# [Gdal-dev] Understanding GEOS projected space

Bas Retsios retsios at itc.nl
Mon Nov 19 10:25:42 EST 2007

```Bas Retsios wrote:

> The x and y as mentioned in formula [1] (4.4.4), the so-called
> "intermediate coordinates" are the scan-angle of the satellite. There
> is a linear relationship between the c and l (column and line of a
> pixel in an MSG-image), and the angle at which this was "seen" from
> the satellite.
>
> Since c and l also have a linear relationship with X and Y (meters, in
> GEOS projection), you must be right when you say that there is also a
> linear relationship (scaling + offset) between (x,y) and (X,Y).
>
> Calculate the relationship, given the following:
>
> The ColumnDirGridStep and LineDirGridStep values found in the header
> files of the MSG images are 3004.03165817 m for bands 1-11, and
> 1000.134348869 m for HRV band 12. Thus not exactly 3km / 1km, but
> slightly more. These values have never changed, since our institute
> installed a receiver for MSG images in 2004.
>
> For bands 1-11, COFF=1856 and CFAC=-13642337, and for band 12, COFF =
> 5566 and CFAC=-40927014. These values have also remained the same for
> all images up to now.
>
> c = COFF + x * CFAC / 65536
> c = X / ColumnDirGridStep

The last part is wrong .. of course you need to add COFF to get c, thus:
c = COFF + X / ColumnDirGridStep

Therewith, the relationship between x and X is a factor:

x * CFAC / 65536 = X / ColumnDirGridStep

thus
X = x * CFAC * ColumnDirGridStep / 65536
and
x = X * 65536 / (CFAC * ColumnDirGridStep)

Best regards,

--
Ir. V. (Bas) Retsios
Software Developer
Geo-information Processing Department
International Institute for Geo-information Science and Earth Observation (ITC)
P.O. Box 6,  7500 AA Enschede, The Netherlands
Phone +31 (0)53 4874 573, telefax +31 (0)53 4874 335
E-mail retsios at itc.nl, Internet http://www.itc.nl

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