Re: [gdal-dev] The GeoTransform Array

Wed, 21 Nov 2012 12:51:31 -0800

On 11/21/2012 5:32 AM, Mateusz Loskot wrote: 
On 21 November 2012 12:06, Even Rouault <[email protected]> wrote:

Selon David Strip <[email protected]>:


The GDAL API tutorial describes this array as:

     adfGeoTransform[0]/* top left x */
     adfGeoTransform[1]/* w-e pixel resolution */
     adfGeoTransform[2]/* rotation, 0 if image is "north up" */
     adfGeoTransform[3]/* top left y */
     adfGeoTransform[4]/* rotation, 0 if image is "north up" */
     adfGeoTransform[5]/* n-s pixel resolution */

The GDAL Data model page says
     Xgeo = GT(0) + Xpixel*GT(1) + Yline*GT(2)
     Ygeo = GT(3) + Xpixel*GT(4) + Yline*GT(5)
where the GT[i]are the coeffs described above.

 From this I conclude that the rotations are not sin/cos of the rotation, but
rather the sin/cos times the
appropriate pixel size. Is that right, or did I miss something?

Yes, for a pure rotation. If the [1], [2], [4] and [5] have no particular
relation, the matrix can represent a combination of scaling, rotation and
shearing. See http://en.wikipedia.org/wiki/Transformation_matrix

Isaac's "Improving the Documentation of Get/SetGeoTransform" post is
worth checking too:

http://lists.osgeo.org/pipermail/gdal-dev/2011-July/029449.html

Best regards,
Isaac's post is quite informative. However, combined with the Wikipedia entry and Even's comment, the post is incomplete as it does not represent the shear coefficients, but that's pretty straightforward to understand.  I think the simplest summary is that the coeffs 1,2,4,and 5 are the terms of the matrix that we get from a concatenation of the rotation, sheer, and scaling matrices.

But that raises a new question about pixel resolution. If I read this carefully, what I conclude is the [1] is the pixel resolution of a transformed pixel in true E/W space. It is not the resolution in the x-direction in the original raster.  Is that correct? If I want the resolution in the original raster, I have to solve for the underlying scale factors, resolutions, shear, and rotation angle. That's six unknowns and four equations. 

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