[Proj] Switch utm from tmerc to etmerc

[Charles Karney]

This change has now been made to the master branch of the source.  The
"utm projection" now follows the NGA recommendation and uses etmerc
instead of tmerc (which is less accurate).  You can expect small
(typically < 1mm, except at high latitudes) changes in the results for
the utm projection.

   --Charles

On 10/06/2015 11:19 AM, Charles Karney wrote:
> Reposted from
>
>    https://github.com/OSGeo/proj.4/issues/316
>
> Last year, NGA updated its recommendations on the algorithms to use for
> UTM from tmerc to etmerc (in proj.4's terminology). I recommend that
> proj.4 follow suit, i.e., move the definition of utm from PJ_tmerc.c to
> proj_etmerc.c.
>
> I took a look at doing this and my initial attempts were stymied by a
> lack of knowledge about the macros that proj.4 uses to construct code.
> So it would be better is someone else could tackle this. Any
> volunteers? I'd be happy to help in checking out the result.
>
> Background:
>
> The NGA paper is "The Universal Grids and the Transverse Mercator and
> Polar Stereographic Map Projections"
>
> http://earth-info.nga.mil/GandG/publications/NGA_SIG_0012_2_0_0_UTMUPS/NGA.SIG.0012_2.0.0_UTMUPS.pdf
>
>
> The error in tmerc is less then 1 mm if you stick to the UTM zones.
> However there's interest in extending UTM well beyond the 6 degree
> zones. For example the point 83N 0E is less than 400km from the center
> of zone 35n. So the scale of 35n UTM projection 1.0011 at this point.
> However
>
> echo 0 83 | cs2cs +proj=latlong +datum=WGS84 +to +proj=utm +zone=35
> +datum=WGS84 -f %.6f
> echo 0 83 | cs2cs +proj=latlong +datum=WGS84 +to +proj=tmerc
> +datum=WGS84 +k=0.9996 +lon_0=27 +x_0=500000 -f %.6f
>
> both return 145723.827486, 9300924.850170, while
>
> echo 0 83 | cs2cs +proj=latlong +datum=WGS84 +to +proj=etmerc
> +datum=WGS84 +k=0.9996 +lon_0=27 +x_0=500000 -f %.6f
>
> returns the correct result 145723.870553, 9300924.845226; so tmerc and
> utm are in error by about 43 mm.
>
>    --Charles