Experimental projections

[Piotr]

Hufnagel and HEALPix are modern projections that relax the requirement of monotonically decreasing parallel length. Denoyer relaxes the constraint of constant scale along parallels. Relaxing that latter constraint is not a definition I would use, ever.

— daan

The Denoyer's relaxation seems to be also used in https://www.giss.nasa.gov/tools/gprojec ... ojections/ .

[Luca_bat_map]

Hi guys!Talking abou experimental projections... I did it again...

A few days ago I was thinking about a projection on a tetrahedron with less disortion and still a nice shape. After a lot of shots I found this arrangment... I hope you like! Not exactly a rectangle but almost...

Enjoy!

tetra-concialdi.jpg (113.85 KiB) Viewed 5157 times

[daan]

That’s a really fine arrangement for reducing distortion over land. I can’t think of one better that’s conformal and with as few interruptions.

— daan

[Luca_bat_map]

Thanks Daan! I found the right projection center that allowed me to crop one face of the tetrahedron in 3 equal parts et voilà

[quadibloc]

I agree that you have chosen a very good orientation for the projection.
In general, I have to admit, I have been quite unsympathetic to this category of projection. While I find the use of the Dixon elliptic functions to create conformal projections fascinating, when a projection is cut and trimmed so that the portions with the most distortion or the most scale exaggeration are located somewhere in the middle of the projection, where a naive viewer of the map doesn't expect to find them, then it seems to me that the scale exaggeration could possibly be more harmful, because it could be more deceptive.
However, a projection like this one forces me to rethink this prejudice. While the scale exaggeration in the Mercator is at the top and bottom of the map, in an "expected" place, it seems clear that the scale exaggeration in the Mercator is much more deceptive than that in yours.
In your projection, the graticule acts as a reference telling the viewer how much scale exaggeration is present in any part of the map, while in the Mercator, one can only guess.

[dummy_index]

Complementary Eckert-Greifendorff projection

ComplementaryEckertGreifendorff.png (135.97 KiB) Viewed 5083 times

(Hammer - Eckert-Greifendorff) × directional path offset

Eckert-Greifendorff projection have less curvature of parallels and more shear deformation on high latitude area than Hammer projection. I wanted some better compromisation.

*path* is a specified meridian thus complex curve, but I successfully obtained the explicit solution of x_offset.

https://dummy-index.hatenablog.jp/entry ... /03/234248

[Atarimaster]

One of my asymmetric experiments. Nothing special, but not too bad either, I think.
Again, I’d like you to guess what it is.

A hint: Images could not be created by Geocart, but a projection that is available in Geocart is involved.

[Atarimaster]

Again, I’d like you to guess what it is.

Since nobody seems to be interested to guess…
It’s an umbezifferte Bottomley, with the limiting parallels at 50°, limiting meridians at 60°, a projection spin by 180°, the resulting image was rotated back.
On the Tissot indicatrix image, I used an areal inflation of 1.35 at 60° N/S, while on the physical map image, it’s 1.2.

[daan]

Tobias,

I don’t think I would have been able to reconstruct that. Knowing how it was constructed, it makes sense, but getting their from scratch would have been very hard.


I do like it.

— daan

[Atarimaster]

A few days ago, I received an email message with the following question:

Do you know of any *uneven* dual-hemisphere projections? Or how someone might go about making one? I’m thinking of something like this:
https://map-projections.net/single-view ... -hemi-110w
… but with the right hemisphere a little wider so that it can fit all of Africa, Europe, and Asia, and the left hemisphere correspondingly smaller. Have you ever heard of something like that?

Well, I don’t think I have ever seen a map like this, but of course it’s an easy thing to do. And I like the results!
I decided to set the boundary cuts to 25°W and 169°W. Here’s the azimuthal equidistant projection in this configuration, with a little extension for Greenland’s coast:

azimuthal-equidistant-with-extension.jpg (75.12 KiB) Viewed 4645 times

But it also works well on non-azimuthal projections, e.g. Mollweide and Strebe 1995:

mollweide.jpg (53.04 KiB) Viewed 4645 times

strebe-1995.jpg (52.03 KiB) Viewed 4645 times

Now, here are my questions:
1. As I’ve said, I don’t think I’ve ever seen this specific arrangement but of course that doesn’t mean that it doesn’t exist. It actually seems a bit unlikely to me that no one ever tried this. So, have you ever seen this somewhere?

2. How would you name a configuration like this?
My first idea was “uneven hemispheres” but these aren’t hemispheres. I thought about “merosspheres” from the Ancient Greek word for part, component, region, but I know nothing at all about Ancient Greek so this might be the wrong word in this context.
Each of the two parts is projected from a spherical wedge or ungula so to call them “ungulae” was my next idea, but then it was pointed out to me that the adjective would be ungulate which might be misunderstandable.
The surface of that wedge is a spherical lune but then, the adjective would be lunatic…
Wikipedia says that a spherical lune is also called biangle but PlanetMath says:
A biangle is a two-sided polygon that is strictly contained in one hemisphere of the sphere that is serving as the model for spherical geometry.
If I get that right, I think the Western part is a biangle but the Eastern part isn’t…

So I’m out of ideas here…