[Proj] Custom projection wildly inaccurate

[Thy, Kristian]

From: Thy, Kristian
> You wouldn't happen to have any information about the transverse mercator approximation?

I think I just stumbled upon something useful:

http://www.gfy.ku.dk/~cct/4geo_k24.htm - at the bottom:

"Det Danske koordinatsystem System 34 er ikke baseret på nogen
 kortprojektion i matematisk forstand. Basis er en tilnærmet
 transversal konform cylinderprojektion (samt 1 for Bornholm).
 Jorden er regnet kugleformet, baseret på middelkrumningsradius
 for Hayford-ellipsoiden (a = 6378388 m, 1/f = 297) i bredden
 56o 08' for Jylland og 55o 20' for Sjælland. Det trigonometriske
 punkt Agri Baunehøj har fået koordinaterne (Y, X) = ( 200 km,
 200 km), så alle danske koordinater er positive. X - aksen peger
 mod Nord og Y - aksen peger mod vest. Afbildningen er iøvrigt
 fastlagt så retningen fra Agri til Lysnet er 24o31'14".17. "

Transl.:

"The Danish coordinate system System 34 is not based on a
 map projection in the mathematical sense. It's basis is an
 approximate transverse conformal cylindrical projection
 (plus another for Bornholm). Earth is defined as spherical,
 based on the average curvature radius for the Hayford
 ellipsoid (a = 6378388 m, 1/f = 297) at latitude 56d08' for
 Jutland and 55d20' for Zealand. The trigonometric point Agri
 Baunehøj is given coordinates (Y, X) = (200km, 200km) such
 that all Danish coordinates are positive. The X axis points
 North and the Y axis points west. The projection is defined
 such that the bearing from Agri to Lysnet is 24d31'14.17". "

For practical purposes, what is officially the X and Y axis in
this projection is switched to conform with other coordinate
systems, and the X axis is then counted as negative from its
origin East of Denmark, meaning that Agri has coordinates
(-200000, 200000) in my data.

The last sentence implies that the Y axis in this projection is
not parallel to geographical North (great). I can't find a value
for this deviance, but I'm willing to forgo that for now, if
someone can help me make up parameters for this projection.

I've tried

C:\>cs2cs -E +proj=tmerc +lat_0=55.29235 +lon_0=12.105661 +x_0=-100000.0 +y_0=100000.0 +to +proj=latlong +datum=WGS84 cs.txt

which gives me

-86714.420 162554.980   12d19'4.069"E   55d51'14.525"N 0.000

but I'm still a bit away from the correct result of
12d20'42.97906" 55d52'40.50251" - I can see I'm missing the
scale factor from the parameters (+k), but I can't find a
stated value for this anywhere.

Kristian


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