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4 Coordinate systems

Having projected the globe or a part of it on a plane, a coordinate system must be inserted in order to place 2 or 3 dimensional sites exactly on the map. In general, global and 2 dimensional and/or 3 dimensional coordinate systems are to be differentiated.

1 Global coordinate systems

Longitude-Latitude: The most frequently used global system is that of the longitude, latitude, and of the height (here: it concerns no projection). The reference planes are the 0 meridian and the equator. The earth is therefore divided into 180 longitudes from Greenwich to the East and West. Beginning at the equator, the earth is also divided into 90 latitudes to the South and North. The height is measured at the geocenter but accordingly definition differences are still existing. The units of the system can be specified in the sexagesimal- (Degree:Minutes:Seconds, letter index to the orientation) or decimal system (pos./neg. degree with decimal places).

2 2 and 3 dimensional coordinate systems

In order to specify sites numerically on a map projection, rectangular (cartesian) coordinates are used - where the positive y-values are pointed to the East and the positive x-values are pointed to the North. The zero point is differently defined in each system - in GRASS usually in the left edge below. In contrast to geographical and geocentric coordinates sites are only available for one defined illustration range (e.g. meridian stripes). Numerous coordinate systems are applied internationally. Besides different zero points and dimension units different ellipsoids and projections are chosen as basis. This results in the fact that a transformation is mostly only possible via a complex calculating operation.
In GRASS several modules are available for this purpose (r.proj and v.proj). Now, we briefly want to introduce theoretical examples of the Gauß-Krüger and UTM coordinate systems, which are used in Germany.

Gauß-Krüger coordinate system

This meridian stripe system has been established in Germany in 1927. The Bessel ellipsoid is the chosen land survey datum, the transverse mercator projection is the projection and potsdam is the datum. The coordinates refer to one meridian stripe each, whereas the longitudes 6^, 9^, 12^ and 15^ as main meridians (x-axis) are valid in Germany. The distortion can be reduced to a maximum of 12 cm per kilometer at the outer meridian stripes because a diagonal axial mercator projection is conducted at each single meridian stripe. The extent complies to 100 km in each direction of the main meridian. Thus, an overlapping of the individual meridian stripe systems of approx. 23 km occurs. The northings on the main meridian are seen as the distance from the equator. In order to avoid negative values with the easting the value +500000 m is adopted for the main meridian. Based on this the distance in meters between a given point and the main meridian can be calculated by reducing or adding 500000 from the easting value. A number derived by the decimal degree of the main meridian divided by 3 is added at first order.
Northing is always calculated as distance from the equator.

Lüneburg lies e.g. in the system of the 9th longitude on 3593000/5902000 (easting/northing) and in the system of the 12th longitude on 4392753/5902298 (easting/northing).

UTM coordinate system

The UTM System (Universal Transverse Mercator) is currently based on the WGS84 ellipsoid. The earth is covered by 60 meridian stripes between 84^ northern latitude and 80^ southern latitude. These stripes are 6 longitudes wide, each. An intersection cylinder is used for the projection in order to avoid distortions of the longitudes at the border meridians. Thus, the central meridian is not equidistant anymore but shows a diminution factor of 0,9996. At Gauß-Krüger the northing is measured in kilometer as the distance of the point from the equator. On the contrary, 10000 km are added on the southern hemisphere in order to avoid negative values. The distance from the central meridian, which has the values 500km like at Gauß-Krüger is defined by the x-values. The appropriate coordinates are indicated with E (East) and N (North). The central meridians can be found at 3^, 9^, 15^ and so on in eastern and/or western longitude. The zones are divided into 8 latitude stripes from the South pole to the North Pole and they are indicated with letters. This system is used for military maps of the United States and of the NATO. According to the international usability of the UTM coordinate system also Germany and/or Europe endeavor the introduction of this coordinate system.