[Proj] Custom projection wildly inaccurate

[Oscar van Vlijmen]

> From: "Thy, Kristian"
> Date: Mon, 20 Nov 2006 10:13:00 +0100
> Subject: RE: [Proj] Custom projection wildly inaccurate
 
> From: Oscar van Vlijmen
>> Another problem is that System 34 is not coupled to any
>> projection. I have heard of a transverse mercator approximation,
>> but an orthographic?
> Now that you mention it, this seems extremely strange. But I just went
> with what was in the official .prj files. You wouldn't happen to have
> any information about the transverse mercator approximation?

There seem to be several approximations. Most straight (read: what you can
do per proj/cs2cs command line alone) projective approximations are bad.
There is really only one way to do it correctly: use the official polynomial
solution.

An interesting approximation, using transverse mercator with some pre- &
postprocessing, can be read in:
Kp2000 - en nødvendighed eller ikke?
Dansk Vejtidsskrift, (6/7) 2001, p. 18-19
Leif Kahl Kristensen, Institut for fysik og astronomi
<http://asp.vejtid.dk/Artikler/2001/06-07%5C2930.pdf>

He gives an approximation for two System34 zones: Sjælland and Jylland/Fynn.
Using his approximation I got for the coordinates you mentioned:
lon =12d 20m 42.97906s; lat = 55d 52m 40.50251s; wgs84 datum.
-> x = 86714.465; y = 162554.937 m
The values you mentioned were:
-86714.42, 162554.98
Kristensen states that his procedure results in an average difference in X
of 5 cm, in Y of 9 cm, with a maximum difference of 18 cm.
For his Jylland/Fynn approximation the differences are larger.

>> The Danish use a 11th (13th?) degree polynomial to convert System 34
>> coordinates to UTM. I haven't seen this polynomial roaming on
>> the internet, so I cannot comment on the accuracy of approximations.
> I had them in my notes from a geodesy course in uni, but they have
> unfortunately been mislaid. At any rate, I am not sure of the copyright
> implications of publishing these polynomials from the tech note I got
> them in.
Algorithms and formulae are usually not copyrightable, but they are
patentable. So, still publishable, more or less, but if patented, commercial
exploitation and sometimes other forms of exploitation are prohibited, at
least in the countries where the patent is valid.
Note: I'm no lawyer, so this is no legal advise!


> I think I just stumbled upon something useful:
> http://www.gfy.ku.dk/~cct/4geo_k24.htm - at the bottom:
I've read this too, but I didn't give it a try.