[Proj] Insignificant difference between Swiss and HungarianOblique Mercator?

[Mikael Rittri]

Many thanks for noticing my letter, and replying.  I think I didn't receive my letter from the list, either.  Strange.

I don't have much to add to your conclusions, but just for the record, I tried your test point with my implementation.  What I have done is to extend somerc with a lat_normal, which may differ from lat_0.  If I do not use lat_normal, it will default to lat_0, and I can reproduce your results for somerc:
        x = 870209.628639 m; y = 299283.552765 m
When I set lat_normal to 47.166666666666666667, to emulate Hungary EOV, I get 
        x = 870209.628632 m; y = 299283.552768 m
with 
        dx = 0.0065 mm; dy = 0.0028 mm (difference from somerc).  
but 
        dx = 0.1 mm; dy = 1.0 mm (difference from Oscar van Vlijmen's test result). 

Possibly, my code is _mathematically_ equivalent to the Hungary EOV, but not _numerically_, for some reason.  Oh well, it is nice know that the error is small.  On the other hand, my extension of somerc with lat_normal does not improve anything. 

  Best regards,
     Mikael 

-----Original Message-----
From: proj-bounces at lists.maptools.org [mailto:proj-bounces at lists.maptools.org] On Behalf Of Oscar van Vlijmen
Sent: den 6 december 2006 14:00
To: PROJ list maptools
Subject: Re: [Proj] Insignificant difference between Swiss and HungarianOblique Mercator?

I didn't receive Mikael Rittri's message with the subject:
  [Proj] Insignificant difference between Swiss and
  Hungarian Oblique Mercator?
dated 2006-12-05
But I found it lurking in the archives. Of course, I could have accidentally deleted the received message myself. In case others have missed it too: the complete message is copied below.

As for the Hungarian EOV projection: I haven't seen any official test points yet, so it is not clear if what I am doing is correct.
But the near-official formulae from the Department of Cartography and Geoinformatics, Eötvös University, Budapest <http://lazarus.elte.hu/gb/geodez/geodind.htm>
give for a
lat = 48; lon = 22;
an "x", "y" of:
299283.5538, 870209.6285 m

Monár Gábor & Timár Gábor give in an article to be found at:
<http://www.fomi.hu/internet/magyar/szaklap/2002/03/mar3.pdf>
an approximation for EOV with an oblique Mercator.
If I understand the parameters correctly:
ellipsoid: GRS67
lat0 = "47d 08m 39.8174s"; lonc = "19d 02m 54.8584s"; alfac = 90; gamma = 90; k0 = 0.99993; x0 = -9370549.28432; y0 = 200000.00114; set no_offset flag omerc(lat,lon,lat0,lonc,alfac,gamma,k0,x0,y0);
Result: x = 870209.5387; y = 299283.5505 m This differs by 9.0 cm and 3.3 mm with the correct values.
The authors state however that in the horizontal direction this approximation is better than 0.17 mm.
Probably I didn't interpret the parameters correctly?

Another approximation with the Swiss omerc projection, where mr. Rittri refers to, has never been discussed on the maptools list, but on the r-sig-geo list.
<http://www.mail-archive.com/r-sig-geo@stat.math.ethz.ch/msg00600.html>
and <.../msg00601.html>
In my understanding the parameters are:
ellipsoid: GRS67
lat0 = 47.14439372222222; lon0 = 19.04857177777778; x0 = 650000; y0 = 200000; k0 = 0.99993; somerc(lat,lon,lat0,lon0,x0,y0,k0);
Result: x = 870209.6286; y = 299283.5528 m Differences with the Hungarian values: 1.0 mm, 0.1 mm.

By the way, the PROJ.4 epsg init #23700 is WRONG, because k0 is not given.

By the road: somerc doesn't use an alpha as external parameter.


Possible conclusions:
* Don't use PROJ.4 epsg init #23700.
* The omerc approximation from Gábor is either too coarse or not easily understandable.
* The somerc approximation as published seems very good, but probably not within 0.014 mm as mr. Rittri seems to indicate.

ORIGINAL MESSAGE:
[--- removed by Mikael ---]
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