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id="docs-internal-guid-901bbad7-aeba-58f4-a438-b75cb81eb596">
<p dir="ltr"
style="line-height:1.38;margin-top:0pt;margin-bottom:0pt;margin-right:5pt"><span
style="font-size:13.3333px;font-family:'Courier
New';color:rgb(0,0,0);vertical-align:baseline;white-space:pre-wrap">As
described in a recent thread, for the next release, proj.4
will switch the default transverse mercator implementation
from tmerc to etmerc.</span></p>
<br>
<p dir="ltr"
style="line-height:1.38;margin-top:0pt;margin-bottom:0pt;margin-right:5pt"><span
style="font-size:13.3333px;font-family:'Courier
New';color:rgb(0,0,0);vertical-align:baseline;white-space:pre-wrap">This
is probably a good occasion to reiterate the history of the
code for the etmerc implementation - especially since the
original author, Knud Poder, turned 90 on October 19th.
Having his transverse mercator implementation becoming the
proj.4 default is a strikingly proper way of celebrating
Poder, among colleagues and collaborators rightfully
considered âthe Nestor of computational geodesyâ.</span></p>
<br>
<p dir="ltr"
style="line-height:1.38;margin-top:0pt;margin-bottom:0pt;margin-right:5pt"><span
style="font-size:13.3333px;font-family:'Courier
New';color:rgb(0,0,0);vertical-align:baseline;white-space:pre-wrap">Poder
wrote the first version of what is now known as etmerc,
around 1961. It was written in Algol-60 and ran on the GIER
computer, built for the Danish Geodetic Institute (see [1]
for details).</span></p>
<br>
<p dir="ltr"
style="line-height:1.38;margin-top:0pt;margin-bottom:0pt;margin-right:5pt"><span
style="font-size:13.3333px;font-family:'Courier
New';color:rgb(0,0,0);vertical-align:baseline;white-space:pre-wrap">The
code was based on theoretical foundations published a decade
earlier, by König & Weise ([2], building on prior work
by Krüger, 1912 [3]).</span></p>
<br>
<p dir="ltr"
style="line-height:1.38;margin-top:0pt;margin-bottom:0pt;margin-right:5pt"><span
style="font-size:13.3333px;font-family:'Courier
New';color:rgb(0,0,0);vertical-align:baseline;white-space:pre-wrap">Poderâs
work was characterized by great care with respect to
numerical precision and accuracy (e.g. by using Clenshaw
summation for recurrence series, and Hornerâs scheme for
polynomial evaluation).</span></p>
<br>
<p dir="ltr"
style="line-height:1.38;margin-top:0pt;margin-bottom:0pt;margin-right:5pt"><span
style="font-size:13.3333px;font-family:'Courier
New';color:rgb(0,0,0);vertical-align:baseline;white-space:pre-wrap">Also,
Poder was noted for his ingeniously implemented âdual
autochecking methodâ (not used in the proj.4 version),
where the same code was used for forward and inverse
projections and was run both ways and compared, to protect
against both coding- and hardware errors. The latter was
very important at a time where the mean time between failure
for computer systems was much shorter than today.</span></p>
<br>
<p dir="ltr"
style="line-height:1.38;margin-top:0pt;margin-bottom:0pt;margin-right:5pt"><span
style="font-size:13.3333px;font-family:'Courier
New';color:rgb(0,0,0);vertical-align:baseline;white-space:pre-wrap">During
the 1970s Poderâs student, Karsten Engsager (the âEâ
in etmerc, âEngsager Extended Transverse Mercatorâ) took
over maintenance and eventually extended König and
Weiseâs numerical series by another term, bringing the
accuracy up to todayâs standard.</span></p>
<br>
<p dir="ltr"
style="line-height:1.38;margin-top:0pt;margin-bottom:0pt;margin-right:5pt"><span
style="font-size:13.3333px;font-family:'Courier
New';color:rgb(0,0,0);vertical-align:baseline;white-space:pre-wrap">In
2008, through the efforts of a.o. Gerald Evenden, Frank
Warmerdam and Karsten Engsager, etmerc was introduced in
proj.4, while in 2013 Charles Karney provided 3 corrections
- stressing the value and importance of open source code
sharing.</span></p>
<br>
<p dir="ltr"
style="line-height:1.38;margin-top:0pt;margin-bottom:0pt;margin-right:5pt"><span
style="font-size:13.3333px;font-family:'Courier
New';color:rgb(0,0,0);vertical-align:baseline;white-space:pre-wrap">Poder
retired 20 years ago, but has been taking active interest in
the maintenance and development of his code ever since.
Switching proj.4 to use a transverse mercator implementation
based on his work is probably the best conceivable way of
celebrating the 90th birthday of a great Nestor of
computational geodesy.</span></p>
<br>
<p dir="ltr"
style="line-height:1.38;margin-top:0pt;margin-bottom:0pt;margin-right:5pt"><span
style="font-size:13.3333px;font-family:'Courier
New';color:rgb(0,0,0);vertical-align:baseline;white-space:pre-wrap">In
celebration of Knud Poder!</span></p>
<br>
<p dir="ltr"
style="line-height:1.38;margin-top:0pt;margin-bottom:0pt;margin-right:5pt"><span
style="font-size:13.3333px;font-family:'Courier
New';color:rgb(0,0,0);vertical-align:baseline;white-space:pre-wrap">/Thomas
Knudsen, Danish Geodata Agency</span></p>
<br>
<br>
<br>
<p dir="ltr"
style="line-height:1.38;margin-top:0pt;margin-bottom:0pt;margin-right:5pt"><span
style="font-size:13.3333px;font-family:'Courier
New';color:rgb(0,0,0);vertical-align:baseline;white-space:pre-wrap">[1]
Thomas Knudsen, Simon L. Kokkendorff, Karsten E. Engsager
(2012): A Vivid Relic Under Rapid Transformation, OSGeo
Journal vol. 10, pp. 55-57, URL </span><a
href="https://journal.osgeo.org/index.php/journal/article/download/200/167"
style="text-decoration:none"><span
style="font-size:13.3333px;font-family:'Courier
New';text-decoration:underline;vertical-align:baseline;white-space:pre-wrap">https://journal.osgeo.org/index.php/journal/article/download/200/167</span></a></p>
<br>
<p dir="ltr"
style="line-height:1.38;margin-top:0pt;margin-bottom:0pt;margin-right:5pt"><span
style="font-size:13.3333px;font-family:'Courier
New';color:rgb(0,0,0);vertical-align:baseline;white-space:pre-wrap">[2]
R. König and K. H. Weise (1951): Mathematische Grundlagen
der Höheren Geodäsie und Kartographie, Erster Band.
Springer, Berlin/Göttingen/Heidelberg, 1951. K</span></p>
<br>
<p dir="ltr"
style="line-height:1.38;margin-top:0pt;margin-bottom:0pt;margin-right:5pt"><span
style="font-size:13.3333px;font-family:'Courier
New';color:rgb(0,0,0);vertical-align:baseline;white-space:pre-wrap">[3]
L. Krüger (1912): Konforme Abbildung des Erdellipsoids in
der Ebene. Neue Folge 52. Royal Prussian Geodetic Institute,
Potsdam. URL <a
href="http://bib.gfz-potsdam.de/pub/digi/krueger2.pdf">http://bib.gfz-potsdam.de/pub/digi/krueger2.pdf</a></span></p>
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