On the surface - The Visualization of Spatial Social Structure - page 207

7.3 Depth cues

The major problem is that if rotation stops, the 3-D effect disappears.
This is unfortunate because it is helpful to stop rotation to get one's
bearings with respect to the axes; the continuous movement can make
it quite difficult to get these bearings.
(Becker, Cleveland and Weil, 1988, p. 252)

The fundamental problem in visualizing nonflat two-dimensional surfaces is
the need to provide depth cues and their unwanted side effects. These are all the
products of turning what is effectively two-and-a-half-dimensional information
into two-dimensional form: something has to be lost.
The simplest method is to perform an isometric projection of the surface,
mapping all the points in three dimensions on to two dimensions (by matrix multi-
plication). The most basic of these transformations adds half the vertical position
of each point to its horizontal position, then scales the vertical position by half
the square root of three and adds to it the height of the point. Three dimensions
are turned into two and a wire-frame image is produced (Figures 7.7 and 7.8).
To aid perception, a hierarchy of more sophisticated techniques can be
employed. The first of these is to use a perspective projection. Objects further
from the viewer appear smaller (Box 7.2). This obviously distorts the image.
Secondly, hidden lines can be removed so that a wire-frame is no longer seen,
but a more natural solid object is put in its place. Now, however, part of the
original object is obscured. A fishnet of parallel lines can be placed over the
surface, their convergence signifying distance. 8
More sophisticated options make the image appear more natural. Lighting
the surface from a particular direction creates shadows and more subtle cues, but
lighting distorts any other colouring being used. Ray-tracing makes the surface
even more realistic, allowing for reflections, or more usefully transparency, but
still takes us further from the original form.
The most useful depth cues are to be found in animation, particularly where
the viewer interactively chooses the direction to view from. Rotation of the object,
even simple rocking, helps greatly, although diving with a camera down across
the surface is more dramatic. Parallax is the property being exploited here - the
apparent displacement of objects as the point of observation changes.
All we are doing when we render more sophistication is to make the image
appear more and more like the real world that we are so good at observing. Ani-
mation and ray-tracing can be combined to produce stunning images. However,
the difficulty then is in gauging how much of the picture seen is a product of the
techniques required to make it look three-dimensional. 9

8 There are means of seeing the effect of depth without animation: 'Stereo vision enhances the
three-dimensional effect of the rotating cloud but, even more importantly, the three-dimensional
effect remains even when the motion stops' (Becker, Cleveland and Wilks, 1988, p. 30).
9 It also remains doubtful how useful stereo vision really is: 'From the test results it can be
learned that for the combined Spatial Map Images the response time is significantly shorter for the