Thomas Knudsen knudsen.thomas@gmail.com
2021-08-28. Last revision 2023-11-24
$ echo 55 12 | kp "geo:in | utm zone=32"
> 691875.6321 6098907.8250kp is the Rust Geodesy coordinate processing program. The obvious abbreviation of coordinate processing is cp, but since cp is the Unix file copying program we substitute k for c - hence kp, which may be taken as a reference to the Danish word for coordinate processing koordinatprocessering.
Incidentally, kp was also the user-id and email address of the late Knud Poder (1925-2019), during his work years at the Danish geodetic institute, GI (and its successor, KMS), from the 1950s until his retirement in 1995.
For many years, Poder was in charge of the GI department for computational geodesy where, for some years around 1980, his deputy was Carl Christian Tscherning (1942-2014), for whom the PROJ transformation program cct was named. Among friends, colleagues and collaborators worldwide, Knud Poder was regarded a Nestor of computational geodesy.
The basic operation of kp is very simple. Any complexity in kp usage is related to the description of the operation to carry out, which is the subject of Rumination 002. The kp command line syntax is:
$ kp "operation" file1 file2 ...
> ...or, with input from stdin:
$ echo coordinate | kp "operation"
> ...or, with output to the file result:
$ kp -o result "operation" file1 file2 ...
> ...Convert the coordinate tuple (55 N, 12 E) from geographical coordinates on the GRS80 ellipsoid to Universal Transverse Mercator, zone 32 coordinates on the same (implied) ellipsoid:
$ echo 55 12 0 0 | kp "geo:in | utm zone=32"
> 691875.6321 6098907.8250While RG coordinates are always 4D, kp will provide zero-values for any left-out postfix dimensions, and try to guess a proper number of output dimensions (unless the -D n option is given):
$ echo 55 12 | kp "geo:in | utm zone=32"
> 691875.6321 6098907.8250
$ echo 55 12 | kp -D3 "geo:in | utm zone=32"
> 691875.6321 6098907.8250 0.0000
$ echo 55 | kp "curvature mean"
> 6385431.75306
$ echo 55 | kp -D4 "curvature mean"
> 6385431.75306 0.00000 0.00000 NaNThe roundtrip option measures the roundtrip accuracy of a transformation
(i.e. how close to the origin you end up after a forward+inverse dance). Knud Poder championed this practise with his ingeniously constructed Poder dual autochecking method, which was essential at a time where computers were less robust than today (more about that below).
$ echo 55 12 | kp --roundtrip "geo:in | utm zone=32"
> -0.0000000000 -0.0000000000The inv option runs the specified pipeline inversely:
$ echo 691875.6321 6098907.8250 | kp --inv "geo:in | utm zone=32"
> 54.9999999996 11.9999999994 0.00000 0.00000The help option gives the list of options:
$ kp --help
KP: The Rust Geodesy 'Coordinate Processing' program
Usage: kp.exe [OPTIONS] <OPERATION> [ARGS]...
Arguments:
<OPERATION> The operation to carry out e.g. 'kp "utm zone=32"'
[ARGS]... The files to operate on
Options:
--inv Inverse operation
-z, --height <HEIGHT> Specify a fixed height for all coordinates
-t, --time <TIME> Specify a fixed observation time for all coordinates
-d, --decimals <DECIMALS> Number of decimals in output
-D, --dimension <DIMENSION> Output dimensionality - default: Estimate from input
--debug Activate debug mode
-r, --roundtrip Report fwd-inv roundtrip deviation
-e, --echo Echo input to output
-v, --verbose... More output per occurrence
-q, --quiet... Less output per occurrence
-o, --output <OUTPUT> Output file, stdout if not present
-h, --help Print help
-V, --version Print versionThe current crop of RG operators is described in the missing manual
On the occasion of Knud Poder's 90th birthday in 2015, I wrote a few words about one of his accomplishments on the PROJ mailing list:
As described in a recent thread, for the next release, proj.4 will switch the default transverse mercator implementation from tmerc to etmerc.
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 “the Nestor of computational geodesy”.
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).
The code was based on theoretical foundations published a decade earlier, by König & Weise ([2], building on prior work by Krüger, 1912 [3]).
Poder’s work was characterized by great care with respect to numerical precision and accuracy (e.g. by using Clenshaw summation for recurrence series, and Horner’s scheme for polynomial evaluation).
Also, Poder was noted for his ingeniously implemented “dual autochecking method” (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.
During the 1970s Poder’s student, Karsten Engsager (the “E” in etmerc, “Engsager Extended Transverse Mercator”) took over maintenance and eventually extended König and Weise’s numerical series by another term, bringing the accuracy up to today’s standard.
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.
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.
In celebration of Knud Poder!
/Thomas Knudsen, Danish Geodata Agency
[1] Thomas Knudsen, Simon L. Kokkendorff, Karsten E. Engsager (2012): A Vivid Relic Under Rapid Transformation, OSGeo Journal vol. 10, pp. 55-57, URL https://journal.osgeo.org/index.php/journal/article/download/200/167
[2] R. König and K. H. Weise (1951): Mathematische Grundlagen der Höheren Geodäsie und Kartographie, Erster Band. Springer, Berlin/Göttingen/Heidelberg, 1951.
[3] L. Krüger (1912): Konforme Abbildung des Erdellipsoids in der Ebene. Neue Folge 52. Royal Prussian Geodetic Institute, Potsdam. URL http://bib.gfz-potsdam.de/pub/digi/krueger2.pdf
Major revisions and additions:
- 2021-08-28: Initial version
- 2022-05-08: Reflect current syntax
- 2023-08-17: Graphical clean up
- 2023-11-20: Reflect the current --help text
- 2023-11-24: Automatic selection of output dimensionality