# Gauss-Krüger

## Description

Also known as Transverse Mercator, this projection is similar to the Mercator except that the cylinder is longitudinal along a meridian instead of the equator. The result is a conformal projection that does not maintain true directions. The central meridian is placed on the region to be highlighted. This centering minimizes distortion of all properties in that region. This projection is best suited for land masses that stretch north–south. The Gauss–Krüger (GK) coordinate system is based on the Gauss–Krüger projection.

## Projection method

Cylindrical projection with central meridian placed in a particular region.

## Lines of contact

Any single meridian for the tangent projection. For the secant projection, two parallel lines equidistant from the central meridian.

## Linear graticules

The equator and the central meridian.

## Properties

### Shape

Conformal. Small shapes are maintained. Shapes of larger regions are increasingly distorted away from the central meridian.

### Area

Distortion increases with distance from the central meridian.

### Direction

Local angles are accurate everywhere.

### Distance

Accurate scale along the central meridian if the scale factor is 1.0. If it is less than 1.0, there are two straight lines with accurate scale equidistant from and on each side of the central meridian.

## Limitations

Data on a spheroid or an ellipsoid cannot be projected beyond 90° from the central meridian. In fact, the extent on a spheroid or ellipsoid should be limited to 10 to 12° on both sides of the central meridian. Beyond that range, data projected may not project back to the same position. Data on a sphere does not have these limitations.

A new implementation called Transverse_Mercator_complex has been added to the Projection Engine which is available in ArcGIS desktop. It accurately projects to and from Transverse Mercator up to 80° from the central meridian. Because of the more complex mathematics involved, performance is affected.

## Uses and applications

Gauss–Krüger coordinate system. Gauss–Krüger divides the world into zones six degrees wide. Each zone has a scale factor of 1.0 and a false easting of 500,000 meters. The central meridian of zone 1 is at 3° E. Some places also add the zone number times one million to the 500,000 false easting value. GK zone 5 could have a false easting value of 500,000 or 5,500,000 meters. Three degree Gauss–Krüger zones exist also.

The UTM system is similar. The scale factor is 0.9996, and the central meridian of UTM zone 1 is at 177° W. The false easting value is 500,000 meters, and southern hemisphere zones also have a false northing of 10,000,000.

## Parameters

### Desktop

- False Easting
- False Northing
- Central Meridian
- Scale factor
- Latitude of origin