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

[Michael Ossipoff]

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 
projections.”

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 
incompatible.

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 
graticule.

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 
specified.

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