World file

A world file is a six line plain text sidecar file used by geographic information systems (GIS) to georeference raster map images. The file specification was introduced by Esri, and consists of six coefficients of an affine transformation that describes the location, scale and rotation of a raster on a map.

The generic meaning of the six parameters in a world file (as defined by Esri) are:

This description is however misleading in that the D and B parameters are not angular rotations, and that the A and E parameters do not correspond to the pixel size if D or B are not zero. The A, D, B and E parameters are sometimes named "x-scale", "y-skew", "x-skew" and "y-scale".

A better description of the A, D, B and E parameters are:

All four parameters are expressed in the map units, which are described by the spatial reference system for the raster.

When D or B are non-zero the pixel width is given by:

and the pixel height by

World files describing a map on the Universal Transverse Mercator coordinate system (UTM) use these conventions:

The above description applies also to a rectangular, non-rotated image which might be, for example, overlaid on an orthogonally projected map. If the world file describes an image that is rotated from the axis of the target projection, however, then A, D, B and E must be derived from the required affine transformation (see below). Specifically, A and E will no longer be the meter/pixel measurement on their respective axes.

These values are used in a six-parameter affine transformation:

which can be written as this set of equations:

where:

The y-scale (E) is negative because the origins of an image and the UTM coordinate system are different. The origin of an image is located in the upper-left corner, whereas the origin of the map coordinate system is located in the lower-left corner. Row values in the image increase from the origin downward, while y-coordinate values in the map increase from the origin upward. Many mapping programs are unable to handle "upside down" images (i.e. those with a positive y-scale).

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