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

[Strebe at aol.com]

Mike,

I have a better idea of where you're coming from now. I see your need, more 
or less, though you seem more interested in precise coordinate inversion than I 
really see the need for. You don't see more maps on the projections you 
describe because not many people share your priorities.

Be careful not to get too cavalier about the other traits. It's very uncommon 
for a map projection to satisfy two metric criteria simultaneously. You may 
mean that you can get good "enough" distance measurements even wit your 
"graduated" equidistant, but good "enough" for you might not be good enough for 
someone else. You certainly can't get the best distance measurements AND the 
equidistant property simultaneously.

I don't think there's a lot more I have to say here. I'll be traveling for 
awhile, so I can't respond in any case.

Regards,
-- daan Strebe


In a message dated 8/1/07 07:30:51, mikeo2106 at msn.com writes:

> 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
> 
> 




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