[OSRS-PROJ] Transverse Mercator revisited
Gerald I. Evenden
gerald.evenden at verizon.net
Tue Oct 14 21:10:09 EDT 2003
[gie at localhost dozier]$ cat biblio.txt
Tomorrow I will truck down to my modest local library and
visit the reference desk hoping I can get a copy of references
 through  below. This process normally take 30+ days
IF successful. I'm from Missouri and I want some solid
proof and not allegations.
According to Dozier, the problem is quite simple as I have
summarized at the end of this email.
The following is a biblography that appears to be related to
the problem of the "global" transverse mercator projection:
 Dozier, Jeff, 1980, "Improved Algorithm for Calculation
of UTM and Geodetic Coordinates": NOAA Technical Report NESS 81,
 Lee, L.P., 1976, "Conformal projections based on
elliptical functions":---this shows up under two publishers:
B.V. Gutsell (Canada, I believe) and Canadian Cartographer
Monograph 16, Toronto: University of Toronto.
 Lee, L.P., 1962, "The transverse mercator projection
of the entire spheroid": Empire Survey Review, 16, 208-217.
 Snyder, J.P., 1979, "Calculating Map Projections for the
Ellipsoid": The American Cartographer, Vol. 6, No. 1.
Strebe makes reference to a "Wallis" however I cannot locate
any bib reference to this name except for a reference to
a Helen Wallis and a Davis Wallis award for cartographic
Incidently, in email communications with Dozier, he claimed
Snyder coded the process of his paper into a pocket
calculator (probably a TI that Snyder loved to work on).
In Dozier's paper, reference  was claimed to be the source
of the base equations for the transverse mercator. The
general expression transverse mercator projection of a
psi + i lambda = arctanh(sn w) - e arctanh(e sn w) (1)
psi = isometic latitude
lambda = longitude (from CM)
e = eccentricity
w = u + i v
sn = one of the Jacobian functions.
The Gauss-Kruger class is defined as:
x + iy = (1-e^2)int_0^w dn^-2t dt
= E(w|e^2) - e^2 (sn w cn w)/dn w (2)
where E is the elliptic integral of the second kind and
cn and dn are additional Jacobian functions. i is
square root of -1. Note x is northing and y easting.
Dozier's statement of the problem is: if you can find w
from equation 1 you can compute x&y from equation 2.
For equation 1 he uses Newton-Raphson and the rest is
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