[Proj] Graduated equidistant has a name. Another projection suggestion.

[Michael Ossipoff]

Strebe says:

Your "equidistant elliptical" is Apianus II.

I comment:

Yes, I’d have been very surprised if someone hadn’t previously suggested 
that obvious and simply-constructed projection.

Strebe continues:

Your "graduated equidistant"
doesn't really have a name;

I comment:

Actually it does have a name. It’s called the “graduated equidistant” 
(cylindrical, conic or azimuthal) projection. The one I recommend is the 
graduated equidistant cylindrical because it possesses the linearly 
interpolable positions property (LIPP).

Perhaps what Daan meant to say was that it didn’t have a name before I named 
it.

Strebe continues:

it's just the equirectangular projection with
standard parallel set to need.

I comment:

…and the Lambert-Lagrange projection is just a use of the Mercator and the 
stereographic. Yes, the graduated equidistant projections are more obvious 
and simpler in their construction, but they are distinct projections in 
their own right, though they use equidistant projections. They have a 
specific rule for setting the north-south scale in each latitude-band. For a 
world map, I’ve suggested a 10 degree graticule and latitude band.

And, for instance, the graduated equidistant cylindrical closely resembles 
Mercator, probably to the point of being difficult to distinguish from it 
without measurement. As I said, it can be regarded as the beginning of an 
approximation to the Mercator.

Should the graduated equidistant projections “have a name”? Yes, anything 
useful should have a name. Those projections, like Apianus II, are obvious 
and simply constructed. I’d be surprised if they haven’t been proposed &/or 
used in the past. Their simplicity and usefulness (especially the 
cylindrical) certainly justify their having a name.

Lastly, I concur in commending Daan for his patience in this exchange. For 
his patience
in continuing to try to talk to someone whose positions  were “evolving” so 
inconsistently that he actually suggested an equal-area compromise when Daan 
claimed that equal area is a necessary attribute for a data map. To quote 
Daan, “it doesn’t get any muddier than that.” And try to imagine Daan’s 
exasperation with someone who was so dishonest or negligent that he even 
mistakenly claimed that he suggested the equal-area compromise in his first 
posting, when actually it was in his second posting, immediately after Daan 
advocated the need for equal-area.

Obviously the inconsistent “evolution” described above is enough to render 
communication impossible, and so yes, commendations to you, Daan.

I’d like to suggest another obvious and simply-constructed projection, one 
that has probably been proposed before:

In the manner of the Aitoff and Aitoff-Hammer projections, start with an 
orthographic map of half of the Earth, in equatorial aspect. Expand it 
east-west to twice its width, resulting in a 2:1 elliptical map. Re-label 
its meridians so that they nominally extend over the Earth’s entire 
circumferance. As with similar maps, the central meridian should be the 
Greenwich meridian, or somewhere around the Europe’s west coast, for 
land-mass centeredness.

This results in an orthographic view of a 2:1 oblate ellipsoid on one side 
of which the Earth’s surface has been copied.

Advantages:

Like the other projections I’ve suggested, the map is so simply-constructed 
that its construction can be explained to anyone. I consider that an 
important property that seems little valued by cartographers. In this case, 
of course, the orthographic’s graphical construction is used in that 
demonstration.

For an uninterrupted world map, it shows an especially realistic-looking and 
attractive portrayal of the Earth.

Disadvantage:

Like the ordinary orthographic, t doesn’t do a good job of showing areas 
near its edges.

It probably already has a name, but for now I’d call it “orthographic 
elliptical” or “elliptical orthographic”.

Michael Ossipoff