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Jeodezi

Jeodezi is Dart version of Jeodezi (which is Kotlin version) which is based of Chris Veness's amazing work Geodesy Functions. Geodesy Functions is written in JavaScript and contains dozens of functions to make calculations about:

  • Geodesic calculations (distances, bearings, etc) covering both spherical earth and ellipsoidal earth models, and both trigonometry-based and vector-based approaches.
  • Ellipsoidal-earth coordinate systems covering both historical datums and modern terrestrial reference frames (TRFs).
  • Mapping functions including UTM/MGRS and UK OS Grid References.

Quick Links

Installation

Run the code below at terminal

dart pub add jeodezi

Or add the code below to your pubspec.yaml

dependencies:
    jeodezi: ^latest_version

Usage

Great Circle Calculations

Distance

To calculate distance between two geographical coordinate, distance method can be used. This method will calculate the distance between two points with Haversine formula. The result will be great circle distance in kilometers.

final istCoordinates = Coordinate(41.28111111, 28.75333333); // The coordinates of Istanbul Airport
final jfkCoordinates = Coordinate(40.63980103, -73.77890015); // The coordinates of New York JFK Airport
final greatCircle = GreatCircle();
final distance = greatCircle.distance(istCoordinates, jfkCoordinates);

If you want to get distance in nautical miles you can use distanceInNm method with the same parameters

Bearing

This method is for the initial bearing (sometimes referred to as forward azimuth) which if followed in a straight line along a great-circle arc will take you from the start point to the end point. Bearing is in degrees 0° to 360°

final istCoordinates = Coordinate(41.28111111, 28.75333333); // The coordinates of Istanbul Airport
final jfkCoordinates = Coordinate(40.63980103, -73.77890015); // The coordinates of New York JFK Airport
final greatCircle = GreatCircle();
final bearing = greatCircle.bearing(istCoordinates, jfkCoordinates);

Midpoint

This method calculates the midpoint between startPoint and endPoint on the great circle. Result type is Coordinate

final istCoordinates = Coordinate(41.28111111, 28.75333333); // The coordinates of Istanbul Airport
final jfkCoordinates = Coordinate(40.63980103, -73.77890015); // The coordinates of New York JFK Airport
final greatCircle = GreatCircle();
final midpoint = greatCircle.midpoint(istCoordinates, jfkCoordinates);

Destination

This method calculates the destination point and final bearing travelling along a (shortest distance) great circle arc for a given start point, initial bearing and distance. Result type is Coordinate

final istCoordinates = Coordinate(41.28111111, 28.75333333); // The coordinates of Istanbul Airport
final jfkCoordinates = Coordinate(40.63980103, -73.77890015); // The coordinates of New York JFK Airport
final greatCircle = GreatCircle();
final bearing = greatCircle.bearing(istCoordinates, jfkCoordinates);
final distance = 1000; // km
final destination = greatCircle.destination(istCoordinates, distance, bearing); // The coordinates of point which is at 1000th km great circle between Istanbul Airport and JFK Airport

Intermediate

This function returns the point at given fraction between startPoint and endPoint

final istCoordinates = Coordinate(41.28111111, 28.75333333); // The coordinates of Istanbul Airport
final jfkCoordinates = Coordinate(40.63980103, -73.77890015); // The coordinates of New York JFK Airport
final fraction = 0.25;
final intermediate = greatCircle.intermediate(istCoordinates, jfkCoordinates, fraction);

Intersection

This function returns the point of intersection of two paths which one starts from firstPoint with firstBearing and the other one starts from secondPoint with secondBearing

final istCoordinates = Coordinate(41.28111111, 28.75333333); // The coordinates of Istanbul Airport
final fcoCoordinates = Coordinate(41.8002778,12.2388889); // The coordinates of Roma Fiumicino Airport
final bearingFromIstanbulToWest = 270.0;
final bearingFromRomeToNorthEast = 45.0;
final intersection = greatCircle.intersection(istCoordinates, bearingFromIstanbulToWest, fcoCoordinates, bearingFromRomeToNorthEast);

Cross Track

This function returns distance from currentPoint to great circle between startPoint and endPoint

final istCoordinates = Coordinate(41.28111111, 28.75333333); // The coordinates of Istanbul Airport
final jfkCoordinates = Coordinate(40.63980103, -73.77890015); // The coordinates of New York JFK Airport
final fcoCoordinates = Coordinate(41.8002778,12.2388889); // The coordinates of Roma Fiumicino Airport
final crossTrackDistanceInKm = greatCircle.crossTrackDistance(fcoCoordinates, istCoordinates, jfkCoordinates);

Along Track

This function returns how far currentPoint is along a path from from startPoint, heading towards endPoint. That is, if a perpendicular is drawn from currentPoint point to the (great circle) path, the along-track distance is the distance from the start point to where the perpendicular crosses the path.

final istCoordinates = Coordinate(41.28111111, 28.75333333); // The coordinates of Istanbul Airport
final jfkCoordinates = Coordinate(40.63980103, -73.77890015); // The coordinates of New York JFK Airport
final fcoCoordinates = Coordinate(41.8002778,12.2388889); // The coordinates of Roma Fiumicino Airport
final alongTrackDistanceTo = greatCircle.alongTrackDistanceTo(fcoCoordinates, istCoordinates, jfkCoordinates);

Max Latitudes

This function returns maximum latitude reached when travelling on a great circle on given bearing from startPoint point (‘Clairaut’s formula’). Negate the result for the minimum latitude (in the southern hemisphere)

final istCoordinates = Coordinate(41.28111111, 28.75333333); // The coordinates of Istanbul Airport
final bearingFromIstanbulToWest = 270.0;
final maxLatitude = greatCircle.maxLatitude(istCoordinates, bearingFromIstanbulToWest);

Crossing Parallels

This function returns the pair of meridians at which a great circle defined by two points crosses the given latitude. If the great circle doesn't reach the given latitude, null is returned.

final istCoordinates = Coordinate(41.28111111, 28.75333333); // The coordinates of Istanbul Airport
final jfkCoordinates = Coordinate(40.63980103, -73.77890015); // The coordinates of New York JFK Airport
final latitude = 60.0; // means 60 degrees north
final crossingParallels = greatCircle.crossingParallels(istCoordinates, jfkCoordinates, latitude);

Example

You can find an example application which uses Jeodezi library in the repo.

Contributing

Jeodezi is a work in progress. Currently only a little part of functions of Geodesy Functions are ported to Dart. There are lots to do and your contributions are most welcome. Feel free to fork the repo and submit Pull Request's. You can help about

  • Unit testing
  • Better example
  • Code refactoring and optimization
  • Issues/bugs

License

Jeodezi is released under the MIT License.