World file

A world file is used by Geographic Information Systems to coordinate raster map images. The standard was created by ESRI corporation of Redlands, California.

Small-scale rectangular raster image maps can have an associated world file for GIS map software which describes the location, scale & rotation of the map.

These world files are 6 line ASCII files with decimal numbers on each line. If the map files end in .jpg or .tif -- then the separate world file ends in .jpw or .tfw for example.

World file Universal Transverse Mercator parameters:

A: meters/pixel in horizontal x Easting direction 
D: rotation about y axis, always 0
B: rotation about x axis, always 0
E: meters/pixel in vertical y Northing direction
C: x Easting UTM coordinate of center of upper left pixel in meters
F: y Northing UTM coordinate of center of upper left pixel in meters

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

x1 = Ax + (By) + C
y1 = (Dx) + Ey + F

x1 = calculated UTM Easting coordinate of the pixel on the map
y1 = calculated UTM Northing coordinate of the pixel on the map
x = column number of a pixel in the image counting from left
y = row number of a pixel in the image counting from top
A = x-scale; dimension of a pixel in map units in x direction
B,D = rotation terms
C,F = translation terms; x,y map coordinates of the center of the upper-left pixel
E = negative of y-scale; dimension of a pixel in map units in y direction

Note:  The y-scale (E) is negative because the origins of an image and a geographic 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.

USGS map of Falkner Island

Example: Original falknermap.jpg is 800x600 pixels (detail shown). Its world file is falknermap.jpw 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 zone is not given so the coordinates are ambiguous -- they can represent a position in any of the 60 UTM zones. In this case, approximate latitude and longitude (41.2, -072.7) were looked up in a gazetteer and the UTM zone was found to be 18 using a web converter.