# GRASS Help System

Coordinate Systems and Projections

A map coordinate system is either a geographic coordinate system (like UTM or latitude/longitude) or an arbitrary coordinate system (like the x,y coordinate system initially assigned to imported satellite imagery) used to reference the locations of objects in a two-dimensional space.

A map projection describes the manner in which the spherical surface of the earth is represented on a two-dimensional surface. It attempts to minimize distortion in area, shape, distance, and direction.

All of the data stored beneath the same GRASS "location" directory must use the same map coordinate system and map projection. This means that latitude/longitude data, Universal Transverse Mercator data, State Plane coordinate system data, and unrectified (x,y) imagery data, should be stored under different GRASS "locations" and "mapsets". Often, one wishes to combine data that are available in different coordinate systems and/or different map projections. To do this, users must convert these data to a common map coordinate system and projection.

The commands listed below are useful to those importing and exporting data to and from GRASS. They can be used to perform map coordinate system and map projection conversions.

m.ll2u
m.u2ll
m.region.ll
r.mapcalc
v.transform

"m.ll2u" converts latitude/longitude (ll) map coordinates to Universal Transverse Mercator (UTM) map coordinates, while "mu2ll" performs the reverse operation. "m.region.ll" converts UTM data falling within the user's current geographic region to latitude/longitude map coordinates.

The user can select from any of the map projections whose ellipsoids of rotation (spheroids) are already known by GRASS when converting to/from latitude/longitude coordinates; the user can specify an ellipsoid other than those listed by adding its equatorial radius and either the polar radius, degree of flattening, or eccentricity squared to the ellipsoid parameter definition file stored in $GISBASE/etc/ellipse.table.

Refer to this file and to the manual entries for "m.ll2u", "m.u2ll", and "m.region.ll" for a description of these spheroids of rotation.

Satellite imagery data are generally made available in an x,y coordinate system. In order to analyze imagery data in combination with other GRASS data layers, it is necessary that all these data be rectified to the same map coordinate system and projection. Several GRASS programs are used to rectify imagery data.

i.points
i.rectify
i.rectify.blk

The user must run i.target to "target" the rectified image to another GRASS database with the new map coordinate system before running these programs. Read the section on Geometric Rectification under the Image Processing section for a more detailed description of the image rectification process.

"r.mapcalc" is a map calculator that allows the user to perform various mathematical functions on raster data layers. The paper "r.mapcalc: An Algebra for GIS and Image Processing" (Shapiro, 1990) describes ways in which "r.mapcalc" can be used to perform various mathematical functions on raster map layers.

"v.transform" transforms an ASCII vector map layer from one map coordinate system into another. It performs the transformation using a set of from 4 to 10 points known in both systems.

See also the references for: "Map Projections - A Working Manual" (Snyder, 1989), "The Department of Defense World Geodetic System 1972" (Seppelin, 1974).

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Automatically created on: Fri Oct 20 10:09:59 2006