Projections and Coordinate Systems - Desktop GIS: Mapping the Planet with Open Source Tools - page 136

the answer back in to the proj command to see whether he gets his
original UTM coordinates:
$ proj +proj=utm +zone=6 +ellps=clrk66 +datum=NAD27 \
+units=m +no_defs
150d30'W 61d15'N

312244.49 6795460.41

Sure enough it worked. He could have specified the latitude and longi-
tude using decimal degrees (-150.5 61.25) and gotten the same result.
PROJ.4 also has a number of other options, including the ability to cus-
tomize the output format to your taste. You can see that PROJ.4 can be
useful for doing interactive transforms.

If you wanted to transform from a UTM projection to an Albers Equal
Area, you would have to do an inverse ( invproj ) to get the latitude and
longitude for the UTM point and then do a forward projection ( proj )
using the Albers parameters to get the final result. The cs2cs program
simplifies this by allowing you to specify both coordinate systems. Let's
convert our UTM point from the previous example to Alaska Albers
coordinates using cs2cs :
$ cs2cs +proj=utm +zone=6 +ellps=clrk66 +datum=NAD27 \
+units=m +to +proj=aea +lat_1=55 +lat_2=65 +lat_0=50 +lon_0=-154 \
+x_0=0 +y_0=0 +datum=NAD27 +units=m +no_defs
312244.49 6795460.41
187115.08 1257043.95 0.00

Now we have Albers coordinates 187115.08, 1257043.95 as a result of
our transformation. You are probably wondering what the 0.00 means.
This is height above (or below) the ellipsoid. Since both datums were
NAD27 and they are both based on the same ellipsoid, there is no dif-
ference. Let's do a datum shift to illustrate how it's done and compare
the results:
$ cs2cs +proj=utm +zone=6 +datum=NAD27 +units=m \
+to +proj=aea +lat_1=55 +lat_2=65 +lat_0=50 +lon_0=-154 +x_0=0 +y_0=0 \
+datum=NAD83 +units=m +no_defs
312244.49 6795460.41
186991.95 1256960.61 0.00

Here we see the result, which is a bit different from the NAD27 result.
The total shift in coordinates is approximately 184 meters. If you don't
believe it, break out your high-school math book and use the distance
formula (Pythagorean Theorem) to check the result.

If you want to transform a lot of points, you can provide the coordinates
to cs2cs from a file to do batch conversions. See the documentation for
cs2cs for details on the available options.