[Proj] Implementation(s) for Oblique Stereographic

[Oscar van Vlijmen]

> From: "Kees Krikke"

> As I understand from EPSG documentation and EPSG database Oblique
> Stereographic (epsg code 9809) (with Roussilhe given as an alias) is not the
> same as the USGS Oblique Stereographic projection.
...
> Anyway, you get into trouble if the wrong implementation is used.
...
> When using proj to convert from or to the Dutch RD system:
...
> Better results (within a couple of centimeters) are obtained when using
> Oblique Stereographic Alternative.

Short answer:

* Use PROJ/libproj/etc sterea
* Or, use the official conversion program RDNAPTRANS(tm)2004. Windows only.
Recent versions also perform grid correction.

Longer answer:

The Dutch RD grid uses its own version of the double stereographic
projection, by the Dutch cadastre also called the Schreiber double
stereographic projection.
I have found that there are only very small differences between (my version
of) PROJ/libproj's sterea and the 'double Dutch' (ermm...) projection. Think
of tens of microns in easting, northing, not centimeters.
Official sources (Het Kadaster) have published the exact formulae for this
projection, including a very good polynomial approximation.
There is an official program RDNAPTRANS available that also performs grid
corrections.
See http://www.rdnap.nl
I have found that the EPSG Guidance Note 7.2 description of this projection
produces good results indeed.

Just ask me if you want more references, mainly in Dutch and available
on-line. Much of it can be found on www.rdnap.nl

A test point, near Westkapelle, far away from datum Amersfoort, using my
stuff; no grid corrections:

units: degrees, meters
lat0 =52.1561605555556; lon0 =5.38763888888889;
x0 =155000.00; y0 =463000.00; k0 =0.9999079;
Bessel 1841 ellipsoid

lat=51d 31m; lon=3d 27m;
RD polynomial solution on the Bessel ellipsoid gives RDxy:
20534.0171854597, 393649.052747085
Analytical solution (Schreiber double projection):
20534.0171628404, 393649.052684693
sterea:
20534.0171705519, 393649.052733924
(not all decimals are significant)