Ao.Geodesy

The Ao.Geodesy namespace supports the calculation of distances and angles between places on earth, which is useful when working with GPS data.

Geographic Position

The GeographicPosition2 struct represents a place on the surface and consists of a pair of angles specifying latitude and longitude.

The GeographicPosition3 struct additionally specifies the altitude, i.e. the height above the surface.

var NewYork = new GeographicPosition2
{
    Latitude  = new Angle { Degrees =  40.712778 },
    Longitude = new Angle { Degrees = -74.006111 }
};

var Tokyo = new GeographicPosition2
{
    Latitude  = new Angle { Degrees =  35.689722 },
    Longitude = new Angle { Degrees = 139.692222 }
};

Spherical Earth

The SphericalEarth class represents earth in the shape of a perfect sphere, that is, every surface point is equidistant to the center.

var Radius = new Length { Kilometers = 6371 };

var Earth = new SphericalEarth(Radius);

Spheroidal Earth

The SpheroidalEarth class represents earth in the shape of a spheroid, where the poles are a little bit closer to the center than the equator.

var EquatorialRadius = new Length { Kilometers = 6378 };
var PolarRadius      = new Length { Kilometers = 6356 };

var Earth = new SpheroidalEarth(EquatorialRadius, PolarRadius);

Neither approach exactly matches reality, and which one to choose really depends on the required precision and other factors. The spheroidal shape is a little bit closer to Earth’s real shape, but calculations on a spherical shape are faster.

WGS84

The World Geodetic System 84 (WGS84) is a standard for geodetic applications and serves as the reference system for the Global Positioning System (GPS). It defines a set of fundamental parameters including both the polar and equatorial radius of the earth.

The static WGS84 class provides an object of the SphericalEarth and SpheroidalEarth classes, respectively, based on the standard’s radii.

var Earth = WGS84.SphericalEarth;

Great-Circle Distance

The earth classes contain methods to calculate the great-circle distance between two places, that is, the distance to travel on the surface from one place to another.

var D = Earth.GreatCircleDistance(NewYork, Tokyo);

Console.WriteLine("{0} km", Round.HalfUp(D.Kilometers));

10849 km

Euclidean Distance

Additionally, one can calculate the Euclidean distance, that is, the shortest distance connecting two places through earth’s interior. Sometimes, this is called the tunnel distance.

var D = Earth.EuclideanDistance(NewYork, Tokyo);

Console.WriteLine("{0} km", Round.HalfUp(D.Kilometers));

9585 km

Bearing

Finally, the earth classes support the calculation of the initial bearing from one place to another, that is, the direction with respect to true north at the starting point, when travelling along a great-circle path to the destination.

var B = Earth.Bearing(NewYork, Tokyo);

Console.WriteLine("{0}°", Round.HalfUp(B.Degrees));

333°

The method returns an angle in \([0°, 360°)\), which can be mapped to a compass direction.

Bearing	Direction
0°	North
90°	East
180°	South
270°	West