SMBC Takes the Mercator Projection into Its Own Hands

SMBC: Mercator
From “Mercator”, SMBC, 24 Feb 2020.

Saturday Morning Breakfast Cereal’s take on the Mercator projection is … not what you’d expect. The punch line is similar to Christopher Rowe’s short story, “Another Word for Map Is Faith”: if you can’t make the map conform to the territory, make the territory conform to the map. Since we’re dealing with the Mercator projection, this requires some … escalation.

Mapping the Canadian Election Results: Technical Details

Bothered by the widespread use of Web Mercator by Canadian news outlets to show last week’s election results, Kenneth Field has posted an article that aims to address the problem. Static maps of Canada tend to use a conic projection like the Albers or the Lambert, and that’s the case for print election maps as well. Online interactive maps, on the other hand, use off-the-shelf tools that use Web Mercator, which results in the sparsely populated territories looking even more enormous. But that doesn’t have to be the case, says Ken, who shows us, with a few examples, how use ArcGIS Pro to create interactive maps using a conical projection.

Meanwhile, Mark Gargul writes in response to Ken’s critique of his cartogram of the election results. Mark describes himself as an amateur and readily admits that other cartograms are “clearly more aesthetically pleasing. On the other hand, I was going for something different with my cartogram—specifically, to try to preserve riding-adjacency as much as possible.”

The other thing Mark was going for in his cartogram was to indicate the urban-rural split: metropolitan areas are given a black border: it’s easy to see which ridings are in Montreal or Toronto; seats that are partially urban and partially rural straddle those borders.

So it’s doing several things at once that may not be immediately apparent.

Previously: A Cartogram of Canada’s Election Results; More Canadian Election Maps.

More Canadian Election Maps

I hit “Publish” too soon last night. Kenneth Field and Craig Williams put together a series of maps showing the Canadian election results in a number of different ways: we have a value-by-alpha map, a proportional symbol map, and two kinds of dot density maps: one showing the winners, one showing all votes per constituency. (One dot equals 100 votes; the dots are spread evenly across constituencies, even when people aren’t. You can’t have everything.) And it’s on the Lambert, not the Mercator.

Speaking of the Mercator. Maps Mania’s roundup of Canadian election results maps notes that the Canadian media’s interactive maps (e.g. CBC, Global, Globe and Mail) invariably resorted to Web Mercator, largely because of the mapping platform used. (In-house infographics team? Don’t be ridiculous.) Web Mercator is singularly bad for Canadian election maps, because Nunavut: it’s the largest electoral district by area (1.9 million km2) and the smallest by population (31,906). It’s enough of a distortion on the Lambert: Mercator makes it worse.

As for cartograms, Ken hated the one I posted last night; Keir points to Luke Andrews’s Electoral Cartogram of Canada, which is a bit nicer, and uses only one hexagon per riding instead of seven. Keir also points to this animation that shifts between a geographical map and a cartogram. It’s hard to recognize Canada in cartograms, because it’s difficult for us to grasp just how many people live in southern Ontario.

Previously: A Cartogram of Canada’s Election Results.

Everything’s Coming Up Spilhaus

John Nelson

John Nelson reports that the Spilhaus projection will be supported in the next version of ArcGIS—version 2.5, to be released in a few months. This odd projection, which centres Antarctica on a world map showing the oceans as a single, uninterrupted body of water; went viral last year. Requests for ArcGIS support soon followed. Thing is, ArcGIS support requires the math behind the projection: figuring out that math took some sleuthing. The Spilhaus is, it turns out, basically an oblique aspect of the Adams World in a Square II projection.

Previously: About the Spilhaus Projection.

A Map Projections Roundup

Three things make a roundup. Here we go:

Here’s a gallery of all 68 map projections supported in ArcGIS 10.7.1 and ArcGIS Pro 2.4, from Bojan Šavrič and Melita Kennedy. Some interesting projections included here, some of which are only suitable for a specific region (such as the complex New Zealand map grid). No Gall-Peters, interestingly.

Chris Whong

Chris Whong uses a clementine as a substitute for Tissot’s indicatrix: “I found myself eating a clementine this morning, and thought it would be interesting to slice up the orange peel on an 8×8 grid to visualize how much of the earth’s surface is represented in WebMercator tiles at zoom level 3. This is kind of an inverse of the Tissot’s Indicatrix above, showing chunks of the spheroid’s surface over the projected tiles that represent them in web maps.”

Alberto Cairo’s short piece arguing that the Mercator projection isn’t a monstrosity doesn’t cover particularly new ground: the Mercator was created for a specific purpose (bearing-based navigation) and is a good choice for small-scale maps, but it has no business on a world map. But it’s probably worth reiterating, since I still see over-the-top condemnations of the projection on colonialist grounds, channeling Arno Peters (which, you know: not new).

Equal Earth Physical Map

On Sunday Tom Patterson announced that the Equal Earth Physical Map is now available for download in JPEG, Illustrator and GeoTIF formats. Unlike its political counterpart, no territorial boundaries appear on this map (though cities do). Not having borders doesn’t mean that Tom and his collaborators won’t get into trouble with the names of natural features, though: I note they use Sea of Japan rather than East Sea, for example (see above). But, importantly, they’ve released the map into the public domain: if you don’t like their labels, or their choice of cities or colours or textures, you can make changes to the map and put out your own version.

Previously: Equal Earth Gets a Wall Map.

Equal Earth Gets a Wall Map

It was announced today at NACIS that the Equal Earth projection is now available as a wall map—which is a necessary thing if it’s going to go toe-to-toe with the Peters map. The political wall map is only available as a download (three versions, centred on Africa and Europe, the Americas, or the Pacific): the 19,250 × 10,150-pixel, 350 dpi file results in a 1.4 × 0.74 m (55″ × 29″) print—assuming you have access to a large-format plotter. Not everyone does, so it’s only a matter of time, I suspect, before they have prints available for sale.

The map shows countries and territories in surprising detail (it includes Clipperton, for example); and while it does show disputed regions as such, its choices of boundaries and nomenclature won’t make it many fans in South Korea or India.

Previously: The Equal Earth Projection; Equal Earth Updates; More on Equal Earth.

About the Spilhaus Projection

Le Cartographe

This image went a bit viral earlier this week. Some context. It’s from an August 2015 blog post at Le Cartographe, in which Alexandre Nicolas discussed (and rendered, above) a projection produced in 1942 by South African oceanographer Athelstan Spilhaus. In Spilhaus’s oceanic projection, centred on Antarctica, the world’s oceans form a single, uninterrupted body of water. Which, you know, it is. The continents form the edges of the map; there is … some … spatial distortion. As Alexandre wrote in 2015, “This projection is rarely used and it’s a real shame!”

Previously: The Penguin Projection (speaking of Antarctica-centred projections).

More on Equal Earth

Equal Earth projection in colour

The Gall-Peters projection is a second-rate projection with first-rate public relations; cartographers’ responses to the projection that focused on its cartographic shortcomings ended up missing the point. Something different is happening with the Equal Earth projection, which was announced last month as a response to Gall-Peters: an equal-area projection with “eye appeal.” It’s getting media traction: the latest news outlet to take notice is Newsweek. So, finally, there’s an alternative that can be competitive on the PR front, without having to mumble something about all projections being compromises until the eyes glaze over.

It’s turning up in GIS packages, too: in D3, in G.Projector and in proj4. There’s even a t-shirt.

Previously: The Equal Earth Projection; Equal Earth Updates.

The Equal Earth Projection

In 2014 cartographer Tom Patterson and his colleagues, Bojan Šavrič and Bernhard Jenny, introduced the eponymous Patterson projection, a cylindrical projection that reduced polar exaggeration while maintaining the familiar shape of continents.1 Patterson, who recently retired from the U.S. National Park Service, has teamed up with Šavrič and Jenny to produce a new projection: the Equal Earth projection.

This projection can be seen as the cartographer’s response to the Peters map: in fact, the team created it in reaction to the furor over the Gall-Peters projection being adopted by Boston public schools. “Our message—that Gall-Peters is not the only equal-area projection—was not getting through,” the authors wrote in the International Journal of Geographical Information Science (mirrored here). “We searched for alternative equal-area map projections for world maps, but could not find any that met all our aesthetic criteria.” Citing their own research into map readers’ projection preferences, they decided against projections like the Eckert IV, Mollweide and sinusoidal and opted to make their own: “a new projection that would have more ‘eye appeal’ compared to existing equal-area projections and to give it the catchy name Equal Earth.”

The end result is a Robinson-like pseudocylindrical projection that nevertheless preserves area—and, like the Robinson, is nicer to look at than a cylindrical equal-area projection like the Gall-Peters. It’s actually kind of impressive that they were able to square that particular circle. The article details their decision-making process and the math behind the projection and is worth a read. It’ll be interesting to see whether this map gains any traction. I wish it well.

Previously: The Patterson Projection; The Peters Projection Comes to Boston’s Public Schools; The Peters Map Is Fighting the Last War; More on Boston Schools and the Peters Map; The 74 on Boston Schools and the Peters Map.

New (17 Aug): Equal Earth Updates.

Google Maps Switches to 3D Globe at Small Scales


Web mapping uses Web Mercator. As Kenneth Field points out, this is fine at large scales, but at small scales you end up replicating the problem of using the Mercator projection on a wall map of the world.1 Zoom out in Apple Maps: using the map layer you get a Mercator; using imagery you get a virtual globe (basically, an orthographic projection you can spin). Ditto in Google Earth. But Google Maps, after some tests and starts, now does this in its map layer—and not just in Chrome, either. This means, among other things, that Antarctica is usably visible, as are the Arctic regions—and, of course, Greenland is its proper size at small scales.