The Bounds of Perspective: Marginal Distortions (page 1)
The Bounds of Perspective: Marginal Distortions
"... human kind
Cannot bear bear very much reality." T. S. Eliot, from "Burnt Norton," 1935 (Eliot,
1963, p. 190)
Fig.8.1 Two central projections of a church
and cloister. Lower right-hand panel [Fig. 169bis]: plan and elevation
of the scene; OE1 is the center of projection used to draw
upper-right-hand panel [Fig. 168], and OE2 is the center of
projection for lower left-hand panel [Fig. 169]. The scene in Fig. 168
subtends 102°; the scene in Fig. 169 subtends 19°.
e turn now to a class of pictures that
arc unacceptable because they do not conform to the robustness of perspective,
that is, they look distorted to all viewers except those who look at the picture
from the center of projection. The existence of such pictures, as we shall see,
constrains central projection, forcing artists to compromise in their methods
of representing scenes. The upper-right-hand panel of Figure 8.1 looks distorted
from all vantage points except the center of projection, just over an inch away
from the page, too close to focus on the lines; the drawing in the lower-left-hand
panel does not look distorted from any vantage point. The two pictures differ
in the distance of the center of projection from the image plane, which is equivalent
to a difference in visual angle subtended by the scene: The first subtends 102°,
whereas the second subtends only 19°. It is not known how big the visual
angle can be before such distortions, called marginal distortions,
appear in pictures made using central perspective. Olmer, in his extensive treatise
on perspective, Perspective Artistique (2 vols.: 1943, 1949), reviewed
the recommendations of artists and writers on perspective and concluded in favor
of a horizontal visual angle of 37° (and a vertical visual angle of 28°),
which he calls perspective normale. In Figures 8.2 and 8.3, he compares
an array of cubes drawn in "normal perspective" with an array of cubes
drawn in what he calls perspective exagérée. In the latter
drawing, he shows that in a central area subtending 37° cubes are not distorted.
In an even more dramatic example (Figure 8.4), he shows that outside the frame
xyx1 y1 ;, which encompasses what he calls the normal visual field
(37° times 28°), the cubes are seen as distorted.
Fig.8.2 Variations of pictures of oblique
cubes seen under normal perspective.
We know that fields exceeding a critical extent cannot be properly perceived without moving one's eyes. Imagine a horse standing some distance away presenting his flank to you. Now image yourself moving toward the horse: As you move closer to the horse, it looms larger; there will come a point when you are so close that you will not be able to see all of it at the same time, unless you move your eyes or turn your head. Furthermore, if you are asked to visualize something, such as an animal, seen at a large distance, and to imagine yourself moving toward it, there will come a point when you will imagine yourself so close to the thing you are visualizing that it seems to "overflow" your "mental screen." Estimates of the size of the visual field that we can encompass in focal attention are difficult to obtain. Using variants on the mental imagery procedure just described, Steven Kosslyn (1978) obtained estimates ringing from 13 to 50°, which bracket Olmer's estimate of the normal visual field.
Fig.8.3 Variations of pictures of oblique cubes seen under exaggerated perspective.
Fig.8.4 Marginal distortions in picture of array of cubes seen from above.