Gauss Map

Gauss is the most commonly used projection in the world; it is similar to a cylindrical inverse, but derives from an orthomorphic cylindrical equatorial projection, originally suggested by Lambert, and later generalized by Gauss (1777–1855) who referred it to the ellipsoid. During the last century, several scholars introduced some modifications and reports on it, such as Boaga for Italy and Krueger for Europe. The UTM system is based on this projection.

The Gauss representation is conformal. The transformed central meridian and equator are straight lines that become the axes of the planar reference system and are called East and North. The transformed meridians and parallels are families of perpendicular curves, symmetric with respect to the East and North axes.

In order to limit the linear distortions, it is necessary to represent an area that is subdivided into longitude bands, called zones. In the UTM system, the Earth has been divided into 60 zones, each 6◦ wide, numbered from 1 to 60 proceeding from West to East and starting from the Greenwichanti-meridian. The area that can be represented in a zone is a small portion of the Earth’s surface and thus it is necessary to join more zones in case wider areas need to be represented. This representation system is called poly cylindrical. Between two adjacent zones, there is always an area of overlap, in which the coordinates of both zones can be expressed.

Every zone is divided into 20 horizontal belts marked by letters and 8◦ wide (up to φ: 80◦).

Every zone has its own planar reference system, which is independent as the

central meridian changes from one zone to another.

Every zone has a false origin located 500 km East of the central meridian, in order to avoid negative coordinates, as at the equator the zone is about 666 km large, and the North coordinate originates at the equator

Every zone is divided into squares 100 km as a side, marked by pairs of letters.

Any point of the globe is bi-univocally determined by

• two numbers: zone;

• three letters: one for the belt, two for the square;

• eight consecutive numbers: four for the E and four for the N.

Source: Burrough P.A., 2000, Principles of Geographical Information Systems, Spatial Information Sys-temsandGeostatistics, ClaredonPress,Oxford,p. 306