[Proj] Insignificant difference between Swiss and Hungarian
Oscar van Vlijmen
ovv at hetnet.nl
Wed Dec 6 08:00:09 EST 2006
I didn't receive Mikael Rittri's message with the subject:
[Proj] Insignificant difference between Swiss and
Hungarian Oblique Mercator?
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
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:
an approximation for EOV with an oblique Mercator.
If I understand the parameters correctly:
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
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
In my understanding the parameters are:
lat0 = 47.14439372222222; lon0 = 19.04857177777778;
x0 = 650000; y0 = 200000; k0 = 0.99993;
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.
* Don't use PROJ.4 epsg init #23700.
* The omerc approximation from Gábor is either too coarse or not easily
* The somerc approximation as published seems very good, but probably not
within 0.014 mm as mr. Rittri seems to indicate.
Mikael Rittri Mikael.Rittri at carmenta.se
Tue Dec 5 07:53:22 EST 2006
I think I have implemented the Hungary EOV projection, which is a
of the Swiss Oblique Mercator (+proj=somerc). In the Hungarian version,
can specify a normal parallel, distinct from the central one. The
parallel gives the center of the first step of the double projection
(ellipsoid -> sphere), while the _central_ parallel gives the center
of the second step (sphere -> oblique cylinder).
I've modified the code of the PROJ.4 somerc, to cover the Hungarian
usage as well, but I am rather surprised: the effect of having
normal parallel != central parallel is about 0.01 millimeters.
Yet, to quote Molnar and Timar,
"its normal parallel slightly but intentionally differs ..." [from the
But I cannot understand the intention, if the difference in projected
is so small. (And I don't read Hungarian; only the abstract is in
I've read on this list that PROJ.4 users do use +proj=somerc for
but I thought the approximation would be worse. Just to rule out the
possibility that I have made a silly mistake: could anyone confirm that
the approximation error is about 0.01 millimeters?
-- Mikael Rittri
Hungary EOV specification: http://lazarus.elte.hu/gb/geodez/geodind.htm
(chapter 2 and 9).
My test points used the projected coordinates roughly in the four
Hungary, which I unprojected with and without the distinct normal
The differences were:
Easting Northing Difference
400000, 0 -> 0.01350 mm
400000, 400000 -> 0.01399 mm
900000, 0 -> 0.01350 mm
900000, 400000 -> 0.01399 mm
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