Interesting projection

[mapnerd2022]

Er... huh? What 3D shape are you using there? A sphere, for some ironic circular logic? (Pun totally intended.)

From what I can tell, what you're doing is projecting the sphere cylindrically (with the Mercator version cut off at 85° so it has square aspect ratio), halving longitude (a la Aitoff/Hammer), projecting the resulting image back to one hemisphere of the sphere using a different cylindrical projection (cylindrical equidistant, always, so in the middle case it's actually the same projection after all, corresponding so far to the methodology of the actual Aitoff projection), and then mapping that sphere using a perspective projection?

I've managed to produce maps pretty similar to yours by performing that process using just G.Projector, so I think that's right. I'm not sure about some of the finicky details, like exactly what height your perspective projection is taken from (I'm pretty sure it's not just an orthographic projection, at least, though it's high enough that it's almost one), but my imitations still look too similar to be mere chance.

Incidentally, using a rectangular image as a texture map for a 3D-rendered sphere (which I think is what your software is doing using the equirectangular projection) is one application for which I would recommend my dihedral projection, since it has the same resolution-efficiency (this is actually one of the main applications that I invented that metric for!) as the equirectangular projection while having less distortion at the extreme points.

The last one is like an even more distorted or worse Fournier II.

...Wait, there is an actual serious projection that looks like this? Now I have to look this up.

Found it (sorta).

...Okay, from what I can tell, it's a worse version of Mollweide? It's a pseudocylindrical projection with the same envelope, but parallels are spaced farther apart near the equator and closer together near the poles, which is the opposite of what you'd want to do if you wanted to bring it closer to conformal.

For all that, though, it still doesn't look anywhere near as bad as the Atarimaster Terrible III projection.

You're right, it's quite remarkable that a projection from the 16th century doesn't look too bad.

[Milo]

You're right, it's quite remarkable that a projection from the 16th century doesn't look too bad.

It would be more remarkable if another elliptical pseudocylindrical projection from a century earlier didn't look better.

[mapnerd2022]

You're right, it's quite remarkable that a projection from the 16th century doesn't look too bad.

It would be more remarkable if another elliptical pseudocylindrical projection from a century earlier didn't look better.

That one should be used in elementary schools. It's so mathematically much simpler than the Mollweide, while looking similar to it, but being it's non equal-area version(aphylactic), plus it's pleasing to to the eye, especially because it looks better than the
Fournier II and, like it, it's elliptical in shape. Plus, it would be easy to explain to elementary school students because of it's simplicity. Of course the being aphylactic part is of no consequence in elementary schools. In that school level, only little flation is needed. Strict equivalence would only be more important in middle schools or secondary schools.

[Atarimaster]

The last one is like an even more distorted or worse Fournier II.

And Greenland is even smaller that in the Bacon globular. I guess that’s a world record – Yay!

Er... huh? What 3D shape are you using there? A sphere, for some ironic circular logic? (Pun totally intended.)

From what I can tell, what you're doing is projecting the sphere cylindrically (with the Mercator version cut off at 85° so it has square aspect ratio), halving longitude (a la Aitoff/Hammer), projecting the resulting image back to one hemisphere of the sphere using a different cylindrical projection (cylindrical equidistant, always, so in the middle case it's actually the same projection after all, corresponding so far to the methodology of the actual Aitoff projection), and then mapping that sphere using a perspective projection?

Well, I just opened images of the three aforementioned projection (and yes, Mercator cut off at Geocart’s default value of 85°3′4.0636″) and used the “projection” tool of a graphics application (PhotoLine) to project it onto half a sphere.
Here’s a screenshot of the process, using different settings to make it more apparent (hopefully) that it’s the half of a sphere:

[mapnerd2022]

The last one is like an even more distorted or worse Fournier II.

And Greenland is even smaller that in the Bacon globular. I guess that’s a world record – Yay!

Er... huh? What 3D shape are you using there? A sphere, for some ironic circular logic? (Pun totally intended.)

From what I can tell, what you're doing is projecting the sphere cylindrically (with the Mercator version cut off at 85° so it has square aspect ratio), halving longitude (a la Aitoff/Hammer), projecting the resulting image back to one hemisphere of the sphere using a different cylindrical projection (cylindrical equidistant, always, so in the middle case it's actually the same projection after all, corresponding so far to the methodology of the actual Aitoff projection), and then mapping that sphere using a perspective projection?

Well, I just opened images of the three aforementioned projection (and yes, Mercator cut off at Geocart’s default value of 85°3′4.0636″) and used the “projection” tool of a graphics application (PhotoLine) to project it onto half a sphere.
Here’s a screenshot of the process, using different settings to make it more apparent (hopefully) that it’s the half of a sphere:

Hahahaha, world record, WORLD record, get it?

[PeteD]

Pseudo graticule lines

Yes, the lines extending in the radial direction look like meridians over Africa and Australia but parallels over Russia and North America.

it suggests it's more a matter of an artist cramming roughly-familiar shapes wherever there's room for them, rather than a software-automated rendering.

Yes. The Northwest Passage has been considerably widened and might now be more attractive for shipping, except for the giant funnel at one end of it. Severnaya Zemlya seems to have been moved from the Russian coast to the northeastern tip of Greenland. Newfoundland seems to have been drawn twice - once at the Gulf of St Lawrence and a second time, enlarged, falling down the funnel. There's a whole archipelago where just Iceland should be. And where's Japan gone?

[Milo]

Yes, the lines extending in the radial direction look like meridians over Africa and Australia but parallels over Russia and North America.

Not quite parallels. The line passing through India veers south before hitting Malaysia. And for that matter, in the other direction, veers north before hitting Arabia.

Yes. The Northwest Passage has been considerably widened

The Canadian Arctic Archipelago appears to be placed roughly correctly relative to Greenland, but not relative to mainland Canada, kind of defeating the idea of it being the the Canadian Arctic Archipelago.

This isn't quite the same as widening the Northwest Passage, as Wikipedia describes it, because Baffin Island is recognizably on the Greenland side (Davis Strait is even narrower than it should be, in fact).

and might now be more attractive for shipping, except for the giant funnel at one end of it

That tends to be inconvenient, yes!

Severnaya Zemlya seems to have been moved from the Russian coast to the northeastern tip of Greenland.

I think you mean northwestern? No, you were right, it's northeast. I had Greenland's orientation mixed up, the direction that the graticule makes to look like Greenland's northern coast is actually its eastern.

It makes me wonder what happened to Franz Josef Land and Svalbard. Actually... no, wait a moment. Found 'em.

On the other hand, Novaya Zemlya is clearly recognizable and roughly in the right place.

Newfoundland seems to have been drawn twice - once at the Gulf of St Lawrence and a second time, enlarged, falling down the funnel. There's a whole archipelago where just Iceland should be.

I think your second "Newfoundland" is actually Svalbard. The archipelago you're talking about (drawn directly north east of Greenland) might be intended as Franz Josef Land, though drawn rather badly if so. Then again, it's a pretty difficult archipelago to draw well.

Iceland itself presumably fell down the funnel with Europe.

And where's Japan gone?

Between Siberia and Greenland, looks like. To the left (north) of Indonesia, roughly like it should be, it's just that the placement of Indonesia itself is totally wrong, and some of the Philippines seem to have been skipped over (I think I can recognize Mindanao, though).

There's a near-horizontal streak which is probably Honshu, and then beyond that, a V-like shape with a final island dotting the end of one arm, which I think represents Sakhalin and the Kuril Islands (the final island might be Paramushir?). Hokkaido seems to be gone for real, though, although it might just be shrunken and folded into the V.

More specifically, I think Sumatra is drawn directly off the New Siberian Islands. Those are where they should be - the west one is flattened, but to the degree you'd expect in a plate carree projection. Left of Sumatra is Borneo, left of Borneo forks off into two minor islands, and beyond those islands lie Mindanao and New Guinea, respectively. Not sure about the identity of the minor islands themselves (Sulawesi seems to be entirely gone).

Java is almost invisible due to overlapping with and being drawn in the same color as the graticule, but if you look carefuly you can see the slight distortions in the graticule that hint at its presence.

[PeteD]

Not quite parallels. The line passing through India veers south before hitting Malaysia. And for that matter, in the other direction, veers north before hitting Arabia.

Well, almost parallels, then, and in any case much more like parallels than like meridians, which is what you'd expect them to be if you look at Africa first. And does the line passing through India also pass through Russia anyway?

This isn't quite the same as widening the Northwest Passage, as Wikipedia describes it, because Baffin Island is recognizably on the Greenland side (Davis Strait is even narrower than it should be, in fact).

OK, a section of the southerly Northwest Passage route through Queen Maud Gulf has been considerably widened. This is the original route taken by Amundsen. Compared to the northerly route through the Prince of Wales Strait or the M'Clure Strait, it has less ice but is shallower.

In any case, while the passage west of Baffin Island may not generally be considered part of the Northwest Passage, this is only because navigating the Fury and Hecla Strait is impractical, so if it were indeed widened as it is in this map, I'm pretty sure it would also be considered part of the Northwest Passage.

Anyway, in both cases, I'm sorry for not being more precise.

I think your second "Newfoundland" is actually Svalbard. The archipelago you're talking about (drawn directly north east of Greenland) might be intended as Franz Josef Land, though drawn rather badly if so.

...

Between Siberia and Greenland, looks like. To the left (north) of Indonesia, roughly like it should be, it's just that the placement of Indonesia itself is totally wrong, and some of the Philippines seem to have been skipped over (I think I can recognize Mindanao, though).

There's a near-horizontal streak which is probably Honshu, and then beyond that, a V-like shape with a final island dotting the end of one arm, which I think represents Sakhalin and the Kuril Islands (the final island might be Paramushir?). Hokkaido seems to be gone for real, though, although it might just be shrunken and folded into the V.

OK, that makes more sense -- thanks for clearing that up. When I didn't see Japan near China and Korea, it didn't occur to me to look elsewhere. I think the southernmost tip of the V is supposed to be Hokkaido.

The map is still a big mess, though.

[Milo]

And does the line passing through India also pass through Russia anyway?

Hard to say. I don't think it reaches Siberia, but I can't tell if it passes through the European part of Russia because that's hidden in the funnel.

In any case, while the passage west of Baffin Island may not generally be considered part of the Northwest Passage, this is only because navigating the Fury and Hecla Strait is impractical, so if it were indeed widened as it is in this map, I'm pretty sure it would also be considered part of the Northwest Passage.

Well, it might not be considered the Northwest passage anymore in that case, since it's at the same latitude as Arabia and the Caribbean

Anyway, in both cases, I'm sorry for not being more precise.

And I'm sorry if my corrections came over as hostile (to you, anyway - any hostility to the map creator is probably intentional).

I think the southernmost tip of the V is supposed to be Hokkaido.

Well, that's the logical place for it. I was going to say Hokkaido should look larger than that, but on second consideration, it's actually not too bad - the key is to notice that the two lines making up the V remain fused for slightly longer than the thickness of the lines alone can justify.

The map is still a big mess, though.

May I take a moment to comment on how cool it is that so many geographic features, generated completely randomly through impersonal geological processes, still have recognizable enough shapes that even when the map is horribly mangled like this they can still be identified?

[PeteD]

And I'm sorry if my corrections came over as hostile (to you, anyway - any hostility to the map creator is probably intentional).

I wouldn't say hostile. It did come across as nitpicking to me, but it can be difficult to gauge the intended tone of written language, especially in the absence of emojis.