Each GRASS location is based on a specific projection and coordinate system defined in the location's PROJ_INFO file in the PERMANENT mapset. Projection conversions for vector data are thus performed by translating vector data from one location into another.
The v.proj module copies GRASS binary vector files between locations, translating the dig and dig_att files and copying the dig_cats file from the current (source) location and mapset to the target location and mapset (which you must also own). The program performs the transformation based on the PROJ_INFO data in the source and target locations.
The v.transform module transforms ASCII vector data in dig_ascii and associated dig_att files between coordinate systems based on a set of control points stored in a points file. Each control point record in the points file has four space- or tab-delimited fields specifying the X and Y (or easting and northing) coordinates in the source location followed by the point's equivalent coordinates in the target location. This control points file can be located anywhere in your directory structure.
v.transform calculates a transformation equation from these control points, and reports residual transformation errors. Acceptable errors depend on map scale: shoot for errors of 3 meters or less at 1:24,000 scale. If the errors are low enough, tell v.transform to proceed with the conversion. Then run r.support on the new map in the target location.
v.transform can be used for geo-referencing raw data in arbitrary coordinates generated from a digitizer or scanner, typically translating these from the imagery location to a real-world location.
Tools for calculating coordinate conversions:
m.proj calculates conversions between supported coordinate systems listed in the /etc/projections file in $GISBASE. It does not actually transform GRASS files. You can enter input coordinates interactively from the keyboard, or redirect them from a text file.
m.region.ll translates UTM coordinates in the current region into lat-long. You must specify the spheroid. If you run m.region.ll help GRASS will print a list of supported spheroids. The 1927 North American Datum (NAD27) is based on the Clarke 1866 spheroid ("clark66"); the 1983 North American Datum (NAD83) is based on the 1980 Geodetic Reference System spheroid ("grs80").
m.ll2u and m.u2ll calculate UTM/lat-long conversions for specified points. The reference manual (or g.manual) entry for m.ll2u contains a brief discussion of spheroids.
m.datum.shift calculates datum and spheroid conversions for a specified point. You have to specify the input lat-long coordinates and spheroid, the output spheroid and appropriate X, Y and Z shift values.