[Proj] Bugs and enhancements to etmerc

Charles Karney charles.karney at sri.com
Sun Jul 21 10:46:25 EST 2013

I've just submitted a patch to the etmerc projection to address
3 issues:

(1) Two terms in the series for converting from conformal
latitude to geographic latitude were wrong.  They now match
Engsager and Poder (2007).  These errors were in the n^5
coefficients and introduced small (about 1 um) errors into the
inverse mapping.

(2) A forthcoming revision of DMA Technical Manual TM8358.2 "The
Universal Grids: UTM and UPS" will recommend the Krueger series
(the same as used by Engsager and Poder) extended to sixth order
in n.  Thus it's a good time to make the upgrade to etmerc to
sixth order.

(3) I've fixed some of the expressions in etmerc to avoid
accumulating round-off errors, e.g.,

   sinh(x) instead of (exp(x) - exp(-x))/2,
   f = e^2 / (1 + sqrt(1 - e^2)) instead of 1 - sqrt(1 - e^2).


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