[Proj] Graduated equidistant projections for convenient co-ordinate
mikeo2106 at msn.com
Wed Aug 1 10:28:44 EDT 2007
Thanks for taking the time to reply. When I added my most recent message
before this one, I just posted it without checking the list archives. If I'd
checked the archives first, my most recent message and this reply would have
been combined in one message.
Sure, a lot of people are interested in the relative areas of the zones of
spatial-distribution maps (which I call "data maps", for short), just as
some people want to easily measure where the zone boundaries are. The
azimuthal equal area data maps suit the former people, but certainly don't
suit the latter people. But the sinusoidal projection offers easy geographic
co-ordinate determinations and also has the equal-area property., and
doesnt misrepresent distances and directions so badly even on world maps,
when the map is interrupted.
Maybe I want to find out if a particular camping or hiking area is inside
the range zone of a certain species of animal or tree. The areas of those
range-zones could be important to a biologist or conservation manager, but
not to the person who just wants to know what species theyre likely to run
Sure, the boundaries arent really precise, but, as I was saying, why
increase the uncertainty by adding position-guessing error?
The data maps Im referring to include all the spatial distribution maps in
atlases, and the species range maps in nature guidebooks.
I didnt mean the tropical, temperate and arctic zones so much as the finer
divisions that tell the particular kind of forest, according to the species
of trees found there. But also of interest are temperature and rainfall
distributions with relatively fine divisions. And population distributions,
I dont run into data maps of regions smaller than a U.S. state, or a
country, but Id be interested in them if I found them.
Some map projections can offer ease of determining geographic co-ordinates,
and still offer one or more of the other properties that you listed. The
equal area property of the sinusoidal is one example. The good route
distances on local projections such as an equidistant conic, and the
accurately calculable route distances and accurate directions on conformal
conic maps are other examples. Someone could calculate route distances as
accurately as they want to on a Mercator map too, of course. Though latitude
determinations arent as easy on those conformal projections as the are on
an equidistant projection, theyre a lot easier than theyd be on an
azimuthal equal area projection (with unspecified center) or a polyconic or
a Chamberlain trimetric.
Though the graduated equidistant projections fall short of conformality,
they approximate it to some degree. To the extent that they do, route
distances can be calculated accurately and directions are accurate.
As for the relative importance of those different kinds of measurements, it
would be nice if the data map could double as a hiking map that gives
usefully accurate route distances and directions. But if the data map
doesnt offer those properties, then the USGS sells maps that do. So I dont
demand those other properties from a data map, even though it could be
convenient to have them in the same map. One thing that I do expect from a
data map: I expect it to tell me where those zone boundaries are. Then there
are other maps that can give me any route distances and any directions that
I need. But if the date map _doesnt_ give me that information (without
prohibitively much calculation work), no other map is going to.
Of course great-circle or loxodrome directions and distances can be
calculated from the geographical co-ordinates of the relevant points.
Yes, what Im talking about is the need for easy and accurate conversion
from map co-ordinates to geographic co-ordinates. It doesnt always have to
be either/or, since some projections combine properties. But, when the
different goals conflict, I ask that the data map do the one thing that no
other map will do for me--tell me easily where its zone boundaries are.
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