Theatre Design & Technology - Summer 1988 - 25

The firSt mathematical formula involved choosing the
proper lenses for the projectors. Using the distances from
the projector to the near edge of the screen as the approximate throw; and the height of the screen as the image size,
it is possible to estimate the lenses needed. Actually, these
calculations have already been done by various manuiacturers, so the smarr bet is to consult the nearest lens data
chart. Available information says that a 1.5" lens renders
an image 3500nun wide x 2300mm high at a distance of
41oomm. A 2.5" lens renders an image 3700 x 2500 at a
distance of 7000mm. 1 These heights almost completely
fill the respective screens, and the widths are more than
enough for the purpose. The catch is that the throw distance in these data is measured along the central axis of
the projector to a perpendicular screen which, in this case,
does not exist. Until a theoretical screen or picture plane
can be established, these are to be regarded as very rough
estimates that may be subject to future revision.
Accurate image size measurements for any oblique angles must be calculated using the standard teclmique as if
creating a perspective rendering of the screen as it appears
from the position of the projector. The perspective view
required here must be an accurate depiction developed
geometrically from a plan. The ground plan of the acting
space may only be the starting point. The operational
"plan" that must be used is actually a section through the
central axis of the projector. In the case of the Caligl.lla
projections, the central axis was tilted, so the section Cutting plane had to be determined from an oblique elevation
perpendicular to the face of the screen (Fig. 21. This section

plane was then taken as the "plan" for calculating the
picture plane and the perspective (Fig. 3).
With center at the projector, an arc is drawn with radius
equal to the distance between the projector and the near
edge of the screen. Then, with center at the near edge of the
screen, a second arc is drawn with radius equal to the
width of the image as derived from the above lens data. [In
the case of Caligl.lla's stage left projector, that distance was
3500mm [11.5'). The second arc is drawn so that it intersects the first arc. A line through the intersection of the
arcs and through the near edge of the screen becomes the
picture plane for subsequent calculations. The observation
point for those calculations is at the projector.
The central axis can be determined by measurement
along the picture plane. The throw distance can be accurately measured along the axis. It is necessary at this point
to check back to the lens data to ensure that the image size
will be correct. Some adjustment of the projector position
may be required. (If the projector is moved, it is obviously
necessary to redraft.)
The picture plane is then represented as an elevation.
The near edge of the screen is at the picture plane and can
be extended to the elevation. The height of the screen can
be accurately scaled at the near edge because it sits at the
picture plane. To locate the apparent position of the far
edge of the screen behind the picture plane, a line is drawn
from the projector through the far edge. The point at which
that line crosses the picture plane is extended to the
elevation.
A line parallel to the screen is drawn through the projec-

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Table of Contents for the Digital Edition of Theatre Design & Technology - Summer 1988