World file

A world file is a plain text computer data file used by geographic information systems to georeference raster map images. The file specification was introduced by ESRI.

Small-scale rectangular raster image maps can have an associated world file for GIS map software which describes the location, scale and rotation of the map. These world files are six-line files with decimal numbers on each line. The name of the file is modeled after the associated raster file. The name of the world file is formed by appending the letter "w" to the end of the raster filename.

An alternative naming convention is also honored, and in fact is more widespread. This convention was developed for filenames that need to conform to the 8.3 file naming convention. The three letters of the filename extension are altered thus: the second letter of the original filename extension is replaced with the last letter, and, the third letter is replaced with the letter "w." If the map files end in  or   -- then the separate world file ends in   or   for example.

Definition
World files do not specify a coordinate system, so the generic meaning of world file parameters are:


 * Line 1: A, pixel size in the x-direction in map units/pixel
 * Line 2: D: rotation about y-axis
 * Line 3: B: rotation about x-axis
 * Line 4: E: pixel size in the y-direction in map units, almost always negative
 * Line 5: C: x-coordinate of the center of the upper left pixel
 * Line 6: F: y-coordinate of the center of the upper left pixel

In a world file using a Universal Transverse Mercator coordinate system (UTM) constantly use:
 * D and B are usually 0, since the image pixels are usually made to aligned with the UTM grid
 * C is the Easting UTM coordinate
 * F is the Northing UTM coordinate
 * Units are always metres per pixel

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:



\begin{bmatrix} x\prime \\ y\prime \end{bmatrix} = \begin{bmatrix} A & B \\ D & E \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} + \begin{bmatrix} C \\ F \end{bmatrix}$$ which can be written as this set of equations:


 * $$\begin{align}

x' &= A\,x + B\,y + C \\ y' &= D\,x + E\,y + F \end{align}$$ where:


 * x' is calculated UTM Easting coordinate of the pixel on the map
 * y' is calculated UTM Northing coordinate of the pixel on the map
 * x is the column number of a pixel in the image counting from left
 * y is the row number of a pixel in the image counting from top
 * A or x-scale; dimension of a pixel in map units in x-direction
 * B, D are rotation terms
 * C, F are translation terms; x, y map coordinates of the center of the upper-left pixel
 * E is negative of y-scale; dimension of a pixel in map units in y-direction

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)

Example: Original  is 800×600 pixels (map not shown). Its world file is  and contains:

32.0 0.0 0.0 -32.0 691200.0 4576000.0

The position of Falkner Island light on the map image is: x=171 pixels from left y=347 pixels from top

this gives: x1=696672 meters Easting y1=4565024 meters Northing

Note that the UTM (grid) zone is not given so the coordinates are ambiguous &mdash; they can represent a position in any of the approx. 1200 UTM grid zones. In this case, approximate latitude and longitude (41.2, &minus;072.7) were looked up in a gazetteer and the UTM (grid) zone was found to be 18T using a web converter or wiki.gis.com coordinates.

Localization
When writing World Files it is advisable to ignore localization settings and always use '.' as the decimal separator. Also, negative numbers should be specified with the '-' character exclusively. This ensures maximum portability of the images.