Györffy's minimum-distortion pseudocylindrical projection

[Atarimaster]

It doesn't even do that great of a job of maximizing the continents, since it's still symmetric. A true continent-biased map wouldn't be symmetric

Canters also offers that kind of map, with no symmetry at all and with symmetry about the central meridian only, again excluding Antarctica from the optimization, and again centered to the Greenwich meridian.

Kind regards,
Tobias

[daan]

In any case, it's probably not a good idea to base your central meridian on things like your favourite beer festival or the largest city along the river that shares your first name etc.

Possibly not a bad idea, either. Naming rights usually go to whoever decides to name it first. You could name it something descriptive but ungainly; you could name it after yourself; or you could name it after something whimsical but just as easily recalled. I’m fine with the Oktoberfest meridian, despite disliking beer.

— daan

[daan]

This paper by Kerkovits makes a compelling case for the (weighted) Airy–Kavrayskiy criterion. Is this one of the papers that you're referring to?

It certainly is. His earlier paper, Comparing finite and infinitesimal map distortion measures, hinted in that direction while confirming my suspicion that finite measures were not terribly useful. My library is presently boxed up (due to remodeling), so I don’t have access to earlier printed work that swayed me.

— daan

[Milo]

I overwhelmingly prefer stereographic (double hemispheric) for the moon and Mars. Because, circular craters dominating the landscape.

Good point! I haven't thought of that. But, of course, it comes with the usual tradeoffs: the sizes of different craters relative to each other will be distorted.

And it has the disadvantage of all two-hemisphere projections: shapes near the interruption are hard to make out. If you do a north-and-south-hemisphere projection of Mars (the only logical way to pick hemispheres, since Mars isn't tidally locked), that's a problem, because Mars actually has a lot of important landmarks near or crossing the equator (particularly Tharsis and Valles Marineris). But on the other hand, it does do a great job of showing the distinctive triangular triangular shape of Vastitas Borealis, which is obscured by cylidrical/lenticular maps.

A non-hemispherical version of the stereographical projection is impractical because it requires infinite space.

And I could argue that the craters actually make shape distortions less of a big deal, since if you know they're supposed to be circular, you can use them as indicators to easily spot how badly-distorted any given region is, and mentally adjust.

Of course, unless you want a map of the Moon as seen from space, for which you would use the Azimutal Ortographic, or the Vertical Perspective.

More importantly, a map of the moon, as seen from Earth.

Technically, the azimuthal almost-orthographic projection of the moon is the oldest map projection ever seen by humans!

But the orthographic projection isn't always the most natural one. If you're making a map of the celestial sphere instead of a solid body, then it's instead the gnomonic projection that matches what the sky actually looks like. (By association, it's also one context where it'd be worth seriously considering using the usually-terrible central cylindrical projection. But even here, equal-area projections have their value too, since they preserve the total amount of light received per unit solid angle of the sky.)

Canters also offers that kind of map, with no symmetry at all

I think this one might look good (except for the poor choice of central meridian) in the OGABO style. The continents look pretty good, even Greenland is less distorted than usual (though still not quite as elongated as it should be).

[Atarimaster]

Canters also offers that kind of map, with no symmetry at all

I think this one might look good (except for the poor choice of central meridian) in the OGABO style. The continents look pretty good, even Greenland is less distorted than usual (though still not quite as elongated as it should be).

I like that you’re adopting my acronym!

So, here‘s Canters W10 – or the “Low-error polyconic projection obtained through non-constrained optimisation” – in the OGABO style, original central meridian and centered to 11.55° E:

Canters W10, centered to the Greenwich meridian

cantersw10.png (79.89 KiB) Viewed 6219 times

Canters W10, centered to 11.55°E

cantersw10-11.55.png (76.99 KiB) Viewed 6219 times

Edit:
I don’t know why there are links instead of the images

[Milo]

So, here‘s Canters W10 – or the “Low-error polyconic projection obtained through non-constrained optimisation” – in the OGABO style, original central meridian and centered to 11.55° E:

Well, some of the continents are definitely rotated compared to how I'm used to seeing them, but orientation aside the actual SHAPES look pretty good.

Of course cutting off Chukchi looks really silly in OGABO. If anything, OGABO maps are also a good place to use the "erratic extension" solution that you demonstrate in https://blog.map-projections.net/blogimg/large/scheme-center-154e-with-extension.png, since the awkwardness of the cut-up boundary isn't shown.

Edit:
I don’t know why there are links instead of the images

Too large. The forum allows a maximum of 800x800.

Though I thought it used to reject larger images entirely rather than upload them but refuse to show them?

[PeteD]

And I could argue that the craters actually make shape distortions less of a big deal, since if you know they're supposed to be circular, you can use them as indicators to easily spot how badly-distorted any given region is, and mentally adjust.

Like built-in Tissot ellipses!

[PeteD]

So, here‘s Canters W10 – or the “Low-error polyconic projection obtained through non-constrained optimisation” – in the OGABO style, original central meridian and centered to 11.55° E:

I didn't used to like Canters W10, but I have to admit it looks good like this. I'd like to add a caveat to my previous comment: if all you're going to plot is the continents excluding Antarctica - no graticule or even a boundary - then it seems preferable to restrict any optimization to the continents excluding Antarctica (and also to allow an asymmetric graticule since it's not plotted anyway).

[PeteD]

And well, I can live with the name “Oktoberfest meridian” although I’m not a Oktoberfest friend at all.

We could try to be objective and name it after the best-known landmark or event located or taking place on a suitable meridian. In Tobias's blog post on the topic, he first shows two candidate meridians for the least bad points to cut through Umnak that correspond to central meridians of 11°33' E and (I think) 11°40' E, then he settles on 11°33' E. In the following, I consider locations anywhere between 11°33' E and 11°40' E. I'm using Google Trends to determine how well-known different landmarks and events are.

Starting with cities, we can see that Munich is the best-known by a wide margin and is also better-known than any city that lies close to this range of longitudes but narrowly misses out. In case you're thinking I've forgotten about Africa, I haven't – it's just that the only candidate city is less well-known than the European ones, despite having a greater population than Munich. (In Africa, the relevant meridians mostly pass through the Sahara and sparsely populated rainforest.)

Since Munich is too large to define a single meridian, we can consider different landmarks and events within Munich and see that the Oktoberfest is the highest-trending by a wide margin with a large asymmetric peak from July to October. Even during the other seven months of the year, it's still the highest-trending landmark or event in Munich overall, although the Allianz Arena is higher-trending on the days of big Bayern Munich matches.

So the Oktoberfest does seem to be the best-known landmark or event in the best-known city on a suitable meridian. Of course, the best-known landmark or event on a suitable meridian overall won't necessarily be in the best-known city, but I haven't managed to find any better-known landmarks or events located or taking place on a suitable meridian. I'd be interested to know whether anyone else can come up with anything.

[Milo]

So I happened to be playing with my geonames database, and remembered this.

Code: Select all

SELECT name, description_short, pretty_coords FROM geonames JOIN feature_codes USING (feature_class, feature_code) WHERE (longitude BETWEEN 11.35 AND 11.833333) AND +feature_class = 'S' AND +feature_code NOT IN ('FRM', 'CH', 'HUT') ORDER BY abs(longitude - 11.55) DESC;

Feature class 'S' is the one that denotes individual buildings, which is a good to look for if you want to be precise. I don't think I need to explain why I decided to exclude 'HUT' buildings. Even with these restrictions, this gives a lot of results (4218, to be exact), but trimming to just the ones that are closer to 11.55 exactly than Oktoberfest, I get:

Code: Select all

Oktoberfest|building(s)|11.5516E 48.1303N
Bavaria Filmstadt|building(s)|11.5514E 48.0656N
Gästehaus Am Rptc|hotel|11.5487E 48.10498N
Auli|bridge|11.55127E 60.10968N
Borgo Tepolini|hotel|11.55125E 42.91017N
Victoria|hotel|11.55122E 45.54359N
Burg Veldenstein|castle|11.54879E 49.6293N
Hådalen skole|school|11.54882E 62.50839N
Jedermann|hotel|11.5511E 48.139N
Minotel Brack Garni|hotel|11.55101E 48.12583N
Hotel Toelzer Hof|hotel|11.549E 47.7615N
Palazzo Regau|palace|11.55086E 45.55027N
Lutherstadt Eisleben|railroad station|11.5508E 51.51819N
Teatro Olimpico|theater|11.54933E 45.55016N
Palazzo Chiericati|museum|11.54935E 45.54909N
Castagna|hotel|11.5494E 45.548N
Best Western Hotel Tre Torri|hotel|11.54941E 45.54797N
Museo Civico Vicenza|museum|11.54946E 45.54859N
Lettenhof|agricultural school|11.54949E 49.92902N
Gastehaus Im Rptc|hotel|11.54969E 48.10497N
Hotel Senator|hotel|11.5497E 48.1375N
Piazza Matteotti|square|11.54972E 45.54917N
München Hackerbrücke|railroad station|11.54972E 48.14189N
Ufficio Teatro Astra|theater|11.55027E 45.54651N
Fernmeldeturm München - Blutenbergstrasse|tower|11.5498E 48.14742N
Grundschule an der Waldmeisterstraße|school|11.54982E 48.19668N
Hotel Fondo Catena|hotel|11.54991E 44.85111N
G Boutique|hotel|11.54993E 45.54814N
Eisleben, Museum "Martin Luthers Geburtshaus"|museum|11.55007E 51.52694N
Kongsdal|estate(s)|11.54998E 55.61799N
Locanda Senio|hotel|11.55E 44.1167N
Bahnhof München-Süd|railroad station|11.55E 48.11667N
Top Hotel Senator|hotel|11.55E 48.138N
Hotel Achterbahn|hotel|11.55E 48.14N
Ludwigslust East|airfield|11.55E 53.3N
Anholt Island Automated Reporting Station|meteorological station|11.55E 56.7N
Lönnbäcken|lighthouse|11.55E 57.85N

The lighthouse is interesting, since lighthouses are designed to be geographic landmarks, and play an important role in navigation. However, any value of 11.55 exactly is suspect, since it may simply have been rounded to two digits. A DuckDuckGo search gives conflicting information: https://www.getamap.net/maps/sweden/vas ... onnbacken/ and https://travelingluck.com/Europe/Sweden ... 4cken.html say Lönnbäcken is 11.550 exactly (with explicit precision), but https://www.marinetraffic.com/en/ais/de ... 1000003876 gives 11.5531. And of course, either way, lighthouses are rather obscure and of little interest to anyone who isn't a sailor.

Above that are a bunch of buildings that sound like SOMEONE has probably heard of them, but I'm not familiar with any of them personally (Oktoberfest included). "Popularity" is not a property recorded in this database.

Feature class 'T' covers natural terrestrial features like islands and hills. It makes sense to sort these by elevation, so here's the ones above one kilometer between 11.545 and 11.555:

Code: Select all

SELECT name, description_short, pretty_coords, elevation FROM geonames JOIN feature_codes USING (feature_class, feature_code) WHERE (longitude BETWEEN 11.545 AND 11.555) AND +feature_class = 'T' ORDER BY elevation ASC;

Code: Select all

Kohlberg|peak|11.54611E 47.63972N|1042
Monte Lefre|peak|11.54903E 46.0597N|1305
Östliches Torjoch|mountain|11.55E 47.51667N|1818
Cima Isidoro|peak|11.55347E 46.01222N|1912
Passo Cinque Croci|pass|11.55019E 46.17531N|2018
Monte Nicola|peak|11.54789E 46.48987N|2164
Ultenspitze|peak|11.5475E 47.05444N|2179
Col di San Giovanni|hill|11.54623E 46.17994N|2251
Roßgrubenkofel|peak|11.54722E 47.02194N|2450
Gamsjoch|mountain|11.54874E 47.41849N|2452
Schafseitenspitze|mountain|11.55E 47.1N|2602
Spritzkarspitze|peak|11.55096E 47.38128N|2606
Grünbergspitze|peak|11.54722E 46.17417N|2790
Rosenjoch|peak|11.55E 47.16667N|2796

Again, the one that's listed as 11.55 exactly is dubious, Wikipedia gives it as 11.543.

Feature class 'P' (cities) again, of course, turns of a lot places, but the biggest ones are Munich and Yaoundé, both with almost 1.3 million people. The biggest one whose longitude is between 11.545 and 11.555 is Vicenza, with over 0.1 million people. Wikipedia gives its area as 80 square kilometers, which would give it a radius of about 5 kilometers. Which is a problem, since we want an accuracy of 1 kilometer here.

...Conclusion? Nah. No conclusions here.

Source: GeoNames allCountries.zip, processed into an SQL database by myself for easier searching.