The transformation of geographic coordinates from universal transverse mercator coordinates

The Army Engineer Topographic Laboratories (AETL) at Fort Belvoir, Virginia, implemented special purpose software to handle their map data. One of the functions of the software was to convert Universal Transverse Mercator (UTM) map coordinates to geographic map coordinates. The conversion was time-consuming and expensive due to a lengthy iterative process; therefore, a different method was sought on the computer.

One method for reducing the computer time is based on a curve-fitting procedure, suggested by an AETL engineer. This procedure is used to provide data to geographic coordinates (X_G, Y_G) from three UTM coordinates (X_T, Y_T). Each of the X_G ‘s is then represented by a quadratic equation dependent on the X_T ‘s; the three X_T points are used to determine the unknown quadratic coefficients; and the resultant equation is then a faster conversion process. The Y_T transformation is done similarly.