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Երկիր (Erkir) - a C++ library for geodesic and trigonometric calculations

Erkir (armenian: Երկիր, means Earth) - is inspired by and based on the great work of Chris Veness, the owner of the Geodesy functions project - provides a set of comprehensive API for geodesic and trigonometric calculations. I would call it a C++ port of JavaScript functions provided by the mentioned Chris Veness' project, however I designed the library to be more object oriented. Thus the code is organized a little bit differently, but the implementation itself is preserved.

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There are no special requirements and dependencies except C++11 compliant compiler. The class is tested with gcc 4.8.4 and MSVC 15.x (Visual Studio 2017). The library is written with pure STL without any third party dependencies. For more details see the CI badges (Travis CI & AppVeyor CI) above.


No installation required. Just incorporate header files from the include/ and source files from src/ directories in your project and compile them. All library classes are in erkir namespace.


The code is virtually split into three domains (namespaces) that represent spherical and ellipsoidal geodetic coordinates and cartesian (x/y/z) for geocentric ones: erkir::spherical, erkir::ellipsoidal and erkir::cartesian correspondingly. Spherical Earth model based calculations are accurate enough for most cases, however in order to gain more precise measurements use erkir::ellipsoidal classes.

erkir::spherical::Point class implements geodetic point on the basis of a spherical earth (ignoring ellipsoidal effects). It uses formulae to calculate distances between two points (using haversine formula), initial bearing from a point, final bearing to a point, etc.

erkir::ellipsoidal::Point class represents geodetic point based on ellipsoidal earth model. It includes ellipsoid parameters and datums for different coordinate systems, and methods for converting between them and to Cartesian coordinates.

erkir::Vector3d implements 3-d vector manipulation routines. With this class you can perform basic operations with the vectors, such as calculate dot (scalar) product of two vectors, multiply vectors, add and subtract them.

erkir::cartesian::Point implements ECEF (earth-centered earth-fixed) geocentric cartesian (x/y/z) coordinates.

Usage Examples:

#include "sphericalpoint.h"
#include "ellipsoidalpoint.h"

int main(int argc, char **argv)
  // Calculate great-circle distance between two points.
  erkir::spherical::Point p1{ 52.205, 0.119 };
  erkir::spherical::Point p2{ 48.857, 2.351 };
  auto d = p1.distanceTo(p2); // 404.3 km
  // Get destination point by given distance (shortest) and bearing from start point.
  erkir::spherical::Point p3{ 51.4778, -0.0015 };
  auto dest = p3.destinationPoint(7794.0, 300.7); // 51.5135°N, 000.0983°W
  // Convert a point from one coordinates system to another.
  erkir::ellipsoidal::Point pWGS84(51.4778, -0.0016, ellipsoidal::Datum::Type::WGS84);
  auto pOSGB = pWGS84.toDatum(ellipsoidal::Datum::Type::OSGB36); // 51.4778°N, 000.0000°E

  // Convert to Cartesian coordinates.
  auto cartesian = pWGS84.toCartesianPoint();

  // Convert Cartesian point to a geodetic one.
  auto geoPoint = cartesian->toGeoPoint();

  return 0;

For more usage examples please refer to the unit tests at /test/test.cpp file.

Building and Testing

There are unit tests. You can find them in the test/ directory. To run them you have to build and run the test application. For doing that you must invoke the following commands from the terminal, assuming that compiler and environment are already configured:

Linux (gcc)

cd test
g++ -std=c++11 -Isrc -Iinclude test.cpp -o test

or using CMake

mkdir build
cd build
cmake ..


cd test
cl /I..\src /I..\include /W4 /EHsc test.cpp /link /out:test.exe

or using CMake

mkdir build
cd build
cmake .. -G "NMake Makefiles"

Performance Tests

I measured performance (on Intel Core i5 series processor) for some spherical geodesy functions (Point class). I used similar approach as Chris Veness did in his tests, i.e. called functions for 5000 random points or pairs of points. And here are my results:

Function Avg. time/calculation (nanoseconds)
Distance (haversine) 162
Initial bearing 190
Destination point 227

of course timings are machine dependent

See Also