Coordinate reference systems (coordinate systems with a datum). The following is adapted from OpenGIS® Spatial Referencing by Coordinates (Topic 2) specification.

A coordinate reference system (CRS) consists of one coordinate system (CS) that is related to the earth or platform through one datum. The coordinate system is composed of a set of coordinate axes with specified units of measure. This concept implies the mathematical rules that define how coordinate values are calculated from distances, angles and other geometric elements and vice versa.

A datum specifies the relationship of a coordinate system to the object, thus ensuring that the abstract mathematical concept “coordinate system” can be applied to the practical problem of describing positions of features on or near the earth's surface by means of coordinates. The object will generally, but not necessarily, be the earth; for certain coordinate reference systems, the object may be a moving platform.

CoordinateReferenceSystem instances and their components shall be immutable. For CRS defined on moving platforms such as cars, ships, aircraft and spacecraft, transformation to an earth-fixed coordinate reference system may include a time element. Time-variability of coordinate reference systems may be covered by creating different CoordinateReferenceSystem instances, each with a different datum, for consecutive epochs. The date of realization of the datum shall then be included in its definition. Furthermore, it is recommended that the date of realization be included in the names of those datums and coordinate reference systems.

Sub-types of coordinate reference system

Geodetic survey practice usually divides coordinate reference systems into a number of sub-types. The common classification criterion for sub-typing of coordinate reference systems can be described as the way in which they deal with earth curvature. This has a direct effect on the portion of the earth's surface that can be covered by that type of CRS with an acceptable degree of error. Thus the following principal sub-types of coordinate reference system are distinguished:

Geocentric: Type of coordinate reference system that deals with the earth's curvature by taking the 3D spatial view, which obviates the need to model the earth's curvature. The origin of a geocentric CRS is at the approximate centre of mass of the earth.

Geographic: Type of coordinate reference system based on an ellipsoidal approximation of the geoid. This provides an accurate representation of the geometry of geographic features for a large portion of the earth's surface. Geographic coordinate reference systems can be 2D or 3D. A 2D Geographic CRS is used when positions of features are described on the surface of the reference ellipsoid; a 3D Geographic CRS is used when positions are described on, above or below the reference ellipsoid.

Projected: Type of coordinate reference system that is based on an approximation of the shape of the earth's surface by a plane. The distortion that is inherent to the approximation is carefully controlled and known. Distortion correction is commonly applied to calculated bearings and distances to produce values that are a close match to actual field values.

Engineering: Type of coordinate reference system that is that is used only in a contextually local sense. This sub-type is used to model two broad categories of local coordinate reference systems:

  • earth-fixed systems, applied to engineering activities on or near the surface of the earth;
  • coordinates on moving platforms such as road vehicles, vessels, aircraft or spacecraft.

Image: An Image CRS is an Engineering CRS applied to images. Image CRSs are treated as a separate sub-type because a separate user community exists for images with its own vocabulary. The definition of the associated Image Datum contains two data attributes not relevant for other datums and coordinate reference systems.

Vertical: Type of coordinate reference system used for the recording of heights or depths. Vertical CRSs make use of the direction of gravity to define the concept of height or depth, but its relationship with gravity may not be straightforward. By implication ellipsoidal heights (h) cannot be captured in a vertical CRS. Ellipsoidal heights cannot exist independently, but only as inseparable part of a 3D coordinate tuple defined in a geographic 3D coordinate reference system.

Temporal: Used for the recording of time in association with any of the listed spatial coordinate reference systems. Any CRS can be associate with a temporal CRS to form a spatio-temporal compound CRS. More than one temporal CRS may be included if these axes represent different time quantities.

In addition to the above principal sub-types, so called because they represent concepts generally known in geodetic practice, two more sub-types have been defined to permit modelling of certain relationships and constraints that exist between the principal sub-types.

Compound: The traditional separation of horizontal and vertical position has resulted in coordinate reference systems that are horizontal (2D) in nature and vertical (1D). It is established practice to combine the horizontal coordinates of a point with a height or depth from a different CRS. The coordinate reference system to which these 3D coordinates are referenced combines the separate horizontal and vertical coordinate reference systems of the horizontal and vertical coordinates. Such a CRS is called a compound CRS. It consists of an ordered sequence of the two or more single coordinate reference systems.

Derived: Some coordinate reference systems are defined by applying a coordinate conversion to another CRS. Such a CRS is called a derived CRS and the coordinate reference system it was derived from by applying the conversion is called the source or base CRS. A coordinate conversion is an arithmetic operation with zero or more parameters that have defined values. The base CRS and derived CRS have the same datum.