An integral part of all spatial data is the coordinate reference system (CRS), which is used to define meaningful distances between data points irrespective of their values. Distances become meaningful as soon as the origin of a particular reference system and its units are known. The origin of a CRS may lie at Earth’s gravity center or at some other arbitrarily defined location. The units of a CRS can be meters, kilometers, degrees or some other arbitrarily defined variables.
In practice, a CRS is used to represent vector or raster data in some geographical space, e.g. on Earth. Unfortunately, Earth is 3-dimensional (at least) and most media for representing space is 2-dimensional or planar (like paper and computer screens). This causes a lot of trouble because it makes a 3D to 2D transformation or projection necessary.
A geographic CRS is used to identify any location on Earth with two coordinates, namely latitude and longitude. Latitude describes the angular distance from the Equatorial plane based on a 3-dimensional spherical or ellipsoidal model of the Earth. Longitude describes the angular distance from the Prime Meridian plane in Greenwich, UK. A projected CRS is based on calculated 2-dimensional Cartesian coordinates, which are linked to real 3-dimensional locations on Earth by a mathematical model.
CRSs and projections in R
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