On the surface - The Visualization of Spatial Social Structure - page 211

to grasp instantly what would result from the rotation of any element in any
direction or pair of directions (Figures 7.9 and 7.10). Surfaces do not show us
three dimensions; they just persuade us to begin to imagine them. Only a part of
visualization is what we see; the other part is what we think.
A major advantage claimed of surfaces is that once one variable is projected
as height, other related variables can be shown, say, as surface colour, contours or
whatever. This method certainly has its merits. It allows two spatial distributions
to be compared before using colour and it dramatically highlights the differences
and distinctions (Figures 7.11 and 7.12).
However, in projecting one distribution as shading upon another as height,
information is lost and confused. It is lost because it cannot be seen (if it is
'behind') and it is lost as our ability to see and compare difference in (illusory)
height is not as good as it is in estimating shades of intensity. 11 It is confused
because colour and shadow are created from the projection used and because
the shading of the second variable creates the illusion of changes in the height
of the first.
Surface shading is not a good substitute for two-colour mapping. The idea
of showing the relationship between four spatial distributions by colouring a
surface with a trivariate map of colour could only work if the underlying surface
were very simple. Where one variable is of great importance and has a relatively
simple spatial structure, surface shading of it can be useful.
A simple surface of, for instance, unemployment (Figure 7.13) can be
coloured by levels of voting for various parties. Major migration streams could
be draped over this, as people, perhaps, flow down from around the mountains
of discontent. To create the idea of an industrial landscape this type of depiction
can be very useful. However, used like this, it is closer to illustration than
visualization - something to present, rather than study.

7.5 Surface geometry

In particular the refutation of Wardrop's conjecture precludes the pos-
sibility of constructing a flat map of a city which correctly represents
travel time. However, since Warntz's conjecture is true we can con-
struct a curved surface which represents travel time.
(Angel and Hyman, 1976, p. 44)

There is value in using surfaces beyond their illustrative purposes and natural
appeal. A surface contains much more information than the mere height mea-
surement, the single variable that is normally extracted from it, and is used in
most '3D' socioeconomic graphics.

11 It is claimed that some perspective views are only useful for illustration: 'Traditional methods
of representing relief such as hachures, contours, hypsometric tints or hill shading, were developed for
topographic mapping and when applied to special purpose maps or thematic maps their effectiveness
is often limited' (Worth, 1978, p. 86).