Coordinate Systems

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Coordinate Systems

Real object coordinates can be expressed in different systems. The main systems are:

Geographic Coordinate System

In a geographic coordinate system, latitude and longitude are used and are represented by two angles from the center of the earth:

Latitude = south to north +90 or 90N = north pole, -90 or 90S = south pole, and 0 is on the equator.
Longitude = east to west. 0 is in England.

An example of coordinates using the geographic: longitude and latitude with optional altitude is shown in Figure 1.2.

Figure 1.2 Geographic Coordinate System

In a geographic coordinate system the angular distance is expressed in degrees and minutes, for example, New York:

Latitude 40 Degrees 59'N
Longitude 73 Degrees 39'W

A geographic coordinate system is defined by:

The unit system of coordinates (angular unit and linear unit).
The prime meridian:

For example, the Greenwich meridian.

The horizontal datum:

A horizontal datum is used to represent the shape of the earth.
The datum is defined by an ellipsoid (the default is a sphere) and a translation of the ellipsoid (position of the ellipsoid relative to the center of the earth), see Figure 1.3:

Figure 1.3 Horizontal Datum

Geocentric Coordinate System

An example of coordinates using the geocentric: three-axis Cartesian system with the center of the earth as the origin is shown in Figure 1.4:

Figure 1.4 Geocentric Coordinate System

A three-axis Cartesian system is defined by:

Its origin, the center of the earth.
Its x-axis, which lies in the plane containing the equator and which is oriented towards the Greenwich meridian.
Its y-axis, which lies in the plane containing the equator and which is oriented towards the longitude 90 Degrees East of Greenwich.
Its z-axis, which corresponds to the polar axis and which is oriented northwards.

A geocentric coordinate system is defined by:

The unit system of coordinates (linear units) on the axes.
The horizontal datum.

Projected Coordinate System

A projected coordinate system is a representation of the earth on a 2-D surface. Units are attached to each axis of a coordinate system. For example, for geographic coordinates:

x- and y-coordinates expressed in degrees
z-coordinate expressed in meters

A kernel unit is defined for each type of unit.

Length in meters
Angles in radians

Coordinate systems are used to display maps and a map projection is used to reduce the dimensions to two. A projected coordinate system is defined by:

The associated geographic coordinate system
The projection
The unit system of projected coordinates

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