[Gdal-dev] Converting Mercator Meters to Degrees

[Chris Portka]

I'm trying to convert a UTM easting value to a value an easting in 
mercator meters and then to its correct longitude.  The conversion from 
UTM to mercator is fine and defined in the following way (I'm given a 
proper UTM easting, northing, and zone):

    OGRSpatialReference utm;
    OGRSpatialReference mm;
    OGRCoordinateTransformation *transform;

    utm.SetProjCS("UTM / WGS84");
    utm.SetWellKnownGeogCS("WGS84");
    utm.SetUTM(UTMzone, TRUE);

    mm.SetMercator(0, 0, 1, 0, 0);
    mm.SetWellKnownGeogCS("WGS84");

    transform = OGRCreateCoordinateTransformation(&utm, &mm);
    if (transform == NULL) ...

    double x = UTMEasting;
    double y = UTMNorthing;
    if (!transform->Transform(1, &x, &y))  ...

However, now I want to convert the easting (only the easting) to its 
appropriate longitude value.  Looking up the conversion from mercator 
meters easting to longitude I get the following conversion:

    longitude = (MMEasting / 6356752.3142) * 57.295779513082322;
    OR longitude = (easting / earthRadius) * RadToDeg;

But this gives me a slightly different value (about .1 degrees smaller) 
than if did the conversion with OGR like this:

    OGRSpatialReference mm;
    OGRSpatialReference latlon;
    OGRCoordinateTransformation *transform;

    mm.SetMercator(0, 0, 1, 0, 0);
    mm.SetWellKnownGeogCS("WGS84");
    
    latlon.SetWellKnownGeogCS("WGS84");

    transform = OGRCreateCoordinateTransformation(&mm, &latlon);
    if (transform == NULL) ...

    double x = MMEasting;
    double y = MMNorthing;
    if (!transform->Transform(1, &x, &y)) ...

I don't want to do this whole conversion though because I only need the 
longitude.  Does anyone have an idea what I could be doing wrong in my 
longitude conversion?  Is there some kind of false easting or something 
that gets set in SetMercator that could be giving me differing values? I 
tried looking at the source for SetMercator, but it doesn't look like it 
sets anything differently.  Any help would be greatly appreciated.

Chris