Three-Dimensional Coordinate Systems

Coordinate systems to specify the locations on the surface of the Earth have been used for centuries. In western geodesy the Equator, the Tropics of Cancer and Capricorn, and then lines of latitude and longitude were used to locate positions on the Earth. Eastern cartographers like Phei Hsiu used other rectangular grid systems as early as 270 AD.

The most commonly used coordinate system today is the geodetic system (latitude, longitude and height). The Prime Meridian and the Equator are the reference planes used to define latitude and longitude. The geodetic latitude of a point is the angle from the equatorial plane to the vertical direction of a line normal to the reference ellipsoid. The geodetic longitude of a point is the angle between a reference plane and a plane passing through the point, both planes being perpendicular to the equatorial plane. The geodetic height at a point is the distance from the reference ellipsoid to the point in a direction normal to the ellipsoid.

Earth-Centred, Earth-Fixed (ECEF) Cartesian (XYZ) coordinates are also used to define three-dimensional positions. These define three-dimensional positions with respect to the centre of mass of the reference ellipsoid. The Z-axis points towards the North Pole. The X-axis is defined by the intersection of the plane defined by the Prime Meridian and the equatorial plane. The Y-axis completes a right-handed orthogonal system by a plane 90° east of the X-axis and its intersection with the Equator.

Universal Transverse Mercator (UTM) coordinates define two dimensional, horizontal positions. UTM zone numbers designate 6° longitudinal strips extending from 80° South latitude to 84° North latitude. UTM zone characters designate 8° zones extending north and south from the Equator. There are special UTM zones between 0° and 36° longitude above 72° latitude and a special zone 32 between 56° and 64° north latitude. Each zone has a central meridian. Eastings are measured from the central meridian (with a 500 km False Easting to ensure positive coordinates). Northings are measured from the Equator (with a 10,000 km False Northing for positions south of the Equator to ensure positive coordinates).

The Military Grid Reference System (MGRS) is an extension of the UTM system. UTM zone number and zone character are used to identify an area 6° in east-west extent and 8°in north-south extent. UTM zone number and designator are followed by 100 km square Easting and Northing identifiers.

The World Geographic Reference System (GEOREF) is used for aircraft navigation. It is based on latitude and longitude, with the globe being divided into twelve bands of latitude and twenty-four zones of longitude, each 15° in extent. These areas are further divided into 1° units identified by 15 characters.

Many nations have defined grid systems based on coordinates that cover their territory. Australia, Belgium, Great Britain, Finland, Ireland, Italy, The Netherlands, New Zealand and Sweden are examples of nations that have defined a National Grid System. For example, the British National Grid (BNG) is based on the National Grid System of England, administered by the British Ordnance Survey. The BNG has been based on a Transverse Mercator projection since the 1920s; the modern BNG is based on the Ordnance Survey of Great Britain Datum 1936 (Airy ellipsoid). The true origin of the system is at 49° north latitude and 2° west longitude whilst the false origin is 400 km west and 100 km north. Scale at the central meridian is 0.9996012717. The first BNG designator defines a 500 km square; the second defines a 100 km square. The remaining numeric characters define 10 km, 1 km, 100 m or 1 m Eastings and Northings