On the surface - The Visualization of Spatial Social Structure - page 200

and so on, against the advantage that the eye is used to recover meaning from
surfaces. That is what our eyes are most often used for. 2
We do not tend to think in three dimensions. However, we can become
confused when forced to do so. As a result, to give just one example, there is far
more two-dimensional than three-dimensional art. It is because surfaces are what
we are used to, rather than being implicitly useful, that we consider them here. We
have evolved two-dimensional vision with a slight appreciation of depth (much
less than many think), but we live in a three-dimensional world. We constantly
estimate three-dimensional structure from a series of two-dimensional images.
We are quite good at it. The challenge is to harness that ability usefully, to
visualize our world through surfaces when it is appropriate to do so, and to do
so effectively.

7.2 Surface definition

To recover the lost information from 4D to 3D, we can continuously
change the position and orientation of the hyperplane, by either a pure
translation or a pure rotation or a combination of both, and obtain
different 3D images reflecting all aspects of the 4D .

(Ke and Panduranga, 1990, p. 222)

...

The surface of an object is the boundary, edge or limit of a shape. 3 It exists
in, and encloses, a dimension one order above its own. It contains and defines
an object, while expressing form itself. Although the surfaces of concern here
are mostly two-dimensional areas in three-dimensional space, it is useful to
drop down a dimension to consider another form of surface, one-dimensional

2 Often those producing some of the very best two dimensional visualizations had in their mind's
eye something more complex they were attempting to simplify: 'To undertake a project such as
the design of this is roughly akin to painting a landscape. One has a mighty scene at one's feet
with extensive views and multi-faceted build up. It lives as clouds sweep over it, the light shifts
and continuously changing aspects stand out. From all these possibilities of continuously changing
pictures the task is to capture precisely that one which is most apposite - for however much the
panorama changes before one's eyes, the picture one paints is, even so, static' (Szego, 1984, p. 17).
3 'It has been found that 90% of people are “3-D blind”, including as many as 70% of engineers
working with 3D graphics. The first problem is in design conception. Workers, unaware that they
are 3-D blind, are designing components which do not accord with reality. Even top professionals
have produced faulty algorithms based on a false 3-D view. Most designers agree with Robin
Forrest that “3-D makes life difficult” so structures have tended to be designed in “two and a half”
rather than true three dimensions. The second problem is in presenting the 2-D picture of the 3-D
artefact. Emphasis has been placed on producing “realism” with a gradually extending set of depth
clues: hidden line/surface removal, perspective, shadows, colour and hue, stereo.

...

We employ
enormously expensive systems such as ray tracing to get closer to realism, but if reality itself allows
for misinterpretation of the scene, as in all illusions, standard depth clues do not provide a solution
and they are not even necessary' (Parslow, 1987, p. 25).