Fast flow-based algorithm for creating density-equalizing map projections

Abstract

SignificanceGeographic maps are a popular means to visualize spatial statistics. Conventionally, each map region is displayed with an area proportional to the actual land area. But equal-area maps can grossly misrepresent demographic data: Densely populated cities should be given more prominence than large, but sparsely populated territories. Cartograms solve this problem by rescaling map regions in proportion to, for example, population or gross domestic products. Until now, it has generally been cumbersome or slow to calculate map projections for contiguous cartograms. Here we describe and benchmark a fast flow-based algorithm that computes cartograms in a matter of seconds, yet maintains the strengths of previous methods—a development which may lead to a more widespread adoption of cartograms.

Optimization-Based Construction of Quadrilateral Table Cartograms

“…Complex-shaped contiguous area cartograms, on which each region is of a similar shape to one on the geographic map, are rather difficult to construct. Up to now, there have been several studies proposing their construction methods [1,2,7,8,[17][18][19][20][21][22][23][24][25]. Among these, the most popular construction method is the diffusion-based method [7], whose mathematical guarantees its operability.…”

The Maximum Flow Problem

“…Gastner et al [30] proposed a flow-based approach having motion equations, which are numerically simpler to handle in comparison to the previous algorithms. This leads to direct parallelization in such a way the computation only consumes little time when handling detailed and complex data.…”

go-cart.io: a web application for generating contiguous cartograms

“…Cartograms are called "contiguous" if they maintain the topology of the conventional map (i.e. regions are displayed as neighbours on the cartogram if and only if they are geographic neighbours) [1]. An example of a contiguous cartogram, showing the 48 conterminous states of the USA with an area proportional to their population, is shown on the right of Figure 1.…”

“…In the past, publications that introduced new cartogram algorithms rarely included computer code. Some authors of more recent publications have posted their code online [1,2], but their software usually requires technical knowledge (e.g. about shell scripting, compiling, GIS) that pose insurmountable obstacles for most users.…”

“…After data are transmitted, a remote server calculates the cartogram transformation with the recently developed fast flow-based algorithm [1]. Because the calculation is entirely server-side, we eliminate any dependence on the client's hardware.…”