[Proj] proj and Dutch RD

[Oscar van Vlijmen]

The transformation and projection parameters for the Dutch RD2000 (RD New)
projection can be found on the website of the Dutch Cadastre:
http://www.rdnap.nl

Two publications are important:

"Het stelsel van de Rijksdriehoeksmeting en het European Terrestrial
Reference System 1989 - Gebruik en definitie",
Kadaster
http://www.rdnap.nl/download/rdnaptrans.pdf

"Coördinaattransformaties en kaartprojecties - Formules en parameters",
MD-rapportnummer: MDGAP - 2000.31,
Ministerie van Verkeer en Waterstaat, Meetkundige Dienst
http://www.rdnap.nl/download/coor-en-proj.zip

>From these publications you can derive the following:

Transformation from WGS84 to Bessel 1841:
dx=-565.036; dy=-49.914; dz=-465.839; rx=-0.40939; ry=0.35971; rz=-1.86849;
ds=-4.0772;
Published test point:
lat=52d 10m 42.7005s; lon=5d 48m 36.5479s; h=90.865;
My transformation: 
lat = 52d 10m 46.270042s, lon = 05d 48m 38.339038s, h = 47.5825 m
The text says: lat = 52d 10m 46.2700s, lon = 05d 48m 38.3390s, h = 47.582 m

Transformation from Bessel 1841 to WGS84:
dx=565.040; dy=49.910; dz=465.840; rx=0.40939; ry=-0.35971; rz=1.86849;
ds=4.0772;
Note the very small asymmetry in the to-from parameters!
Published test point:
lat=52d 10m 46.2700s; lon=5d 48m 38.3390s; h=47.582;
My transformation: 
lat = 52d 10m 42.700443s, lon = 05d 48m 36.547865s, h = 90.8649 m
The text says: lat = 52d 10m 42.7005s, lon = 5d 48m 36.5479s, h = 90.865

The RD projection is the double stereographic projection (sterea in
PROJ/libproj).
Central Point: Amersfoort:
52.156160556 N, 5.387638889 E, h = 0.0 m
or in dms: 52d 09m 22.178s N, 05d 23m 15.500 E
Double stereographic projection, k = 0.9999079; x0=155000; y0=463000;
x,y in meters.

Published test point:

lat=52d 12m 34.567s; lon=4d 23m 45.678s; on Bessel 1841 ellipsoid
lat0=52d 9m 22.178s; lon0=5d 23m 15.500;
x0=155000; y0=463000; k0=0.9999079;
I got with my version of sterea: x = 87232.21066, y = 469408.51174
The text ("Coördinaattransformaties en kaartprojecties") says:
x = 87232.211, y = 469408.512 m
The text says that these figures are calculated with the polynomial
expression for the double stereographic projection, whereas (lib)proj uses
the exact solution. The RD series development has a stated accuracy of 0.2
mm or better. Furthermore the text notes that these figures are before grid
interpolation. Therefore some differences can be expected using the official
transformation tool RDNAPTRANS, which uses grid corrections.

> GRASS uses
> towgs84=565.036,49.914,465.839,-0.4094,0.3597,-1.86854,-4.0772
How amusing...

It can be advised to update applications and data files according to the
published data.
I am no representative of the Dutch Kadaster, so the data mentioned above
cannot be used for any legal purposes.
But you can verify the data yourself; references are given above.