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Simple Gauss-Krüger transformation for C++

This project provides a C++ implementation of coordinate transformation between geodetic coordinates and grid coordinates of Gauss (Transverse Mercator) projections, using the Krüger-n series developed to fourth order.

A lot of inspiration comes from the Java implementation made by Kodapan, primarily in the way classes are used. That project is in turn a port of the Javascript implementation made by Arnold Andreasson. The equations and numbers used are directly based on the formulas published by Lantmäteriet (the Swedish National Land Survey), especially the document called Gauss Conformal Projection (Transverse Mercator) - Krüger's Formulas, published in 2008, and tests are implemented to check the calculations against reference points provided by Lantmäteriet.

This C++ implementation was originally developed for coordinate conversion in the public transport application Fahrplan since using Proj4 seemed overly complex, and the intent is to make it simple to include in other projects wishing to use it. Although it was developed in a Swedish context, with Swedish coordinate systems to test with, it is thought to be useful also for other coordinate systems using the Gauss-Krüger projection.

Except the library, a simple command line tool is included so you can play around with the transformations.

Dependencies

The library itself requires no more than standard library components. To build the test, Boost Test is required, and for the command line tool, Boost Program Options is required (tested using version 1.54 of Boost).

Usage

The library can be compiled and linked dynamically or statically, or included in your project as source code files. In the former cases, it has to be compiled first:

$ make lib

Code

The values in the following example are taken from Parametrar till approximativa transformationssamband för direktprojektion mellan SWEREF 99 och RT 90, published by Lantmäteriet (projection: 7.5 gon V 0:-15). If you have more than one projections using the same ellipsoid, the ellipsoid values can be put in a class of their own:

#include <iostream>
#include "gausskruger.h"

class GRS80 : public gausskruger::Projection
{
public:
    double flattening() { return 1 / 298.257222101; }
    double equatorialRadius() { return 6378137.0; }
};

class RT90_75_gon_V : public GRS80
{
public:
    double centralMeridian() { return 11 + 18.375 / 60.0; }
    double scale() { return 1.000006; }
    double falseNorthing() { return -667.282; }
    double falseEasting() { return 1500025.141; }
};

int main(int argc, char* argv[])
{
    RT90_75_gon_V projection;
    double lat, lon, northing, easting;
    lat = 67 + 52.654 / 60;
    lon = 21 + 3.615 / 60;
    projection.geodeticToGrid(lat, lon, northing, easting);
    std::cout.setf(std::ios::fixed);
    std::cout.precision(3);
    std::cout << "Northing: " << northing << "\nEasting: " << easting << std::endl;
    return 0;
}

Command line tool

First build the tool:

$ make cli

Example of direct transformation from SWEREF 99 to RT90 (same values as from the library usage example):

$ ./gausskruger --invflattening 298.257222101 --radius 6378137 --meridian 11.30625 \
                --scale 1.000006 --falsenorthing -667.282 --falseeasting 1500025.141 \
                67.877566667 21.06025
Northing: 7563929.530
Easting: 1908686.715

To see all options, run the tool without options or with --help:

$ ./gausskruger --help
Usage: gausskruger <projection> [options] latitude longitude
       gausskruger <projection> [options] -r northing easting

Projection parameters (mandatory):
  -i [ --invflattening ] arg inverse flattening of the ellipsoid
  -a [ --radius ] arg        equatorial radius, a.k.a. semi-major axis of the
                             ellipsoid
  -m [ --meridian ] arg      longitude of the central meridian
  -s [ --scale ] arg         scale factor along the central meridian
  -n [ --falsenorthing ] arg false northing
  -e [ --falseeasting ] arg  false easting

Options:
  -h [ --help ]              print this help
  -d [ --decimals ] arg (=3) number of decimals
  -r [ --reverse ]           reverse transformation (grid to geodetic), default
                             is geodetic to grid

Tests

To verify the calculations, tests have been implemented to check the reference points provided by Lantmäteriet. The following documents have been used:

  • Kontrollpunkter för SWEREF 99 TM
  • Kontrollpunkter för de lokala SWEREF 99-zonerna
  • Parametrar till approximativa transformationssamband för direktprojektion mellan SWEREF 99 och RT 90
  • Kontrollpunkter RT90 ↔ SWEREF 99

To run the tests, execute the following:

$ make test
$ ./test_reference_points
Running 101 test cases...

*** No errors detected

License

gauss-kruger-cpp is licensed under the Boost Software License 1.0.