Abstract
Cartograms are popular for visualizing numerical data for administrative regions in thematic maps. When there are multiple data values per region (over time or from different datasets) shown as animated or juxtaposed cartograms, preserving the viewer's mental map in terms of stability between multiple cartograms is another important criterion alongside traditional cartogram criteria such as maintaining adjacencies. We present a method to compute stable stable Demers cartograms, where each region is shown as a square scaled proportionally to the given numerical data and similar data yield similar cartograms. We enforce orthogonal separation constraints using linear programming, and measure quality in terms of keeping adjacent regions close (cartogram quality) and using similar positions for a region between the different data values (stability). Our method guarantees the ability to connect most lost adjacencies with minimal-length planar orthogonal polylines. Experiments show that our method yields good quality and stability on multiple quality criteria.
Highlights
M ANY datasets are georeferenced and relate to places or regions
We focus on Demers cartograms (DC) [5] which represent each region by a square whose area exactly matches the data value, similar to Dorling cartograms [6]
The results show that our linear programming (LP) efficiently computes stable DCs; see Figures 1 to 3 for example DCs computed by our method using the recommended default setting
Summary
M ANY datasets are georeferenced and relate to places or regions. A natural way to visualize such spatial data is to use cartographic maps. While choropleth maps work well for data that correlates to region sizes, when the data is not correlated it has the drawback that the visual salience of large and small regions is unequal. It is difficult to compare colors to each other, and colors are not the most effective encoding for numeric data [1], requiring a legend to facilitate relative assessment. One way to overcome these drawbacks is with cartograms, which reduce spatial precision in favor of clearer encoding of data values: the map is deformed such that each region’s visual size is proportional to its data value. The visual salience of a region correspond to its data value, and comparison of magnitudes becomes a task of estimating area – which is a more effective encoding for numeric data [1]. Preservation of relative directions: spatial relations such as north-south and Manuscript received April 19, 2005; revised August 26, 2015
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