Projection Connections: A Very Nerdy Poster

Friends, I’m excited to offer to you a new poster. Not a map this time around, but something map-related. A 16 × 24-inch tangled web showing how 100+ different map projections are all related to each other:

Click for a full PDF download. Note that this file may be updated if corrections are needed, so check back!

Projections are a niche topic even among cartographers, so I don’t exactly expect this to go viral. However, I do believe that it has value as an educational tool, and can serve as a nerdy addition to your classroom, office, or GIS lab. I’m offering the PDF to download on my usual pay-what-you-want basis. Grab it, have a look, and if you can, consider sending some support my way via the buttons:

The best support you can give is to spread the word, and tell more people about this project. A nerdy, niche effort like this needs help to connect to the people who will most appreciate it.

Now that we’ve gotten the poster into your (virtual) hands, let’s talk about the details.

Background

I suppose the theme of my side projects this year has been projections. First there was the set of Projection Collection trading cards (sold out, sorry), then my deep dive into the Fuller Projection, and now this. I’ve always been fascinated by projections, and it was a favorite topic to cover when I was an instructor. Nonetheless, I’m no mathematician, so my understanding of how they work, and how they relate to each other, is mostly rooted in analogy and hazy recollections of high school trigonometry.

That brings me to sources. I didn’t figure any of this stuff out; I just collected and organized it. Most of what you see on the poster is derived from just a few places. First off there’s the documentation for G.Projector, a NASA tool that deals in a wide variety of obscure projections. And then there’s the documentation for daan Strebe’s excellent GeoCart, which is another piece of heavy-duty projection software that goes beyond what you find in Arc or QGIS. Side note: I did a livestream a few months ago about GeoCart if you want to see it in action. Then there’s Snyder & Voxland’s An Album of Map Projections (which daan Strebe also draws from a lot). And finally, a few leads came from Wikipedia.

I first learned about a couple of these connections several years ago. I don’t quite remember how or where, but I found out that the Mercator projection was equivalent to a Lambert Conformal Conic with the standard parallels set opposite each other across the Equator. And that if you moved both those parallels up to a pole, you got a Stereographic. My mind was suitably blown, and I saved it as a fun fact to share with people. This year, while working on The Projection Collection, I spent a lot of time on daan Strebe’s site looking up details, and I often saw his notes (usually derived from Snyder/Voxland) about how projections were related to each other. I started to realize there were a lot of these connections out there, and I thought it might be fun to diagram them in some way.

Design

This is, I think, my first non-map poster. Almost all of my design work is cartographic, but I’ve appreciated the chance to explore a new space, even if my efforts were graphically simple. And, originally, it started a lot simpler. My initial rough draft had only about ¼ of the content.

Colleagues like Fritz Kessler pointed me in the direction of many more connections that I had missed, and I started putting in the hours of research to track down as many of these things as I could find. I just started haphazardly throwing projections onto the chart, with the understanding that I would clean things up later. A month later, I had this chaotic tangle:

Now it was time for organizing all the lines into something that could reasonably be followed by a human eye, which was maybe the most laborious part of the project. There was a lot of trial and error, not only of where to put things but also how to style connections. I originally wanted the sort of flowing, curvaceous lines that I’ve used in several other projects. But, attempts at that weren’t working out very well (I don’t even have any draft images to share; that’s how quickly I abandoned that idea). Instead, I did a simple grid with 90° angles. It was just much easier to get my head around and permitted me to take on the task of disentangling this web.

In my rough draft, everything had been top-to-bottom. Lines connected to the top of each rectangle and exited at the bottom. But, for my expanded draft, I abandoned that. There were just so many connections to be made that I let them flow in any direction. This was very helpful in minimizing the number of places where one line crosses another (I got it down to just one!).

You all probably know by this point how much I love working in monochrome, so that’s what I stuck with for this one. I admit that if I’d color-coded the lines, rather than using different patterns, it would probably be a little easier to read. But, since I wasn’t making anything critical (or that someone hired me to do), I thought I’d have fun with it at the expense of a little functionality. Also, I’m really pleased with the hatched shadow underneath the rectangles.

Because connections could flow in any direction, arrows were needed, and I spent at least half a day poking at designs for those. Originally, I experimented with arrows that appeared only occasionally along the lines.

I initially settled, somewhat halfheartedly, on that first example, with the big gaps. I put them all in place and declared my draft finished. I was still a little unsatisfied, but it was time to be done with this.

Then I went back and did a final check on everything to make sure it was correct, and I found a couple of places where I needed to show two kinds of line at once. For example, the Briesemeister uses both a particular set of parameters for the Hammer, and also involves stretching it. I struggled with how to cleanly show two patterns at once (it would have been a lot easier with color!), before stumbling on the idea of enclosing the patterns in chevrons, which, for Briesemeister, I could just alternate. This solved my problem, and also left me with an appearance that I liked much better overall for every line. It was both more pleasing and more readable.

I applied the effect in Illustrator using pattern brushes. I also manually adjusted the lines in many areas to get the chevrons to line up more attractively.

Finally, I spent a while carefully setting up knockouts at places where lines overlapped each other, or where they overlapped the striped pattern.

Final Notes

I’m pretty pleased with the outcome, and I hope you find some use for it, entertainment or otherwise. I recognize that it does not have a lot of practical mapmaking value. It doesn’t tell you anything about when/how to use any of these projections. And in any case, most of these projections are quite obscure, while some more popular projections (Robinson, Equal Earth, etc.) aren’t on here (because they’re not obviously connected to another projection).

But, I think it’s useful for piquing our curiosity and getting us to dive deeper into the fascinating world of projections, which for many of us are mysterious tools that we use every day without really understanding. It would be a thrill to see this make its way into a class (virtual or physical) somewhere.

5 thoughts on “Projection Connections: A Very Nerdy Poster

  1. Thanks so much! There’s a legend for the lines in the upper-right. They signify different categories of derivations.

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