Douwe Osinga's Blog: WorldSizer

Friday, October 21, 2016

When I was 11 or so, I saw my first Times World Atlas. I was blown away. It was so much better in every way compared to the school atlas I was used to. The maps were huge, detailed and beautiful. The thematic maps and diagrams visualized everything from land use to economy to desertification.
Countries resized to reflect their populations

These days, with Google Maps and data visualizations of every type, you don't hear so much about atlases other than that people cut up old ones to sell the individual maps as wall decorations. There was one type of visualisation in the Times World Atlas that impressed me very much that I haven't seen online though: resized countries.

The idea is that you change the size of a country according to some statistic while trying to minimize the overall distortion of the map. As a kid, I wondered how you would calculate this - now I am pretty sure they just had an artist do their best. It is therefore with some pride that I am publishing an algorithm here to do something similar online: WorldSizer.

It's a two step process. The first, offline step takes the country data from the CIA Factbook and the shape information from Natural Earth. The CIA data is nice, because it is more evenly edited than, say, Wikipedia, but does need some massaging. Especially the country codes used by the CIA are seen nowhere else. One wonders if this has ever led to the wrong government being thrown over in a small Latin American country.

The shape files from Natural Earth have one or more shapes per country. The first step is to apply an area preserving projection to the shapes. Resizing a mercator map according to population would only cause confusion since it would still show India too small and Canada too big. The next step replace the points of the shapes with list of indexes into a global list of points. Here we also try to make sure that points on shared borders are only stored once. Since now points on borders are shared, we modify the shape of one country, it will also modify the shape of the other.

The online step takes the output of this and allows the user to pick a measure that the world will be "resized" to. For each country, we calculate the deflation or inflation factor needed to reflect the chosen measure. Then in an iterative process, we calculate for each shape how far the current area is off from the target area. If the shape is too small, all points of the shape are pushed away from the center, if the shape is too big, they are pushed towards the center.

For islands, this is enough. For countries that share borders, a tug of war process plays out. Especially in a region where all shapes need to grow or shrink, it takes a while for things to stabilize. Each shape also tries to maintain its original shape - for example, if you look at the map for population, you see India grow and sort of fall out of Asia as a blob before regaining its normal shape (only much bigger).

The shared borders and the country shape maintenance keep continents mostly in shape, too. But without extra care, islands will just drift into the mainland or each other. We stop this from happening by calculating "bridges". For each island, we look for a larger land mass nearby and anchor it to it. This keeps Ireland next to Great Britain, Great Britain next to France and Sri Lanka close to India.

Finally, we create some bridges by hand. Neither Spain nor Morocco are islands, but we'd still don't want them to crash into each other. Similarly, we attach Yemen to Somalia, Australia to New Zealand and Sweden to Denmark. In some situations this still leads to overlap. If you use proved oil reserves as a measure, the Middle East of course increases in size by a lot. But it has nowhere to go, so it pushes into the Mediterranean and squashes Syria into Greece.
More sad: scaled to number of people living with AIDS
One could add more bridges to force more map preservation, but this does come at a cost. The more forced the map, the less freedom the model has to preserve the shapes and get to the target sizes and it starts to behave more and more like a water balloon where you squeeze on one side and it just bulges out on the other.

As usual the source code is on GitHub. It should be fairly straight forward to use the worldsizer.js on another website with different data.