Chalker Continental Composites

[quadibloc]

I was looking through my web page, when I noticed one projection I came up with there - with some inspiration from the Strebe projection, but based on Wagner VII -

would be a perfect candidate for improvement with your technique.

[PeteD]

Nice find!

Projections where the southern hemisphere is wider than the northern often depict the Antarctic worse than the Arctic and could therefore benefit from your interruption scheme: conic projections, Canters W10, cupola, Hill eucyclic, Hatano asymmetric, Strebe 2011.

On the other hand, for the scale to match along the parallel at 60 S on both sides of the interruption, the base projection has to be quite narrow in the southern hemisphere. This is the criterion for "the rolling thing to work", as I've put it in my previous posts, but even if you're not planning to roll the inset along the bottom of the base projection, this would still be a nice property for the map to have, and its absence was one of Milo's initial criticisms:

If you want everything to line up properly, though, you can't just arbitrarily make the cut at 60° and expect it to work. You have to pick the cutoff [and/or adapt the base projection] such that the lengths of the cutoff parallel on the cylindrical map and the azimuthal one are equal, and they connect smoothly.

While nice to have, it's debatable whether or not this property is essential. Denoyer didn't seem to think it was. It's a pity that the projections that could most benefit from improving their depiction of Antarctica will have a large and sudden jump in the scale along the parallels at 60 S.

[dchalker]

I was looking through my web page, when I noticed one projection I came up with there - with some inspiration from the Strebe projection, but based on Wagner VII -
would be a perfect candidate for improvement with your technique.

Cool, nice! If we can get an optimized illustration spun up, I'd be happy to feature the Quad-Wagner Continental Composite as an example of "a modified Wagner VII developed by Quad with the Chalker-Denoyer modification". You make it, you describe the specs, you name it, I'll include it. (Is quad Savard? Savard = quad? Is that right?)

While nice to have, it's debatable whether or not this property is essential.

It's not essential, imo. It's essential to offer that option, but not use it every time. I'm opening with something along the lines of "Insets may be sized according to the purpose and desired functionality of the composite", then listing the range of sizing options to consider and what each achieves. It only needs to roll at a 1:1 for certain applications, like printing on a cup or making a dual-display clock.

[Atarimaster]

While nice to have, it's debatable whether or not this property is essential.

Hmmm.
To me, this simply doesn’t work, not even in a artistic application. Because it feels like two unrelated maps – there is “no flow” (don’t know if it’s clear what I’m meaning here).

(Note: That is not the original asymmetric Wagner, but the approximation I presented a few years ago.)

[dchalker]

To me, this simply doesn’t work, not even in a artistic application. Because it feels like two unrelated maps – there is “no flow” (don’t know if it’s clear what I’m meaning here).

I understand what you mean. You need to be able to visualize the wrap, which is harder when the meridians don't match up. Aside from the meridians, though, I do think this is a visually nice-looking map (suitable for a classroom wall poster). I like that it shows the southern continents with less angular distortion than most other rounded maps I've seen. (That's why I use cylindrical from the equator down in my previous example, the Apian-Chalkerdome.) Maybe I'm biased bc I love the topology overlay, though. Beautiful, is that baked into the d3 starter kit or addon?

Ah! I see you also figured out where to comment out the border line; just found that as well. Looks like that was just drawing a duplicate border, because there's still a thinner main border after removing this.

Code: Select all

//.attr("stroke", "black")
//.attr("stroke-width", "1px");

[Atarimaster]

Beautiful, is that baked into the d3 starter kit or addon?

No, that image was composed in Geocart out two instances of the “generalized Wagner” and one of the azimuthal equal-area projection. But it should be able to do that in d3, as well.

[dchalker]

No, that image was composed in Geocart out two instances of the “generalized Wagner” and one of the azimuthal equal-area projection. But it should be able to do that in d3, as well.

Ah, got it! Finally figured out I can turn the borders off for compositing in Geocart, which is nice.

Apian-Chalker Continental Composite, aka the Chalkerdome

apianchalkertopo.png (691.54 KiB) Viewed 16234 times

You can double the size of Antarctica to roll it (or slide at double the rate of rotation).

I don't know how to search historical maps, but anybody seen anything like this? Elliptical top with cylindrical mid/bottom? I might have to name it after some predecessor, but idk.

Finally pulled the trigger on that Geocart license, in any event.

[PeteD]

Something's gone wrong. The scale along the central meridian in the equirectangular part looks greater than the scale in the Apian II part, which in turn looks greater than the scale in the azimuthal part.

You can double the size of Antarctica to roll it

No, you can't, because then you would double the scale along the meridians in the inset.

I've said it's debatable whether or not it's essential for the scale along the parallels to match on either side of the interruption, but with a base projection whose defining feature is true scale along the meridians, it's absolutely essential for the scale along the meridians to match.

If you want to roll the inset without sliding, then either the southern hemisphere of the base projection must be quite narrow or the interruption latitude must be much closer to the equator. There's no way around this.

[PeteD]

I think this is what you were going for:

Chalkerdome.png (122.2 KiB) Viewed 16256 times

[PeteD]

I don't know how to search historical maps, but anybody seen anything like this? Elliptical top with cylindrical mid/bottom?

The closest projection that I know is the Baker dinomic, which uses the Mercator between 45° N and 45° S. There's also Györffy A, where the middle section looks cylindrical but isn't quite.