# Geotransform Tutorial¶

## Introduction to Geotransforms:¶

A geotransform is an affine transformation from the image coordinate space (row, column), also known as (pixel, line) to the georeferenced coordinate space (projected or geographic coordinates).

A geotransform consists in a set of 6 coefficients:

GT(0) x-coordinate of the upper-left corner of the upper-left pixel.
GT(1) w-e pixel resolution / pixel width.
GT(2) row rotation (typically zero).
GT(3) y-coordinate of the upper-left corner of the upper-left pixel.
GT(4) column rotation (typically zero).
GT(5) n-s pixel resolution / pixel height (negative value for a north-up image).

## Transformation from image coordinate space to georeferenced coordinate space:¶

X_geo = GT(0) + X_pixel * GT(1) + Y_line * GT(2)
Y_geo = GT(3) + X_pixel * GT(4) + Y_line * GT(5)


Note that the pixel/line coordinates in the above are from (0.0,0.0) at the top left corner of the top left pixel to (width_in_pixels,height_in_pixels) at the bottom right corner of the bottom right pixel. The pixel/line location of the center of the top left pixel would therefore be (0.5,0.5).

## In case of north up images:¶

GT(2), GT(4) coefficients are zero.
GT(1), GT(5) is the pixel size.
GT(0), GT(3) position is the top left corner of the top left pixel of the raster.