Theatre Design & Technology - Summer 1981 - 35

~-------

~I
Planar Perspective Cone of Vision
Cylindrical Perspective Band of Vision

Full-scale Assumption

Figure 5

s
3 feet
- = - - = .6::: tan 30°
d
5 feet

ence plane to replace the proscenium arch. The position of
the reference plane is a special problem when the plane is
curved. For this reason a full-scale perspective assumption is
developed (Fig. 5). A cylinder five feet in radius and six feet
high is imagined as suspended two feet above the floor. This
provides a vertical angle of about 60°. This figure provides a
simple computed ratio of viewing distance to drawing height,
and provides an acceptable viewing angle.

Band of Vision
The terms angle of view, cone of vision, and band of vision
are a potential source of confusion. Band of vision is unique to
cylindrical perspective. In normal planar perspective, the
terms angle of view and cone of vision are used interchangeably. In planar perspective the three-dimensional concept of cone of vision is represented in plan or elevation as
angle of view. In cylindrical perspective, the concept of angle
of view controls only the vertical dimension. This is because
the horizontal dimension is curved and can be extended from
140° to 360°. Therefore, the term band of vision is used to
express the vertical angle of view in cylindrical perspective
(Fig. 6). The 140° angle is the angle of horizontal peripheral
vision where detail is not seen as sharply as in the accepted
45° to 60° angle of view used in design drawings.
The 60° band of vision is selected so that objectively
straight horizontal lines do not become excessively arched
when the drawing is viewed flat. When viewed strictly as an
anamorphic drawing, the cylinder height should be extended
to 90° or the curved lines will seem straight since the viewing
is strictly limited to one position.

Drawing Sizes
A cylindrical drawing should be large enough that a portion
of it can be viewed at an approximately 45° angle of view.
This will also make it large enough to be viewed as an anamorphic drawing. Many designers' working situations will require
a compromise between the desired large drawing size and the
small drafting table. The range of sizes are presented to allow
a compromise between the perceptual ideal and the practical
limitations. For example, the starred (.) 24" high drawing size
in the table of scaled drawing sizes can be developed on a
standard drafting table 2'6" by 3'6" with the use of tracing paper and overlapping construction (Fig. 7). At this size oneeighth of the 360° cylinder, a 45° wide segment, can be projected at a time.
The awkwardness of developing a large freehand grid can
be overcome by photographing a portion of a smaller grid and
projecting a slide of the grid onto the drawing surface. The
size of the grid can be adjusted by changing the position of
the projector or by adjusting a zoom lens on the projector.
USITT /Summer, 1981

Figure 6

- - -......
_ _ _5_0

Suggested scaled drawing sizes

Figure 7

Suggested Scaled Drawing Sizes
for Simplified Computation of Vertical Dimensions
by Hand-Held Calculator

t cylinder height
viewing distance

s
d

Circumference
Drawing
Length for
360 0 View
(27Tr)

Viewing
Distance
(radius)

Cylinder
Height
(2 x s)
60 0 Band

A
B

10"
16!"

12"
20"

5'3"

C·

20"
25"
331"

24"
30"
40"

10'6"
13'1 "
17'5"

50"
100"
2j"
5"

60"
120"
3"
6"

26'2"
52'4"
14 fG"

E
F

8'9"

28i"

.6 :::: tan 30°

Vertical
Scale
XU = l'

2" = l'
3.33" = l'
1" = 3'
4" = l'
5" = l'
6.66" = l'
1" = 1j'
10" = l'
20" = l'
j" = l'
1" = l'

Engineering
Scale

10
60
50
40
30
20
10
40
20

* The suggested compromise between ideal perceptual size
and convenient working size.
Note:
A. The 10" viewing distance is the smallest practical drawing size for
viewing as an anamorphic drawing. The cylinder should be viewed
with one eye closed.
B. The 16 1" viewing distance can be viewed with both eyes but is
somewhat small for viewing comfort.
C. The 20" and 25" viewing distances are ideal for viewing both as
an anamorphic drawing and as a flat drawing. People tend to adjust their viewing distance to arms length when inspecting a handheld painting or drawing. The drawing, however, begins to become excessively long when a 360° view is constructed.

Theatre Design & Technology

Table of Contents for the Digital Edition of Theatre Design & Technology - Summer 1981