5 Abstract coordinate systems 29

Example transverse Mercator map projection

1. 
   As noted in [SNYD] and [LLEE] the closed solution for the transverse Mercator forward and inverse conversions were developed by Prof. E. H. Thompson in 1945 and were formally published by L. P. Lee in 1962 [LLEE] with the permission of Professor Thompson. In 1980, J. Dozier published a report that adapted Lee’s results to a computerized solution, including complete program listings in the C language [DOZI]. The formulation used here is further adapted by Craig Rollins of the National Geospatial-Intelligence Agency, Arnold, Mo. USA to include a central scale factor, a non-zero latitude origin and false easting and false northing offsets for both the easting and northing components.
   
2. 
   The complex functions sn(w |²), cn(w |²) and dn(w |²) are called Jacobian elliptic functions in [ABST] and [DOZI] and are called Jacobi functions in [LLEE].
   
3. 
   The domain of the inverse mapping equations covers the main region of interest. This domain can be extended to a larger region whose exact specification is complicated to define.