[Proj] old german topo

Clifford J Mugnier cjmce at lsu.edu
Sat Jul 24 14:04:10 EDT 2004


I was surprised to hear of a Transverse Mercator projection on such an old
topo map of German territory since it was so difficult to compute by hand.
Remember now, that Gauss was the first to use it in the early 1800s (for
the survey of Hannover), and he had a staff of several Ph.D. students to do
the "grunt" work for him.  Its main purpose (the Gauss-Conform TM), for
Gauss was to facilitate the survey computations rather than to be used for
a cartographic projection.  The subsequent plane-table mapping for
cadastral surveying (tax mapping) probably was on the Müffling projection
because it was so "easy" to cast under field survey conditions.

The most common projections found in old German applications were the
"Solnder" (nowadays called the Cassini-Soldner) and the "Müffling."  Both
are aphylactic projections, although the Cassini-Soldner is slightly closer
mathematically to the Transverse Mercator than the Müffling.  The more
common name for that projection is the Polyhedric or the "Polyeder."

The ellipsoidal Müffling uses the identical mathematics as the
two-dimentionsional version of the 3D "Local Space Rectangular" (LSR)
coordinate system used in 3D computational photogrammetry.  It is (almost)
the ellipsoidal equivalent of the gnomonic projection.  ALL aphylactic
projections (Müffling/Polyeder, Cassini-Soldner, Bonne, and Polyconic) were
developed to facilitate drafting in the field for plane table and alidade
compilation.  For survey computations, they are awful.  (See my comments in
my ASPRS column on Hong Kong.)

The EXACT ellipsoid parameters and the EXACT number of significant digits
published is critical to high-precision applications of geodetic
transformations.  Variations abound that are correct for certain places for
certain eras.  Exactly when a certain set of defining parameters is correct
has to be discerned from government survey notes and publications.  It is
an EXACT science, but it is also remarkably obscure and esoteric.

Major General von Müffling was one of the first officers in command of the
Topographic Engineer Corps of the Austro-Hungarian Empire.  (See my columns
in PE&RS on Austria, Hungary, Poland, etc. for more details.)

Clifford J. Mugnier
Chief of Geodesy and
Associate Director,
Department of Civil Engineering
Baton Rouge, LA  70803
Voice and Facsimile:  (225) 578-8536

"Paul Kelly" <paul-grass at stjohnspoint.co.uk> wrote:

> On Sat, 24 Jul 2004, Maciek Sieczka wrote:
> [...]
> > As to the datums I tried 3 different ones and I'm not sure which one is
> > really suitable here. I believe I had a best result with the first of
> > the mentioned below. Though the reprojection result was very similar
> > in each case (max 1-2 m difference) I would like to know which one
> > is right if somebody can tell me.
> None of them are "right"; they are all only approximations to the shift
> between the two datums. Number 1 is for central West Germany, number 2
> southern west Germany, and number 3 seems to be general for the whole
> the potsdam datum is used in. However there is also a more accurate
> 7-parameter transformation for all of Germany on the CRS website (and
> in GRASS).

First I'd like to explain myself. Before I got to understand that there are
different datum transformation parameters available for Potsdam datum I
had propably accidently selected the "2." mentioned below when setting up
the mapset in Grass. After that I got to the
understood a bit more and came to conclussion that "1." would be better
"right" :), ok) in my case - my maps are within 50°20'N - 52°20'N. And
your message I finally noticed different Potsdam datum paramteres available
in Grass. Briefly that's why I was, in error, reffering to the "2." as to
the "GRASS 5.3, datum: potsdam". Sorry for that.

> > 1. +towgs84=584.8,67.0,400.3,0.105,0.013,-2.378,10.29
> > taken from the
> > http://crs.bkg.bund.de/crseu/crs/descr/eu-countrysel.php?country=DE ->
> > DE_DHDN / GK_3 -> Transf. -> DE_DHDN (Middle) to ETRS89
> >
> > 2. +towgs84: 597.1,71.4,412.1,0.894,0.068,-1.563,7.58
> > GRASS 5.3, datum: potsdam
> >
> > 3. +towgs84=606.0,23.0,413.0
> > GDAL 1.2.0, potsdam bessel, Potsdam Rauenberg 1950 DHDN

> So it all depends on which part of Germany your map covers, and e.g. if
> is not in an area that any of the widely available transformations covers
> (e.g. former part of Germany that is now in Poland?)

Yes, former part of Germany, now in Poland, circa 50°45'N, 15°30' - 15°

> then for maximum
> accuracy you would have to derive your own transformation using locations
> of churches as was suggested. But I wouldn't know how to do that...

Then me neither for sure.

I've noticed that all the German/Bessel 1841 systems on the CRS site
mention slightly different ellipsoid inverse flattening than Grass:

Grass 5.3: 299.1528128
CRS:        299.15281285

Propably not a big difference but how big anyway?

One thing more about the projection I've remembered that the guy I got the
map from mentioned the name "von Müffling". He seemed to know about
the cartography even less than me (would you believe it?) but according to
him the projection was "multilateral projection elaborated by general major
von Müffling" (my own translation from Polish). I treid a brief search
this general but nothing. Is it telling anything to anybody?


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