Theatre Design & Technology - Summer 1981 - 37

Figure 11

Figure 12

The vertical distance from the horizon is read as 30 on the appropriate engineering scale.
This computation makes measured perspective practical in
cylindrical perspective because precise vertical positions can
be exactly located on the perspective. A special additional advantage is that the plan and elevation scales need not be the
same as the finished perspective. (This method also has application for linear perspective. See Paul S. Hoffman's article in
TD& T, Winter, 1978.)

Grid Units
The units in the drawing grid represent five feet. This unit is
chosen because it allows convenient computation in units of
ten and is the average eye level of a standing person. The grid
is symmetrically developed for simplicity and because scenic
flats in most studio theatres are ten feet high.

The 90 0 Angle of View Perspective
The cylindrical grid is developed from a perspective with a
90 0 viewing angle. This 90 0 drawing is twice as wide and
twice as high as the selected viewing distance. In the case of
the 20" viewing distance, the 90 0 perspective is 40" square.
The top and bottom of the 90 0 curvilinear grid is usually eliminated, making the completed 60 0 curvilinear band of vision in
this example 24" high. The example is a suggested compromise between ideal size and workable size in Figure 7,
above.
The distance point (DP) in a 90 0 perspective falls on the
picture edge (Fig. 10). Thus the intersections of the vanishing
orthogonals (CV-5', 10', 15', 20', 25') with line O'-DP forms
the horizontal increments in perspective (5', 10', 15', 20', 25'
beyond the picture plane).
USITI/Summer, 1981

Drawing the Freehand Grid
The freehand curvilinear perspective grid is developed from
the 90 0 perspective as follows (Fig. 11).
1. Draw concentric half circles the distances of the depth increments from the horizon in a space to the right of the 90° perspective.
2. Construct the half cylinder in a space to the right of this construction. Use the formula for Y, the circumference, 27Tf/2. (If there
is not sufficient space, as little as Va cylinder [45°] can be developed and traced to form a complete grid, because the figure is symmetrical.)
3. Divide the half circles and the half cylinder into eighteen 10°
segments. A protractor or adjustable triangle is used for dividing
the circles. The half cylinder is divided by laying any convenient
measure with one end against the half cylinder and marking off
eighteen segments. These segments are projected to the half cylinder with a T-square and an adjustable triangle.
4. Number the corresponding segments to avoid confusion when
projecting points from the half circles to the half cylinder.
5. Project points from the half circles to the corresponding degree
increments on the half cylinder using the T-square.
6. Connect these points forming curved lines.
7. Project the 60° cone of vision to the half cylinder forming a 60°
band of vision.
8. Retrace these arcs forming a complete 180° or 360° grid (Fig.
12).

This grid represents a Cartesian co-ordinate grid projected
onto a cylinder. The completed grid consists of two sine wave
patterns 90 0 out of phase. The horizontal increments from
one segment form the orthogonals of the next segment. The
completed grid can be viewed as a cylinder to demonstrate
the anamorphic properties of cylindrical perspective.
The plan grid for this perspective projection is similar to
grids used for developing planar freehand perspective grids
(Fig. 20). The squares represent 5' units.
Theatre Design & Technology

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