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 A very short introduction to Coordinate Reference Systems
31.12.2000
"There exist various coordinate reference systems in which a geographic location may be described mathematically by coordinates. In each system, the position gets its own coordinate  values. These values differ in a numerical sense, but represent the same geographic position.
When collecting data stored in different coordinate reference systems, each definition has to be known together with its geometric relationship to a standard system. Only then, it is possible to transfer all data into a standard coordinate reference system."
Stefan A. Voser
Fig. 1: From the earth surface to the plane of a map projection
The main coordinate reference systems for describing a geographic position mathematically are geodetic reference systems and map projections (Fig. 1).
Geodetic reference systems are used for describing the figure of the Earth and positions on it: ellipsoids (and the sphere) are used for describing the horizontal position, whereas geoids are the gravity related model for referencing the elevation. Geodetic reference systems have a datum, describing the position and orientation of the model in relation to the Earth and its surface.
Map projections are used to map the curved surface of an ellipsoid or a sphere to a plane. They have various characteristics, e.g. mathematical properties as different metric deformations, or they are validated for specific geographical extent etc.
Not considering the correct definition of the systems together with their relations may effort positional errors of hundreds of meters or more.
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