These data exceeds latitude limits and no errors, no asterisks in output. Is
> this error and where it can be contains ?  Any ideas ? Thanks in advance.

With my complex transverse Mercator (impoved Dozier):
(assuming x=easting, y=northing):

x=7.41094e6; y=6.16614e6;
// WGS84
lat0=0; lon0=38.99999952571766; x0=0; y0=0; k0=1;
it_type=1; // iteration type
-> lat=27.998246; lon=107.510519 deg

Back: 
lat=27.998245807358206; lon=107.51051923345856;
etc.
-> x=7410940.0000; y=6166140.0000

For the "ultrawide" or "exact" transverse Mercator projection the input data
are not so strange.
But since more "common" TM functions like tmerc work with approximations,
they have a very limited range. Going from latitude, longitude to easting,
northing, the developer could check for an excessive (e.g. >7 deg) departure
from the central meridian, but going from easting, northing to latitude,
longitude, it's not so easy to check for valid input.