[Proj] Implementation(s) for Oblique Stereographic

[Kees Krikke]

Thanks Oscar,

I'am aware of the sterea and RDNAPTRANS options. Even if the RD projection
is a odd one, it is well documented and the conversion between RD and other
coordinate systems is not my problem.  

I just wanted to point out that there is a problem when a coordinate system
uses "Oblique Stereographic projection". The problem is that there is more
than one implementation of this projection. In the EPSG document
(http://www.epsg.org/guides/docs/G7-2.pdf) a remark is made that the USGS
implementation of Oblique Stereographic is considered a different
projection.

So if a coordinate system use Oblique Stereographic projection (epsg code
9809) you need to know if the epsg (Roussilhe) or usgs implementation should
be used. (If I am wrong here than proj4 needs to use sterea or a more exact
implementation of the EPSG Oblique Stereographic projection whenever it sees
epsg code 9809 and the problem would be solved.)

For example if you use the "proj +init=epsg:28992"command (28992 being the
epsg code for the dutch RD coordinate system) you will  get the stere
conversion because that is the implementation proj uses whenever it sees the
9809 code. For RD this would be wrong because the sterea conversion provides
better results. (I understand that this is also true for the Polish Uklad
1965 system.)

In proj4 you can easily change the epsg file so the sterea conversion is
used, but other applications (even if they rely on proj4, such as gdal) just
look at the projection codes (such as 9809) and use just the implementation
that is linked to this code. (for gdal: I think this is the stere
implementation)

An improvement for proj4 would be to implement the epsg and usgs
implementation and make sure the epsg file refers to the correct
implementation.

But at this time my problem is that I'm not able to use gdal to reproject
images from/to the RD coordinate system. (without modifying or making s/w)

A long term solution would be to identify multiple "Oblique Stereographic
projection" implementations and make sure that for each implementation a
unique epsg code is determined that can be used in geotiff images. (also
codes for other geo code systems would be needed)

Any thoughts on this subject?

Cheers,

Kees Krikke




-----Original Message-----
From: proj-bounces at lists.maptools.org
[mailto:proj-bounces at lists.maptools.org] On Behalf Of Oscar van Vlijmen
Sent: 25 October 2005 22:11
To: PROJ.4 and general Projections Discussions
Cc: Kees Krikke
Subject: Re: [Proj] Implementation(s) for Oblique Stereographic

> 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)



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