Easting and northing

In geodesy left-handed Cartesian coordinate systems are used. The x-axis (abscissa ) is regarded as the major axis, the y-axis (ordinate) obtained by rotating the x-axis by 100 gon (90 °) in a clockwise direction to the origin.

The x- axis points in the maps and plans usually up the y-axis to the right. At the national coordinate shows the x - axis to the north and the y- axis to the east. In comparison with right-handed Cartesian coordinate system of the mathematics, the x and y axes are thus reversed. The " geodesic positive " direction of rotation is clockwise and not like the " mathematically positive " counterclockwise.

The height ( also called applicate) as a third coordinate was - if at all - isolated long determined and verified by the position coordinates. Because of this separation of position and height, there was no need for three-dimensional calculation. Win in the extent, however, as well as in three-dimensional space geodesy references in importance, for example, by satellite positioning, so does the importance of three-dimensional coordinate systems.

Local coordinates

In local coordinate systems, that is, coordinate systems, which are (for now) not connected to a national reference system, the x -axis and the zero point can be appropriately selected. You can for example be the main axis of a structure or a polygon side and not have to show to the north. The y -axis is from the axis to the right. To avoid negative positive coordinate values ​​can be added to the coordinates, which is shifted to the origin. When measuring lines in Orthogonalverfahren positive ordinates mean that a point lies to the right of the Messsungslinie, points with negative ordinates on the left.

National coordinate

Coordinate origin

Is for the longitude of the fundamental point or, correspondingly, the central meridian of a transverse Mercator projection to place a coordinate value 0 arbitrarily fixed, depending on the extent of the imaged area as well as other practical considerations, a coordinate value ( "false easting ", see adjacent figure). Thus one obtains for each displayable point a positive " right value" ( y- value ). As with the north-south direction ( " high value " x - value ) will proceed accordingly, resulting usually a restriction on the first quadrant of the coordinate system, ie Although all quadrants are defined, practical uses but only coordinates of the first quadrant.

Right value (y - value )

Right value is referred to as a plane in Cartesian coordinate systems, the geographic distance between a coordinate of the (in this case vertical ) abscissa or x -axis. The legal value thus indicates the distance to the nearest central meridian and thus corresponds to the y- value, or the English " easting ".

For better handling in practice to avoid negative legal values ​​( for areas west of the abscissa and the reference meridian ) by instead of zero (ie, the central meridian ) randomly select a defined legal value sets (referred to as "false easting " in the English language, see above).

For example, the origin of the Swiss National Survey was shifted by 600 km to the west in the area of Bordeaux, to prevent any confusion of easting and northing value: coordinate values ​​below 400,000 m must be high values ​​there, Higher values ​​are always right values ​​so that no order of the coordinate components to define needs and permutations can be detected based on the values ​​. The Finnish YKJ system shifts the coordinate origin even by 3,500 km to the west in order to obtain horizontal and vertical always 7-digit coordinates. A false easting of 500 km for the central meridian as in the UTM coordinate system ensures that all valid ranges of values ​​of the right value ( 6 digits) holds 100000-900000.

Example, in the Gauss -Krüger system (with 500 km false easting ). R 4541238 R shows that it is the right value. The first number ( in this case 4), the code for each longitude so dar. here for the central meridian 12 ° E (4.3 = 12). The remaining numbers now show in meters, how far the point is away from the central meridian, after having deducted the 500 km. The desired line ( only with an associated high value results in a point) thus lies 41.238 km east of longitude 12 ° E ( or Zone 4)

High value ( x value )

A high value of the measured distance in the north direction of a coordinate of the base point to its horizontally extending base line of the coordinate system is referred to (here the y -axis). The term high value thus corresponds to the x value or the English " northing ", where by appropriately selected positions of the y- axis (eg for Europe on the equator ) is also always positive high values ​​can be achieved.

Easting and northing value form the two-dimensional coordinates of a point.

Applications

Due to the spherical shape of the Earth Cartesian coordinate systems can only depict areas limited in size and with virtually no distortion ( isometrically ). They went from a local historical fundamentals point trigonometric survey of land and were stretched along a central vertical (longitude zero, the central meridian ), which typically but not necessarily the meridian of the fundamental point corresponded. Modern coordinate systems be used as reference or central meridian longitudes divisible by 3.

Practical applications of Cartesian coordinate systems in geodesy are

  • Gauss -Krüger coordinate systems
  • The UTM coordinate system
  • The Austrian Federal signaling network
  • The Swiss coordinates
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