Cartograms and OpenStreet Map Data

OpenStreetMap data distorted using a gridded cartogram based on Voronoi polygons from pub centroid locations.
Rendered with Maperitive.

The original OpenStreetMap data for the same area with Mapnik rendering.

I've been fascinated by cartograms ever since I was a child. I think the first one I ever saw was the one shown below.

Cartogram of Parliamentary Constituencies in the United Kingdom around 1960
from Reader's Digest Complete Atlas of Britain and Ireland (1965) p. 133.
Source: Unkee E. on Flickr.

Consequently the recent availability of a plugin for generating cartograms in Quantum GIS meant that I just had to fiddle around with it. Although I like cartograms I like even more to see the detailed mapping distorted in the same way as the cartogram. There are many famous cartoons exploiting a distorted view of the world to make both humourous and serious points. (I recommend the excellent book called Mental Maps by Peter Gould and Rodney White for many other examples).

View of USA from 9th Avenue, a well-known New Yorker cover cartoon.
Source: Wikimedia.

As is traditional in this blog my starting point was locations of pubs. Pubs are distributed very unevenly being concentrated in the city centre and along major roads. They are therefore a fairly good way of enlarging the centre of a city in a cartogram. The other virtue is that there are not too many pubs: early experiments with the cartogram plugin showed that I had to be conservative in the data I used.

My first step was to create Voronoi polygons from the nodes representing the pubs. This is a simple operation available in Quantum GIS. In this way every part of the area under consideration was assigned to a single pub. by assigning an arbitrary area constant to each polygon and using this as the driver of the cartogram plugin it is very easy to produce a basic cartogram.

Voronoi polygons for pubs in central Nottingham.
The outline of the road network is shown to provide a little context.

However, my main goal was to distort ALL the underlying OpenStreetMap data in line with the cartogram distortion. To do this I overlaid a regular grid of squares 200 m on the side over the pub Voronoi polygons. These grid squares were then merged with the pub polygons so that each polygon was split into many smaller ones. An arbitrary area value was calculated for each (as a percentage of the original pub polygon) and scaled so no value was less than 1 (to avoid the plugin crashing). Once again a cartogram was produced, but this time a number of the vertices had known starting co-ordinates arranged in a regular fashion. Each smaller polygon was uniquely identified by a compound key made from the pub polygon and the original grid square.

Gridded Voronoi polygons as above, but with a 200m square grid added.

The basic cartogram derived from the gridded Voronoi polygons above.
Shading indicates all polygons corresponding to an individual pub.

With the basic cartograms created I imported them into PostGIS and then found the co-ordinates of all the vertices both in the original input data and the cartogram data. I filtered out only those co-ordinates which were at the vertices of the original grid squares and calculated simple X and Y offsets for each of these points. The offsets could then be applied to all points in the standard node table of an Osmosis snapshot schema. (I added a very simple interpolation of X and Y co-ordinates within each grid square as well). In practice I carried out all operations in the British National Grid (EPSG: 27700) and then converted back to WGS84 at the final step.

Finally I extracted the (distorted) data from my snapshot schema and stored it in the OSM XML format. To render the modified data I used Maperitive which is pretty much perfect for this purpose. The final result is shown at the head of this blog entry.

I leave it as an exercise  for the reader to find any useful purpose for this process!