Gauss–Krüger Projection

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Introduction

Gauss–Krüger projection is a map projection based on the Transverse Mercator projection, developed by the German geographers Carl Friedrich Gauss and Johann Heinrich Krüger. It is widely used for large-scale topographic maps and precision surveying, and is adopted as part of the national coordinate system by many countries, notably Germany, Russia, and China.

Projection Composition

Data based on the Gauss-Krüger projection are mainly provided in the following formats:

1. Plane Cartesian coordinates (X, Y)
2. Longitude and latitude corresponding to the reference ellipsoid (in degrees or radians)
3. EPSG code (for example, China’s three-dimensional zones are based on EPSG:4490 and divided by zones)

In addition, GIS software saves and exchanges data in the following formats:

1. Shapefile (.shp)
2. GeoTIFF (.tif)
3. GML (.gml)
4. CSV (including coordinates), etc.

Pros

1. High precision: Based on the transverse Mercator projection, it minimizes the deformation in the east-west direction and provides extremely high precision even in narrow longitude areas.
2. Divide regions by region: Set a projection origin for each region, and each region is divided into 3 degrees or 6 degrees to ensure the calculation accuracy in each region.
3. Already included in the national standard: Many national measurement standards in China use this projection method and are widely used by government departments and research institutes.
4. Clear coordinate calculation: The conversion formula from geographic coordinates (latitude and longitude) to plane rectangular coordinates has been formulated, and the program is easy to implement.

Cons

1. Inconvenient cross-zone conversion: Since the origins of each zone are different, coordinate conversion and adjustment need to be performed under the same coordinate system when processing cross-zone areas.
2. Poor international compatibility: Compared with WGS84 and UTM (Universal Transverse Mercator), it lacks international standardization, so additional conversion is required to share and integrate data with other countries.
3. Confusion in longitude zone settings: Since China has 3-degree and 6-degree zones, and there are differences in longitude zone settings in other countries, extra care needs to be taken when managing zone numbers and central meridians.

Application Scenario

The Gauss–Krüger projection is widely used in urban planning, land use, precision surveying, forest management, water resource surveys, and other tasks that require high-precision location information within a specific country or region. In China, it is the mainstream projection in areas such as cadastral surveying, administrative division mapping, and infrastructure design. It is also commonly used in local government geographic information systems (GIS) and CAD drawings.

Example

1. Gauss–Krüger projection centered on Greenwich.

2. Gauss–Krüger projection of the entire Earth’s surface with the central meridian as the prime meridian.

Related GIS Projections

Mercator Projection

Wagner Projection

Lambert Azimuthal Equal-Area Projection

Robinson Projection

References

1. https://pro.arcgis.com/en/pro-app/latest/help/mapping/properties/gauss-kruger.htm
2. https://en.wikipedia.org/wiki/Transverse_Mercator_projection
3. https://manifold.net/doc/radian/gauss-kruger_projection.htm