The particular projection chosen depends on the purpose of the project, and the size, shape and location of the area of interest. For example, normal cylindrical projections are good for maps which are of greater extent east-west than north-south and in equatorial regions, while conic projections are better in mid-latitudes; transverse cylindrical projections are used for maps which are of greater extent north-south than east-west; azimuthal projections are used for polar regions. Oblique versions of any of these may also be used. Conformal projections preserve angular relationships, and better preserve arc-length, while equal-area projections are more appropriate for statistical studies and work in which the amount of material is important.
Projections are defined by precise mathematical relations, so the method of projecting coordinates from a geographic reference frame (latitude-longitude) into a projected cartesian reference frame (eg metres) is governed by these equations. Inverse projections can also be achieved. The public-domain Unix software package PROJ.4  has been designed to perform these transformations, and the user's manual contains a detailed description of over 100 useful projections. This also includes a programmers library of the projection methods to support other software development.
Thus, converting a vector map - in which objects are located with arbitrary spatial precision - from one projection into another is usually accomplished by a simple two-step process: first the location of all the points in the map are converted from the source through an inverse projection into latitude-longitude, and then through a forward projection into the target. (Of course the procedure will be one-step if either the source or target is in geographic coordinates.)
Converting a raster map, or image, between different projections, however, involves additional considerations. A raster may be considered to represent a sampling of a process at a regular, ordered set of locations. The set of locations that lie at the intersections of a cartesian grid in one projection will not, in general, coincide with the sample points in another projection. Thus, the conversion of raster maps involves an interpolation step in which the values of points at intermediate locations relative to the source grid are estimated.
In some cases it is convenient to do the conversion outside the package, prior to import or after export, using software such as PROJ.4's cs2cs . This is an easy method for converting an ASCII file containing a list of coordinate points, since there is no topology to be preserved and cs2cs can be used to process simple lists using a one-line command. The m.proj module provides a handy front end to cs2cs.
Vector maps is generally more complex, as parts of the data stored in the files will describe topology, and not just coordinates. In GRASS GIS the v.proj module is provided to reproject vector maps, transferring topology and attributes as well as node coordinates. This program uses the projection definition and parameters which are stored in the PROJ_INFO and PROJ_UNITS files in the PERMANENT mapset directory for every GRASS location.
r.proj converts a map to a new geographic projection. It reads a map from a different location, projects it and write it out to the current location. The projected data is resampled with one of four different methods: nearest neighbor, bilinear, bicubic iterpolation or lanczos.
The method=nearest method, which performs a nearest neighbor assignment, is the fastest of the three resampling methods. It is primarily used for categorical data such as a land use classification, since it will not change the values of the data cells. The method=bilinear method determines the new value of the cell based on a weighted distance average of the 4 surrounding cells in the input map. The method=bicubic method determines the new value of the cell based on a weighted distance average of the 16 surrounding cells in the input map. The method=lanzcos method determines the new value of the cell based on a weighted distance average of the 25 surrounding cells in the input map. Compared to bicubic, lanczos puts a higher weight on cells close to the center and a lower weight on cells away from the center, resulting in slightly better contrast.
The bilinear, bicubic and lanczos interpolation methods are most appropriate for continuous data and cause some smoothing. The amount of smoothing decreases from bilinear to bicubic to lanczos. These options should not be used with categorical data, since the cell values will be altered.
In the bilinear, bicubic and lanczos methods, if any of the surrounding cells used to interpolate the new cell value are null, the resulting cell will be null, even if the nearest cell is not null. This will cause some thinning along null borders, such as the coasts of land areas in a DEM. The bilinear_f, bicubic_f and lanczos_f interpolation methods can be used if thinning along null edges is not desired. These methods "fall back" to simpler interpolation methods along null borders. That is, from lanczos to bicubic to bilinear to nearest.
If nearest neighbor assignment is used, the output map has the same raster format as the input map. If any of the interpolations is used, the output map is written as floating point.
Note that, following normal GRASS conventions, the coverage and resolution of the resulting grid is set by the current region settings, which may be adjusted using g.region. The target raster will be relatively unbiased for all cases if its grid has a similar resolution to the source, so that the resampling/interpolation step is only a local operation. If the resolution is changed significantly, then the behaviour of the generalisation or refinement will depend on the model of the process being represented. This will be very different for categorical versus numerical data. Note that three methods for the local interpolation step are provided.
r.proj supports general datum transformations, making use of the PROJ.4 co-ordinate system translation library.
To avoid excessive time consumption when reprojecting a map the region and resolution of the target location should be set appropriately beforehand.
A simple way to do this is to check the projected bounds of the input map in the current location's projection using the -p flag. The -g flag reports the same thing, but in a form which can be directly cut and pasted into a g.region command. After setting the region in that way you might check the cell resolution with "g.region -p" then snap it to a regular grid with g.region's -a flag. E.g. g.region -a res=5 -p. Note that this is just a rough guide.
A more involved, but more accurate, way to do this is to generate a vector "box" map of the region in the source location using v.in.region -d. This "box" map is then reprojected into the target location with v.proj. Next the region in the target location is set to the extent of the new vector map with g.region along with the desired raster resolution (g.region -m can be used in Latitude/Longitude locations to measure the geodetic length of a pixel). r.proj is then run for the raster map the user wants to reproject. In this case a little preparation goes a long way.
When reprojecting whole-world maps the user should disable map-trimming with the -n flag. Trimming is not useful here because the module has the whole map in memory anyway. Besides that, world "edges" are hard (or impossible) to find in projections other than latitude-longitude so results may be odd with trimming.
# calculate where output map will be r.proj input=elevation location=ll_wgs84 mapset=user1 -p Source cols: 8162 Source rows: 12277 Local north: -4265502.30382993 Local south: -4473453.15255565 Local west: 14271663.19157564 Local east: 14409956.2693866 # same calculation, but in a form which can be cut and pasted into a g.region call r.proj input=elevation location=ll_wgs84 mapset=user1 -g n=-4265502.30382993 s=-4473453.15255565 w=14271663.19157564 e=14409956.2693866 rows=12277 cols=8162 g.region n=-4265502.30382993 s=-4473453.15255565 \ w=14271663.19157564 e=14409956.2693866 rows=12277 cols=8162 -p projection: 99 (Mercator) zone: 0 datum: wgs84 ellipsoid: wgs84 north: -4265502.30382993 south: -4473453.15255565 west: 14271663.19157564 east: 14409956.2693866 nsres: 16.93824621 ewres: 16.94352828 rows: 12277 cols: 8162 cells: 100204874 # round resolution to something cleaner g.region res=17 -a -p projection: 99 (Mercator) zone: 0 datum: wgs84 ellipsoid: wgs84 north: -4265487 south: -4473465 west: 14271653 east: 14409965 nsres: 17 ewres: 17 rows: 12234 cols: 8136 cells: 99535824 # finally, perform the reprojection r.proj input=elevation location=ll_wgs84 mapset=user1 memory=800
# In the source location, use v.in.region to generate a bounding box around the # region of interest: v.in.region -d output=bounds type=area # Now switch to the target location and import the vector bounding box # (you can run v.proj -l to get a list of vector maps in the source location): v.proj input=bounds location=source_location_name output=bounds_reprojected # Set the region in the target location with that of the newly-imported vector # bounds map, and align the resolution to the desired cell resolution of the # final, reprojected raster map: g.region vector=bounds_reprojected res=5 -a # Now reproject the raster into the target location r.proj input=elevation.dem output=elevation.dem.reproj \ location=source_location_name mapset=PERMANENT res=5 method=bicubic
The 'gdalwarp' and 'gdal_translate' utilities are available from the GDAL project.
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