[Proj] Graduated equidistant projections for convenient co-ordinate transformations

[Michael Ossipoff]

Daan--

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 
doesn’t 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 they’re likely to run 
into.

Sure, the boundaries aren’t really precise, but, as I was saying, why 
increase the uncertainty by adding position-guessing error?

The data maps I’m referring to include all the spatial distribution maps in 
atlases, and the species range maps in nature guidebooks.

I didn’t  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, 
etc.

I don’t run into data maps of  regions smaller than a U.S. state, or a 
country, but I’d 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 aren’t as easy on those conformal projections as the are on 
an equidistant projection, they’re a lot easier than they’d 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 
doesn’t offer those properties, then the USGS sells maps that do. So I don’t 
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 _doesn’t_ 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 I’m talking about is the need for easy and accurate conversion 
from map co-ordinates to geographic co-ordinates. It doesn’t 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.

Mike Ossipoff