Volume visualization - The Visualization of Spatial Social Structure - page 259

To see this space we could again resort to time-slices, in this case taken from
an animation showing the development with one frame for every month in the
period. However, with only a few hundred cases, more elaborate software can be
employed where the spheres are actually placed in an abstract three-dimensional
space and a camera is flown around it, recording the views of specific interest
(Figures 9.9 and 9.10). Again these are shown here as individual frames, but no
longer time-slices, as they were taken at an angle through the block and show an
image looking into it, obscured only when cases are eclipsed by one another. 7
As can be seen in the illustrations, the cases are very evenly spread in population
space (Figures 9.11 and 9.12).
The actual space in which we place the cases is a very important consid-
eration. A simple Euclidean space has only been used here to show how that
image differs from a more useful one obtained when a more appropriate two-
dimensional population cartogram is used. Determining the relationship between
time and space is not simple. Here it was somewhat arbitrarily chosen to make
one year equal to twenty-five kilometres, or the square root of three hundred
thousand people.
The idea of a physical distance being proportional to the root of the number
of people makes sense as soon as you imagine area, distance squared, being
proportion to the number of people, as on a population cartogram. Next you
have to think of every person's life having equal volume, not their presence
having equal area, and time is included where the relationship between people,
time and space has then to be formulised.
The distribution of the childhood population at risk from leukaemia hardly
altered over the 1966 - 1983 study period (Figure 9.13). A more thorough study
would have to consider carefully the construction of a volume cartogram, in
which every life was equal and placed as close as possible to those with whom
it shared life, as well as being near their immediate ancestors and offspring (if
any). The relationship between time and space would depend on how far and
how frequently people tended to move in their lives.

9.4 Three-dimensional graphs

We need to be able to tell which three-dimensional subspace of the
Euclidean data space we are looking at. We also need to see how the
point cloud is oriented in that space. To satisfy these needs we draw,
in a corner of the screen, an object called the coordinate axes.
(McDonald, 1988, p. 185)

7 Before we begin looking at leukaemia, we can assume, from past research, that we may not find
any discernible patterns: 'The limited amount of geographic variation for certain cancers may also
provide insights into aetiology. Leukaemia rates were nearly constant across the country, similar to
the minor international differences that have been reported. This suggests that the role of environ-
mental exposures may be less important or conspicuous than for other cancers' (Melvyn Howe in
Blot and Fraumeni, 1982, p. 190).