Chalker Continental Composites

[Milo]

The HEALPix projection uses a cylindrical equal-area projection near the equator and a Collignon projection near the poles. Not quite elliptical, but similar concept. In the most-used variation, the Collignon part is interrupted into four gores, kind of giving the appearance of a cut-up-and-unfolded cube despite not being a true polyhedral projection.

[dchalker]

Nice catch, Pete! Corrected the image on the previous page, if anybody wants the corrected topo image. Not sure the exact "correct" way to fix the problem, but for the moment I've used a stretch/squish. Equirect is probably the wrong choice. I'm exploring other combinations next, trying to define each of the "idealized" combinations that retain some consistent principle (whether area or distance or whatever), best splice location, etc. (so far I'm thinking equator works well to avoid any crazy angular distortion)

Good examples, hopefully nothing closer pops up. Adding just a touch more novelty to what I'm presenting is good.

Here, I demonstrate the "rolling" function at 90 degree intervals

apianchalker-rotate.png (542.19 KiB) Viewed 15954 times

For the clock, Antarctica could roll across, then reset like a typewriter - OR, imagine: an upright rotating cylinder with a cylindrical projection on it, with a solar indicator fixed at the top showing global time, and a rotating contiguous Antarctica at the bottom showing local time. I think that's my clock. (Maybe the other way around makes better sense, idk, got to prototype and try it out.) Lame text description, still gotta work on the concept art for it... And figure out how to search historical clocks. Probably reinventing the wheel.

Symbolically something like this. I'll get a mockup running in the browser eventually, now that I've got such perfect art to do it.

chalkerclockart.jpg (198.91 KiB) Viewed 15939 times

[quadibloc]

I think I actually saw that map with the birds in my recent web searches! (That is, not your drawing, but your inspiration.)
Anyways, funny you mention the Baker dinomic. I ran across that recently, and it reminded me of the world map in the infamous Monarch Flour Atlas.
This atlas was available in 1959 as a premium with Monarch flour.
On the back cover was an Azimuthal Equidistant, centered on London, showing world air routes.
The map of Canada was on the Simple Conic projection, I believe.
The world map was on a Mercator projection with round (instead of pointy) caps in the extreme north - sort of like the Baker dinomic, but only on one side.
All the other maps in the atlas were on the Mercator projection!
Obviously a really lazy atlas; they licensed a couple of maps from the Canadian government, and then used pieces of one Mercator wall map for the rest of it. (The publisher was Copp Clark; they manufactured a Mercator wall map, so they had one to use. This publisher also was licensed to manufacture, on behalf of Parker Brothers, Monopoly boards for use in Canada, so that tariffs on importing the boards themselves would be avoided; this was back before NAFTA. Basically, as I understand it, they were a printer that started out being in the business of making and sellling things like ledger books, diaries, and pre-printed forms; Canada being small, they had to branch out, so they started making board games - including some of their own, like Stock Ticker - and being a tiny book publisher as well.)
Of course, it's specifically because the Mercator projection is conformal that it's even possible to get away with this. Obviously, it would never be possible to make an atlas were all the maps were part of an uninterrupted equal-area projection, as that would be absurd and look horrible.
Oh, wait. High-quality paper was actually wasted in printing the Peters Atlas of the world. Somebody does something ridiculous and stupid, but, hey, the atlas was being given away except for a small charge for postage. But then years later, someeone else does something even worse.

[Milo]

Of course, it's specifically because the Mercator projection is conformal that it's even possible to get away with this. Obviously, it would never be possible to make an atlas were all the maps were part of an uninterrupted equal-area projection, as that would be absurd and look horrible.

Not the exact same projection, but the same type of cylindrical projection with varying standard parallels could work fairly well, and all it requires is scaling by different factors in the x and y directions, which is hardly harder than resizing a map normally, something that you'd already have to do to make the Mercator atlas works. (Conical projections also have standard parallels, but changing them is a more involved affair than rescaling.)

If you're willing to use oblique aspects, then nearly any projection can be made to work well for any region, but that requires a lot more work since you actually have to compute each map separately, so you gain little from using the same type of projection for all of them, except thematic elegance.

[quadibloc]

Incidentally, Copp Clark had both a map of Canada on the Simple Conic, and a map of the world on the Mercator Projection handy because they printed maps of these two types which adorned the walls of classrooms across Canada.
Now, we've all heard of the deleterious effects of constant exposure to maps on the Mercator Projection. But these maps did something else harmful as well: they promoted tooth decay!
https://mrsnicholsonhome.com/2014/08/29 ... from-1952/
That's because they were given for free to schools across Canada by Neilson's... with pictures advertising their chocolate bars in the corners.
Canadians of a certain age will vividly remember this evidence of the struggle between impecunious local school boards and local ratepayers.

[PeteD]

Nice catch, Pete! Corrected the image on the previous page, if anybody wants the corrected topo image. Not sure the exact "correct" way to fix the problem, but for the moment I've used a stretch/squish.

Are you sure it's corrected? The Apian II and equirectangular sections now look like they match, but the inset still looks slightly too small. The diameter of the inset should be π/3. If the equirectangular projection is the plate carrée, which it seems to be, then 60° of longitude should also correspond to a distance of π/3, meaning the width of the inset should be equal to the distance between 30° W and 30° E of the central meridian. However, it's slightly, but visibly, less than that. On the other hand, if the equirectangular projection has a standard parallel away from the equator, then the inset should actually be wider than the distance between 30° W and 30° E of the central meridian, which it clearly isn't.

For the clock, Antarctica could roll across, then reset like a typewriter - OR, imagine: an upright rotating cylinder with a cylindrical projection on it, with a solar indicator fixed at the top showing global time, and a rotating contiguous Antarctica at the bottom showing local time. I think that's my clock. (Maybe the other way around makes better sense, idk, got to prototype and try it out.)

Would the solar indicator also roll across like Antarctica? If so, then surely it would make sense for this solar indicator to indicate the local, i.e. solar, time by being aligned with the meridian where the Sun is currently overhead. I don't understand the connection between Antarctica and clocks. Our way of measuring the passage of time isn't derived from any movement of Antarctica with respect to the rest of the globe.

Symbolically something like this. I'll get a mockup running in the browser eventually, now that I've got such perfect art to do it.
chalkerclockart.jpg

I also don't understand the eagles. I see from Wikipedia that in the Iliad, Zeus sent an eagle as a good omen and Diomedes was the first to see it, but this seems like a pretty minor event. More significant seems to be the story that when Diomedes died, Venus turned his followers into birds, but they aren't specifically eagles. As far as I can see, albatrosses would seem to be the most suitable birds because their scientific name, Diomedeidae, is derived from Diomedes. Am I missing something?

[dchalker]

I also don't understand the eagles. I see from Wikipedia that in the Iliad, Zeus sent an eagle as a good omen and Diomedes was the first to see it, but this seems like a pretty minor event. More significant seems to be the story that when Diomedes died, Venus turned his followers into birds, but they aren't specifically eagles. As far as I can see, albatrosses would seem to be the most suitable birds because their scientific name, Diomedeidae, is derived from Diomedes. Am I missing something?

There is a Greek myth about the Omphalos of Delphi, the "world navel" or center of the world, that says Zeus sent out two eagles to map the edges of the world and locate the center. Presumably, the two eagles would meet in the middle somewhere and return back the way they came. The resulting Omphalos at 22°30′E is not terribly far from my Antidiomedian Meridian. The name Diomedes means "Zeus-minded." Didn't know that about their scientific name, but the albatross would be a suitable substitute I suppose. I'm just leaning into the myth.

Would the solar indicator also roll across like Antarctica? If so, then surely it would make sense for this solar indicator to indicate the local, i.e. solar, time by being aligned with the meridian where the Sun is currently overhead. I don't understand the connection between Antarctica and clocks. Our way of measuring the passage of time isn't derived from any movement of Antarctica with respect to the rest of the globe.
rosses would seem to be the most suitable birds because their scientific name, Diomedeidae, is derived from Diomedes. Am I missing something?

Nope, it remains fixed facing the same direction as Antarctica while the cylinder rotates. The numbers can be affixed to the cylinder itself, and slide by the fixed indicator. I have a mockup working in the browser now, I just haven't added the numbers to the art yet:

clockmockup.png (845.03 KiB) Viewed 15856 times

Antarctica simply provides an extra face, supporting a dual clock function. It's not that Antarctica itself is tied to time, but it *does* rotate once per day just like the rest of the planet, opening up double-functionality. This clock tracks where the "dayside" is, for both sections. Both images are set to mimic their natural 24-hour cycle. One "slides", the other rotates. One set with Diomedian time, the other set with local time (configured to the time zone of interest). Since the numbers themselves would move with the maps, there are no hands to read. Just imagine a strip of numbers 0-23 at the top, and around the wheel. You simply read the top-center number and bottommost number. (or whichever you are interested in at the moment)