Geography Reference
In-Depth Information
three-dimensional landscape surface and the space-time lines above it, doing so can lead to
difficulties in visual interpretation. This is because the space-time lines attached to different
points on the surface are no longer visually comparable, because they are offset in the vertical
plane by different amounts depending on the height of the landscape surface to which they
are attached
In some low-lying study areas, as in parts of the Netherlands (Kraak 2003), this problem
may be largely ignored. In other areas, where it is known that topography has little influence
on space-time patterns, this problem may be solved by adopting the age-old fiction of the
traditional 2D map: a flat world. However, in many hillier and mountainous areas, where
it is important to understand how the landscape surface impacts on people's movement
patterns, terrain height must also be shown in the cube. In such cases,
z
-axis contention
becomes a serious problem that threatens to undermine the benefits of this particular 3D
visualization technique.
One possible solution may be to attach the bases of all space-time lines to an arbitrary plane
above the highest point of the landscape surface, although this may make it difficult for the
interpreter to relate the two sets of information. As previously mentioned, this stacking tech-
nique is used in several visualizations of spatial point-located data (e.g. Chuah
et al.
, 1995;
Schmidt
et al.
, 2004), and also in numerous 3D meteorological visualizations where a single
surface layer is displayed some way above a globe. In one example (Aoyama
et al.
, 2007), the
suspended isosurface showing land-surface temperatures is visually related to the plane base
map of the USA below it by having the outlines of regions of interest in the former projected
down onto the latter. However, where the
z
-axis is used to display data for several variables,
this results in a stack of multiple 3D thematic layers displayed above a reference surface. Even
more complex techniques are needed to relate the locations of objects on one layer to those
on other layers. In oil reservoir visualizations (e.g. Calomeni and Celes, 2006), the inclusion
of vertical lines representing boreholes partly reduces this problem. In general, however, and
despite the undeniable artistry of some of the complex visual models, one begins to wonder
whether one has reached the limits of 3D data visualization as an exploratory and interpre-
tive tool. Rather than overload the
z
-axis, it might be more effective for the analyst to resort
to map overlay analysis or, as discussed in the next section, to adopt some form of dimension
reduction techniques in order to simplify the data before or during the visualization process.
10.3.6 The 'dimensionality curse'
The challenge of what Robertson, Mackinlay and Card (1991, p. 189) refer to as 'intellectually
large data collections' is a problem that is only partly solved by moving from 2D to 3D
visualizations. Although it is possible, as previously discussed, to display very large numbers
of objects in 3D scenes with powerful hardware and clever algorithms, visualization limits
are rapidly reached as the number of dimensions (i.e. variables, fields or attributes) increases
above a relatively small number. As Bertin (1967, 1977) fully appreciated, the graphical sign
system cannot be used to display more than a handful of variables in a single scene, and
this remains the case even after it has been augmented with additional visual variables (e.g.
transparency, blur, and specular highlights), or extended into the third dimension through
complex articulated glyphs and icons.
Even when 3D symbols are used to encode up to half a dozen data variables, this is still a long
way away from being able to satisfy the needs of many analysts, whose datasets commonly
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