Chalker Continental Composites

[quadibloc]

I was going to introduce him to the free program G-Projector that he could use.

G.Projector is good at showing the basic forms of many projections, but it doesn't have the sort of customizability to create arbitrary interruptions/insets, unless you do your own postprocessing in an image editing program (which is going to handle some things poorly, like borders).

Hey, I didn't even know that Geocart could do this. Particularly the trial version.
And G-Projector doesn't do elliptic integral projections, particularly not the advanced ones like the Cox projection which are based on the Dixon elliptic functions.

[dchalker]

All good, thanks! I appreciate the criticism. "Transformation", "interruption", "formalized arrangement" - I'm happy to call the method whatever you like, or whatever implementation it takes in the software should devs choose to add it. I appreciate the examples of adjacent ideas and concepts, but I do maintain that there are some key novelties of this method (shared boundary at 60°S + alignment of the meridians) that differ from any example I've found (UNTIL that Denoyer-Geppert example just posted by quad...), which ensure one contiguous composite with proper spatial placement (critical for applications like the game design use posted above). (Also using Florence meridian to prevent "cutting" continents with the antimeridian, though I suppose that's optional, it might be worth adding that additional detail to the definition of the method.) AFAIK, none of them (including Denoyer-Geppert) have generalized the method for wider use. (And I have more formal work to do in that area myself, writing the paper and defining precisely how to scale the transformed/interrupted portion for different cases.)

As far as the resulting maps go, it is technically true that the composite maps produced are not pure "projections". It makes no difference to me whether the map is called the Chalker-Peters projection or the Chalker-Peters composite. I developed the method and I applied the method to create specific implementations, and I named them. By what standard can GGV be named a projection/composite named after its creators/influencers, but these can't? I am not pursuing any form of copyright or trademark or licensing anything (as suggested above) and regard these ideas as free to the public. (Projections are mathematical concepts anyway, there is no "plagiarism" involved - particularly when the original name of the base projection is preserved.) Anyway, I don't care who acknowledges my contribution or not. Nobody is obligated to use my name. I've done work in other fields anonymously without using my name and people critique that, too, so I decided to attach my real name to this project.

[daan]

By what standard can GGV be named a projection/composite named after its creators/influencers, but these can't?

Of course you are free to do as you see fit. However, Goldberg et al were roundly mocked for their “innovation”, and not just by this forum’s members. See, for example, the critique by cartographic giant Matthew Edney.

Cheers,
— daan

[dchalker]

Looks like Matthew Edney is correct to criticize the overselling of GGV as something "radically new" and revolutionary. I generally agree with those critiques. As far as I see, he doesn't appear to question their right to name their own method or their own map configuration. I'll be careful to avoid overselling this as some revolutionary innovation, and to use the term "composite projection" to avoid offending those with stringent technical definitions. Those are all good points, thank you.

And I've just noticed you are the creator of the software, daan, so thank you again. It was easy to pick up and quickly create exactly what I was imagining in my head with no training or special knowledge. I do hope you are interested and able to implement the Chalker "interruption" as a feature (including Florence meridian for best effect!).

[PeteD]

Welcome to the forum! I'm sorry your first posts here were met with sarcasm. I'll try to keep any criticisms that I have constructive.

AFAIK, none of them (including Denoyer-Geppert) have generalized the method for wider use.

Perhaps not, but given its use with the Denoyer projection, it seems fairly obvious to apply this interruption scheme to other projections that also don't depict Antarctica very well.

Also using Florence meridian to prevent "cutting" continents with the antimeridian, though I suppose that's optional, it might be worth adding that additional detail to the definition of the method.

It's well-known that all these projections can use the Florence meridian or even more optimal central meridians in order to avoid cutting through the Chukchi Peninsula. I don't think specifying the Florence meridian would contribute to the inventiveness of your interruption scheme.

However, while I don't think it's particularly inventive, I have to say that I do rather like your interruption scheme! I think it may have been better received if you hadn't used the terms "projection" or "transformation" to describe it.

[dchalker]

Thanks, Pete. I agree 100% it "seems obvious". I've been baffled nobody was doing this already, like why is everybody just ok with Antarctica being a long rectangle if the solution is so obvious? I searched and couldn't find any examples of this method before (and I do appreciate being corrected). Due to that pre-existing example, it's really the combination of these two operations (Meridian change *and* azimuthal inset) that make these "composite projections" unique. The Meridian change is essential to the applications (games & art), and that's where my focus is.

I don't disagree with the case presented for 11.55°E, but I have enjoyed entertaining the idea of an antimeridian monument on St. Lawrence.

[quadibloc]

However, Goldberg et al were roundly mocked for their “innovation”, and not just by this forum’s members. See, for example, the critique by cartographic giant Matthew Edney.

The National Geographic map mounted on pivots was a nice touch; I remember it from when I first read that book in my local public library.
But I also remember, I think from Deetz and Adams, an account of a similar idea which had an advantage over that.
Instead of using the Azimuthal Equidistant, the inventor used the conic conformal projection, with standard parallel 30 degrees, and duplicated the projection twice to make it fill the circle.
Rotating disks were placed one above the other, with the Northern and Southern hemispheres so projected, so that one could turn the disks to make a map of any part of the world one liked with North at the top! (EDIT: This was due to Commander A. B. Clements, of the U. S. Shipping Board, and indeed it was in one of the editions of Deetz and Adams.)

Goldberg et al deserved the mockery that came their way, but one can note, in their defense, that maps in the projection they described tended not to appear in atlases very often - even maps showing the Eastern and Western hemispheres had gone out of fashion.
So without extensive research, they might well have thought their idea new. Rather than mocking them for their failure to do a more comprehensive literature search, I think they mainly deserved mockery for thinking that their projection was a good idea.
But then, I came up with this kind of map, and I thought that it was a good idea:

although since taking the conic conformal, and putting it in a transverse aspect are both well-known things, I did not claim a great deal of originality.
Of course, its sneaky idea was this: some people will turn up their noses at interrupted projections, but will accept dividing the globe into Eastern and Western hemispheres. What I did to keep areal distortion within limits in this conformal projection was to recognize that a cylindrical projection has to be "interrupted" at one meridian, and so I felt that I had the liberty to sneak in one interruption in each hemisphere which would also be legitimately characterized as being at the limits of the area mapped, and thus legitimate and not a "real" interruption.

[Milo]

Thanks, Pete. I agree 100% it "seems obvious". I've been baffled nobody was doing this already, like why is everybody just ok with Antarctica being a long rectangle if the solution is so obvious?

I find these arrangements to be rather ugly. They portray Antarctica as separate enough that it's hard to tell its relationship to the rest of the world (of your examples, only the Chalker-Lagrange comes even close to showing where Antarctica lies relative to Australia, and it still doesn't do a particularly good job of that, plus the massive distortion of Alaska makes focussing so much onto portraying Antarctica, specifically, correctly into a joke), yet attached enough that it gives the whole thing a weird shape. People are comfortable with maps that look like rectangles or circles. A circle hanging off a rectangle? That's just awkward. And why the central meridian? If I had to choose just one meridian to attach Antarctica, I would go with where it comes closest to linking up with another continent: South America.

Your video game map isn't doing quite the same thing. It is quite clearly treating the Antarctica inset as being square, not circular like all of your high-resolution examples. (Or, quite, possibly, you took the circular inset and padded it into a square by adding some fictitious water, which I suppose isn't going to stand out by the standards of a low-res video game map, but still isn't particularly accurate.)

For most purposes it's better to do as atlases have always done: have a world map that shows the entire world contiguously, even if some of it is distorted, and then put whichever part you necessarily compromised on (probably Antarctica) in a separate map for the rare cases that people actually care what it looks like. Alternatively, polyhedral maps allow you to split the world into "parts" with locally low distortion that also carry over into each other smoothly. The Peirce quincuncial projection, for example, looks quite good everywhere (including Antarctica) except for four discrete singularity points in the middle of the ocean, and it wraps around in a way that is quite convenient for video game use (as well as more "serious" numerical simulations). The math on that one can be a bit fiendish, and conformal projections aren't ideal for many applications, but I'm trying not to be too blatant about plugging my own invention... aww, dammit.

Of course you are free to do as you see fit. However, Goldberg et al were roundly mocked for their “innovation”, and not just by this forum’s members.

In that thread, I also already floated the idea of attaching cylindrical and azimuthal projections together, although I suggested doing so for both poles.

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 such that the lengths of the cutoff parallel on the cylindrical map and the azimuthal one are equal, and they connect smoothly. (For example, look at the Chalker-Peters map, and observe how the spacing between parallels suddenly changes suddenly and dramatically between the two components.)

For equal-area projections, for example, you get "cutoff_parallel = asin(1-cos(standard_parallel)^2/2)". For equidistant projections, you get "cutoff_parallel = pi/2-cos(standard_parallel)".

In both cases, any reasonable implementation (i.e., the cylindrical part doesn't look hideously ugly) would end up with the cutoff being far closer to the equator than 60°, therefore passing through continents rather than just the southern ocean. This makes sense: even the strip between 30°S and 30°N already covers 50% of Earth's surface, so expecting the cylindrical component to get a much bigger share than that is just greedy.

Goldberg et al deserved the mockery that came their way, but one can note, in their defense, that maps in the projection they described tended not to appear in atlases very often - even maps showing the Eastern and Western hemispheres had gone out of fashion.
So without extensive research, they might well have thought their idea new. Rather than mocking them for their failure to do a more comprehensive literature search, I think they mainly deserved mockery for thinking that their projection was a good idea.

Even if nobody has done the exact same thing as you before, if it's still very similar to long-known techniques, then you're not being all that original. If you just want to devise a cute new map projection? Fine. If you want to claim that you're actually solving a problem previous mapmakers have struggled with? Better make sure it's not a solution that those previous mapmakers were perfectly aware of, but chose not to use because of obvious flaws.

[quadibloc]

Even if nobody has done the exact same thing as you before, if it's still very similar to long-known techniques, then you're not being all that original. If you just want to devise a cute new map projection? Fine. If you want to claim that you're actually solving a problem previous mapmakers have struggled with? Better make sure it's not a solution that those previous mapmakers were perfectly aware of, but chose not to use because of obvious flaws.

I certainly wasn't trying to say that originality is unimportant.
The way I was thinking about it was like this:
The "new projection" those people had come up with indeed isn't one that you usually see in atlases today. Most of the examples shown of it were really old ones.
So they missed them because they failed to look harder. That's a fault on their part, sure. But it seemed to me they had a bigger fault... which explained why they didn't look harder, too.
They claimed that their "new projection" was revolutionary, that it lowered distortion compared to other projections.
If it really was that good, then if someone had invented it before, we would be using it all the time, wouldn't we?
But the notion that it had lower distortion than anyone else had ever achieved... that was so preposterous as to be laughable. Compared to that, their failure to realize it was done before back in the 15th century or whatnot seemed to me to be small potatoes indeed.
However, that doesn't mean that projecting the world as two hemispheres is useless. I can think of a very good application for it.
This thread began with the illustration of the Chalker Transformation being applied to the Peters projection. This has inspired me to devise what I shall modestly call the Chalker-Savard Transformation.
It consists of two steps:
Replace the Western Hemisphere of a projection by an azimuthal projection.
Replace the Eastern Hemisphere of a projection by an azimuthal projection.

cst.jpg (88.4 KiB) Viewed 5853 times

Here is the Peters Projection, after applying the Chalker-Savard transformation. Clearly, it's an improvement!

[dchalker]

To be clear: you are saying that this procedure (interrupt at 60S, contiguous azimuthal projection below, Bering antimeridian, rotating Antarctica to the new meridian, and scaling the two parts to match) and the entire class of new and useful composites produced by it with distinct and desirable characteristics lacked by other maps are insufficiently original to warrant a formal paper and description? I should stop writing and just walk away?

No.

I get that it is simple. I get that the steps are not original. The combination of steps is and the generalization to produce a whole new class of composites is. The formal scaling method will be (just eyeballing it for these examples). Consider the basic Chalker composite projection, nothing more than a simple cylindrical projection with the Chalker interruption. Simple, yes, but nobody else is doing that. I made it; I named it. Who do I share credit with? Marinus of Tyre and al Biruni, I guess. Other than those two people, yes, if I ever discover some other obscure historical example of the Chalker composite, then I'll happily acknowledge the earlier name. I don't know if Denoyer originated the method (contiguous azimuthal interruption), or copied it from someone earlier, but he did show using it with different meridians, so "Denoyer interruption" is fine if that's what devs call the thing, I don't care, but the composites I create (with the special feature of no continental interruptions) are still my novel composites I get to name.

Chalker-Peters was the first I showed because Peters agreed with me regarding the Bering antimeridian, and the scaling works best with equal area so that the cylinder rolls up and Antarctica wraps under, a perfectly sized circle for the bottom. I'm using one as a penholder now. My game map works (and came long before any of these Geocart sketches, which I just threw together for the sole purpose of sharing my idea with anybody else who wants to use it). I've designed an awesome logo that I plan to use ingame. You can find my process aesthetically distasteful or unoriginal, that's fine. It still works. It still makes useful things that afaik didn't exist or weren't formally described before (and didn't have names yet), which I am now implementing in multiple areas. They have functionality, which does not require third-party approval. Nobody is forcing you to like the maps or use them, only inviting you to.

Federation of Earth logo (Chalker-Cox triangle, N boundary at 89N)

chalkercox89.jpg (104.05 KiB) Viewed 5848 times

quad, that "Chalker-Savard" illustration doesn't apply the Chalker interruption at all! To use the Chalker name, ya gotta cut off those two projections at 60S and put an azimuthal Antarctica. I think that'd look quite nice, especially with the right meridian. The point is to keep the continents whole. It should look more like the Chalker-Lagrange.