[Proj] Lambert Conformal Conic

[OvV_HN]

There are more disturbing differences with respect to the Lambert 
projection.
Like the French IGN according to the publication "Transformaton.pdf", the 
Belgian NGI work with fixed values of two projection constants. In normal 
applications, they are calculated.
This can give differences.

Let's focus our attention first to the publication:

"Coördinaattransformaties en kaartprojecties"
Ministerie van Verkeer en Waterstaat, Directoraat-Generaal Rijkswaterstaat, 
Meetkundige Dienst
3e herziene uitgave, December 2000
MD-rapportnummer: MDGAP - 2000.31
Ch. 4.5 "De Lambert-projectie"
http://www.rdnap.nl/download/coor-en-proj.zip

Yes, this is a publication from the Netherlands, but the Belgian Lambert72 
projection is carefully delineated with an example. The mentioned projection 
constants are the same as are published by the Belgian NGI in an old 
publication.

Remarkably: the test point mentioned on the NGI page
http://www.ngi.be/NL/NL2-1-4.shtm
cannot be reproduced by the (correct) algorithm, published in the more 
recent publication, also found on that web page
<http://www.ngi.be/Common/Lambert2008/Transformation_Geographic_Lambert_NL.pdf>
The given results can however be reproduced if you take the projection 
constants, mentioned in the still available publication 
"Coördinaattransformaties en kaartprojecties" mentioned above.

The Belgian example at hand reads:

Lambert 1972 projection
lat = 50d 40m 46.461s N; lon = 5d 48m 26.533s E;
Published grid coordinates: X = 251763.204; Y = 153034.174 m
With the published projection constants
p = 0.7716421928
k = 11565915.812935
I get:
251763.20419; 153034.17402
But with the exactly calculated projection constants I get:
251763.20416; 153034.13255
Note the large difference in Y.
The reason for this difference is that there is a small error in the 
published projection constants.
These numbers were used for many years.

You can also calculate the Lambert 1972 with the standard LCC procedure, but 
with an adjusted lat1, lat2, x0 and y0. Depending on the truncation of these 
numbers, you can get slightly different values.
For instance, with
lat1 = 49d 50m 0.00204s; lat2 = 51d 10m 0.00204s;
x0 = 150000.01256; y0 = 5400088.4378;
I get:
251763.20461; 153034.17552


The same problem occurs with the Hungarian EOV projection (not supported by 
PROJ): small differences are obtained whether one uses the published values 
of certain projection constants, or if one calculates them exactly.


Oscar van Vlijmen



----- Original Message ----- 
From: "Irwin Scollar" <al001 at uni-koeln.de>
To: <proj at lists.maptools.org>
Sent: Sunday, April 26, 2009 11:14 AM
Subject: [Proj] Lambert Conformal Conic


In France, the Institut Géographique National
(IGN) has abandoned mapping using four Lambert
secant conic zones which were in use after World
War One based on the NTF (Nouvelle Triangulation
de la France) of the late 19th and early 20th
century and the Clarke 1880 ellipsoid.

....

A discussion similar to the recent one concerning
the Transverse Mercator about the accuracy and
speed of the different approaches for computing
conformal grid values with the Lambert Conic
secant projection for France and elsewhere would be greatly appreciated.

Irwin Scollar