[Proj] Roussilhe Projection

[Oscar van Vlijmen]

>>> Oscar, what do you exactly mean saying "[errors corrected by OvV]"?
>> Errors in the original text in Geodeta Magazine
>> <http://www.atomnet.pl/~geodeta/2000/59text1.htm>
>> corrected by me, as completely accounted for in my email dated 2005-10-20
>> 17:45
> Ok, thanks. What are the results when you don't apply your changes? Are
> the results closer to Transpol's then? I'm wondering if it's possible
> that Transpol could contain the same bug and that's why your results are
> slighlty different...

Several points are missed here.
(1) It is pointless calculating something with procedures containing blatant
errors. I believe the errors in the article are of a typographical nature,
not of a structural nature. For instance, in the inverse projection variable
yQ was misspelled as yG and an important square root sign was forgotten.

(2) The differences between my implementation and Transpol are not
significant. See it the mathematical way. The differences are smaller than 1
in the least significant digit, which is very likely a rounding problem, not
a difference in maths or a bug.

(3) It has no practical use trying to get a higher precision than 0.00001
meters = 10 microns, because that's what we're talking about: the
differences in x65,y65 between the formulae from the article and Transpol.


> Also, could take a look at
> http://www.geonet.net.pl/gfx/pliki/uklady_new.doc, pages 22-25 mainly,
> and say what you think of it's Uklad 1965 formulae? The author is R.
> Kadaj, the same one who is the author of Transpol software distributed
> by GUGiK. Sorry I didn't mention it before, but I guess it is the most
> important source available. It should be taken for official I think, as
> the author is also an author of the official coordinate transformation
> software for Poland. Sorry, only in Polish again.

Roman Kadaj is probably also the author of the official document "Wytyczne
Techniczne G-1.10 " (technical guideline G-1.10) describing the Polish
projection systems. See literature reference #4 in his article.

Sorry, but in my opinion the author has tried his best to obfuscate the
procedures, so I hardly understand what he is doing. Of course I am hampered
by my weak knowledge of Polish, but still.

It looks to me that chapter 10 describes (in an obfuscated way) a nearly
exact method, very similar to the article in Geodeta Magazine. Probably the
only difference is that the author uses complex math (with real and
imaginary parts of variables).
Chapter 11 describes an alternative method as used in the Gugik-80 system,
where the original System 65 is approximated by complex polynomials with for
every zone a different set of parameters. In some way the polynomials are
based on Transverse Mercator values.
Don't ask me how. The text seems to say, for instance, that mu0 in zone 1 is
equal to the x-coordinate of the [Transverse] Mercator [projection] of the
central point. I played a bit around, but in no way I can reproduce the
given value of 5605231.5783400 m.

If you could provide a complete and accurate translation into English of the
chapters 10 and 11 of said article (tables not necessary), then a further
analysis would be possible. Or not, due to inexplainable mysteries in the
text.