Theatre Design & Technology - Summer 1981 - 43

In the second example, the circular form of Paradise (unit
6) is developed using the twelve point construction which is
only possible in linear perspective. The procedure for development is similar to the previous example (Fig. 24).
1. A circle centered on the horizon over the figure indicates that
most, though not all, of the figure falls within the 45° cone of vision.
2. Those points within the cone of vision are connected by a
straight line to determine the vanishing point for the plane. The
other orthogonals are adjusted to vanish to this same vanishing
point.
3. The twelve point construction can be completed after the linear
perspective lines are established. The circle is drawn by connecting the twelve points with the aid of a French curve.

Conclusion
Accuracy in perspective drawing is a relative concept. Any
perspective projection of an object onto a plane produces a
distortion of its true shape and size. The problem is what kind
of distortion and how much distortion is acceptable in a design drawing. The public is exposed to wide angle photographs in printed media because of the availability of wide
angle lenses. Wide screen projection in motion pictures also
affects one's viewing habits, making wide angle distortions
acceptable. The influence of photography has made the 60°
cone of vision acceptable for design rendering. But when the
angle of view approaches 90° the distortion of the objects at
the edge of the vista makes their true shape hard to understand. The fisheye lens is another method of capturing a wide
angle view on a planar surface that has not been discussed. It
is unacceptable as a design drawing because the distortion is
so dramatic that the perspective system always dominates the

M. C. Escher, High and Low, 1947.
Perhaps one of the most successful of all Escher's prints dealing
with the ambiguities of drawing is High and Low. This print turns the
curvilinear grid vertically showing the system's ability to integrate
separate views. The scene is presented twice, simultaneously and
from two different views.

USITT /Summer, 1981

subject matter. Secondly, since both horizontal and vertical
lines are curved in the fisheye image, development of the image is extremely awkward. The fisheye image is the planar
projection of an image on a spherical surface, making development of the true surface possible only with a complex mapmaking technique known as orange peeling. The panoramic
view produced by cylindrical perspective is an ideal compromise between the need to capture a wide angle view and
the need for accuracy. Small segments of the curved vista are
approximately consistent with the 45° cone of vision in linear
perspective. The representation of objectively straight horizontal lines as curved can be overcome by careful selection of
the station point. Curved lines can also be eliminated by viewing the drawing as a cylinder.
The concept of space as simultaneously curved and right
angle co-ordinate is fascinating when it can be explored with
this simple working method. Whether the designer works consistently in environmental situations or in proscenium theatres
where an element occasionally falls outside the acceptable
cone of vision, the tool of cylindrical perspective is a valuable
resource.

Annotated Bibliography
Baigell, Matthew. Thomas Hart Benton 1889-1975. New York: Harry
N. Abrams, Inc., 1973. Painting, pp. 122-123.
Corliss, Mary and Carlos Clarins. "Designed for Film: The Hollywood
Art Directory," Film Comment, May/June 1978, pp. 27-58. Ed
Grave's rendering, pp. 28-29. George Jenkins discusses the
curved picture plane, p. 45.
Dobling, Jay. Perspective: A New System for Designers. New York:
Whitney Publishing, Inc., 1956. Wide angle perspective is used as
an argument for simplified linear perspective constructions.
Dubery, Fred and John Willats. Drawing Systems. New York: Van
Nostrand Reinhold, 1972. Three wide angle paintings are discussed with the aid of diagrams, pp. 67-76. Vincent's Bedroom, p.
74.
Edkins, Diana. "Panorama: A Long Look at Some Long Looking Pictures," Modern Photography, August 1978, pp. 82-93. Currently
available panoramic cameras are demonstrated.
Eichenberger, Fred. Wide Angle Perspective Systems: With an Emphasis on Cylindrical Perspective. Raleigh, N.C.: North Carolina
University and Parnell Press, 1970. The cylindrical perspective
system is presented in terms of computer language.
Ernst, Bruno. The Magic Mirror of M. C. Escher. New York: Ballantine
Books, 1976, pp. 42-57. The article discusses Escher's intuitive
constructions for his curvilinear prints including High and Low, p.
52.
Fielding, Eric. "Broadway and Hollywood, George Jenkins for Film
and Theatre, Designs on Both Coasts," Theatre Crafts, March/
April 1980, p. 20+. Linear rendering and cylindrical photograph of
the newsroom setting from All The President's Men are printed, p.
22.
Gioseffi, Decio. "Perspective," Encyclopedia of World Art, XI. New
York: McGraw-Hili Book Co., 1966, pp. 215-216. The article summarizes the development of curvilinear perspective theory in the
fine arts.
Hoffman, Paul S. "Perspective Rendering by Hand-Held Calculator,"
Theatre Design and Technology, Winter, 1978, pp. 5-12. The article is a complete presentation of the use of the hand-held calculator in linear perspective.
Pirenne, Maurice Henri Leonard. Optics, Painting and Photography.
Cambridge, Mass.: University Press, 1970, pp. 145-150. Photographic experiments prove the validity of linear perspective and the
error of the theory of the eye structure as justification for curvilinear drawing.
Stuckey, Carles F. "Blossoms and Blunders: Monet and the State, II,"
Art in America, Sept. 1979, pp. 109-125. Installation floorplan, p.
117.
Vero, Radu. Understanding Perspective. New York: Van Nostrand
Reinhold Company, 1980. Pp. 116-129. Spherical perspective is
justified in terms of the structure of the eye with the aid of paintings
and diagrams.D
Tim Palkovic is Assistant Professor of Theatre at the State University
of New York at Plattsburgh.
Theatre Design & Technology

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