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

strebe at aol.com strebe at aol.com
Mon Aug 6 08:37:58 EDT 2007


I am not here to crush your soul. You seem a good deal more knowledgeable and interested in map projections than most, which I'm happy to see and certainly want to encourage.

On the other hand, your jargon is idiosyncratic and your analysis of the issues surrounding your thesis seem to evolve as we talk. These make it hard for me to engage you in conversation. When a person wishes to announce that the world ought to be doing things differently, then it behooves the person to exercise due diligence. That includes a rigorous analysis and vocabulary of the domain. Without both, conversation gets distracted by the parties involved just trying to figure out what the other is saying.

Since I'm the only other one participating in this discussion I have to think everyone else is long bored of it. (It's also probably off-topic by some people's assessment.) I'm not going to address each of your points. As an illustration of talking past each other in your latest post:

You write:


2. When you said that it’s very uncommon for a map projection to satisfy two 
metric criteria simultaneously, I pointed out that the sinusoidal does, 
because it’s equal-area, and it gives accurate and easy directly-measured 
lat/long co-ordinates. Accurate directly-measured lat/long positions are a 
“metric criterion” no less than is equal-area. 


Equal-area is a rigorous concept. "Giving accurate and easy directly-measured lat/long coordinates" is not, and it is not a "metric criterion". You have performed no rigorous studies of this property of the sinusoidal, and neither has anyone else. I could easily claim some other projection is better than sinusoidal for "accurate and easy directly-measured lat/long coordinates", and then we'd be reduced to "Yuh huh!" "Nuh uh!". If, on the other hand, I were to claim the sinusoidal is not equal-area, you could trot out the rigorous definition of equal-area and clearly demonstrate that I am wrong.

So. How ought I engage your assertion in (2)? This assertion is peripheral to your thesis, so, to me, it's whack-a-mole digression. I've chosen to engage it here as an example of why this conversation is proving difficult for me. On the other hand, since you seem earnest, I haven't wanted to just say I'm done trying.

You have brought up azimuthal equal-area several times as an example of a projection not to use for the class of maps you're interested in. That's fine, I suppose, but something of a red herring, since I never mentioned it, much less defended it. In the first place, maps are often plotted on inappropriate projections, so it would not surprise me if you have stumbled onto such a thing. But more importantly, and back to your thesis, it's not clear to me how often the cartographer shares your priorities. You may want to think of a map as one that fits your notion of a "data map", but people may be using it for many other purposes as well.

If the only purpose for the map truly is to easily determine lat/long positions, you're best off with a plate carrée, regardless of how distorted it gets as you move away from the equator. As soon as you start making concessions to other uses, well, suddenly the waters muddy a lot.  There aren't any easy answers when you compromise because suddenly everyone interested in the map wants a different balance of compromises.

You started out claiming a "graduated equidistant" is the
answer. That's already a compromise away from the "easiest"
determination of lat/long. You've now evolved to an "interrupted
sinusoidal". That's about as muddy as it gets. Many projections could be argued to provide similar compromises, or a "better" balance of those compromises [better for whom?]. And, most glaringly, how many interruptions are there, and where are they? The more interruptions, the greater the accuracy... but the less usable for any purpose that spans an  interruption.

What, then, is your thesis?

A) There is a class of maps whose primary function is to allow people to easily determine geographic coordinate. Therefore the projection must be suited to that function alone.


B) The primary use of ground cover maps is an easy determination of geographic coordinates of the extents of the ground cover. Therefore these maps should be drawn on the projection that makes that determination easiest.


C) Ground cover maps serve several functions. The most important is an easy determination of geographic coordinate, but allowances must be made for other uses.


D) Something else.

If (A), "the" solution is plate carrée. If (B), the solution is plate carrée. If (C)... well... that would be a fine subject for a professional paper. It would have to include use cases; relative preponderances of those cases in the real world; identifying the compromises involved; identifying projections that address those compromises; and then analysis of how well each projection addresses each need. Presumably this would also include studies of how efficiently and accurately people can measure geographic coordinates on each projection.

If (D), then I am completely lost, and I must apologize for not following your arguments well.


-- daan Strebe



-----Original Message-----

From: Michael Ossipoff <mikeo2106 at msn.com>

To: strebe at aol.com; proj at lists.maptools.org

Sent: Sun, 5 Aug 2007 11:22 am

Subject: Re: Graduated equidistant projections for convenient co-ordinate transformations

In your postings, you’ve told why you consider accurate distances to be 
important, and you said, “You certainly can’t get the best distance 
measurements and the equidistant property simultaneously.” 


But, for conic, azimuthal and cylindrical maps, equal-area projections 
typically have about twice as much percentage scale variation as do 
equidistant projections or conformal projections. 


So your statement could be answered, “…but you certainly can get better 
distance measurements with equidistant projections than with equal-area 


You said that data maps should be equal-area, and that you want the most 
accurate directly-measured distances. You want two goals that are mutually 


In your most recent posting, you say: 


“Your post is quite long. I can't really get into a whack-a-mole game of 
responding to each of your points only to have several more spring up in 
their places.” 


Actually there were only a few “points” in my posting (some were 
considerately accompanied by clarification-examples), and each “point” was a 
direct answer to one of your main objections to what I had said. . 


1. I answered you statement that equidistant projections don’t give the best 
distances, where you were referring to distances measured directly from the 
map (No, they only give the best such distances when compared to those of 
equal-area and conformal projections). 


2. When you said that it’s very uncommon for a map projection to satisfy two 
metric criteria simultaneously, I pointed out that the sinusoidal does, 
because it’s equal-area, and it gives accurate and easy directly-measured 
lat/long co-ordinates. Accurate directly-measured lat/long positions are a 
“metric criterion” no less than is equal-area. 


3. When you kept complaining that the data map projections that I was 
suggesting don’t give the best directly-measured distances,  I pointed out 
that it isn’t reasonable to judge a data map by how good a navigational map 
it is. I pointed out that it’s difficult to find a scenario in which someone 
needs accurate directly-measured distances from a nature guidebook range-map 
or a rainfall-distribution map in an atlas. No one wants or needs accurate 
directly-measured distances from those special purpose maps. Their only 
purpose, their whole point, is to show where their zones are. 


But, aside from that, an equidistant conic does very well by directly 
measured distances. Equidistant conic was one of my data map suggestions, 
though it wasn’t my first choice. 


4. Lastly, I said that the sinusoidal would please all data-map users, by 
easily, accurately and directly giving the two kinds of information 
(position and area) that people actually need, want and use from a data map. 


Those were my “points”. I said them because I wanted to, not to get a reply. 
 Nor do I care _why_ you don’t reply to them. But it isn’t because I threw 
out a careless and seemingly unlimited chaff of “points” to beset you like 
moles popping up in your yard everywhere. As I said, they were a few direct 
answers to your main criticisms of what I had said. 


I hadn’t attacked you or lowered myself to off-the-subject criticisms such 
as you resorted to. 


Having said what wanted to say, it isn’t important whether or not you reply 
to it. But it’s dishonest to resort to the claim that you didn’t answer 
because my “points” were too many and too frivolous to bother with. To 
resort to that dodge, are we displaying some authority-conceit? Much better 
if you had just not replied. 


You continued: 


I will just note that I don't seem to have the trouble you have in 
determining geographic coordinates on a map as long as the map comes with a 


I reply: 


It’s reassuring to hear that you don’t have any trouble determining accurate 
geographical co-ordinates from an azimuthal  equal area map of a continent, 
with a widely-spaced graticule, when the projection’s center (in map 
co-ordinates and lat/long co-ordinates) and its orientation are not 


You continue: 


On a medium-scale map (a whole state, for instance) it's easy enough to 
arrive a lat/long coordinate accurate to a few seconds' accuracy in a minute 
or two. 


I reply: 


Maps showing such a small region constitute a tiny fraction of the data maps 
published in atlases and guidebooks sold to the general public. So your 
success with state maps doesn’t help a whole lot. 


You continued: 


It just takes two measurements and a short calculation. That's FAR easier 
than trying to correct for the projection's vagaries in assessing distances, 
whether the map is conformal or not. 


I reply: 


…except that no one needs or uses accurate directly-measured distances 
gotten from a nature guidebook range map or a rainfall distribution map in 
an atlas. 


Michael Ossipoff 



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