As the designer's elevational drawings are prepared, it may be difficult to show certain distorted walls or angled pieces of scenery in true size and shape. Most of these unusual pieces can be reasoned out with common sense and visual imagination. Occasionally, however, there are shapes that defy all solutions and the designer wishes he had an extra trick up his sleeve. The draftsman has a few tricks that every scene designer should know, not only to develop the elevation of a box set, but to help find the true size and shape of any distorted piece of scenery, platform, or three-dimensional object.
In a sense, the average interior setting is a partially closed solid, and the designer's elevations are a scaled pattern of the solid unfolded from the inside. The draftsman refers to these patterns as developments. Most of the surfaces in scenery are plane surfaces bounded by straight lines and are easy to develop. A plane surface, when angled, is usually perpendicular to at least one of the three principal planes of projection. The resulting perpendicular projection or edge view reveals the true angle of the plane. Problems arise when a plane surface is askew or angled to all three principal planes of projection.
Although an askew plane is a complexity of plane surfaces, often a piece of scenery may be further complicated by containing curved surfaces. A curved surface may be based on a single curve or a double curve that can limit it as a developable surface. Many single-curved surfaces can be developed; however, some have warped surfaces that can only be approximated. Double-curved surfaces such as the sphere cannot be developed or, at best, only crudely approximated. And of course, irregular surfaces or free forms cannot be developed at all.
By now it can be seen that to be able to analyze the surface and structure of a solid it is going to be necessary to become familiar with many geometric shapes. So back to geometry to review some of the planes and solids that frequently occur in scenery. A basic knowledge of geometric structure helps to tell at a glance how to develop a solid or whether it can be developed at all.