11.7 Coordinates

The most popular types of charts employ Cartesian coordinates. The same real tuples in the graphs underlying these graphics can be embedded in many other coordinate systems, however. There are many reasons for displaying graphics in different coordinate systems. One reason is to simplify. For example, coordinate transformations can change some curvilinear graphics to linear. Another reason is to reshape graphics so that important variation or covariation is more salient or accurately perceived. For example, a pie chart is generally better for judging proportions of wholes than is a bar chart ([35]). Yet another reason is to match the form of a graphic to theory or reality. For example, we might map a variable to the left-closed and right-open interval $[0,1)$ on a line or to the interval $[0,2\pi)$ on the circumference of a circle. If our variable measures defects within a track of a computer disk drive in terms of rotational angle, it is usually better to stay within the domain of a circle for our graphic. Another reason is to make detail visible. For example, we may have a cloud with many points in a local region. Viewing those points may be facilitated by zooming in (enlarging a region of the graphic) or smoothly distorting the local area so that the points are more separated in the local region.

[43] contains many examples of ordinary charts rendered in different coordinate systems. A simple example suffices for the data in this chapter. Figure 11.12 shows a transposed version of Fig. 11.7. The result of this coordinate transformation (a rotation composed with a reflection) is to make the city names more readable.

Figure 11.12: transpose(city $\ast$ (pop1980 + pop2000)), ylog