True Length and Shape
The development of a full-size pattern of a surface, such as the patterns used in sheet-metal work, is infrequent in the theatre. Most of the surfaces are too large to be developed at full scale. Also, because most curved surfaces in scenery are not structural themselves, it is occasionally necessary to use full-scale lofting to find the true size and shape of the structural member that is supporting the curved surface rather than to find a pattern of the surface itself. Angled planes are worked out at full scale in the same manner or at a large scale on the drafting board.
The graphic solution of any true-size- and-shape problem involves the use and understanding of two basic descriptive geometry concepts. Most problems in the theatre can be solved by knowing how to rotate a line to show it in true length and angle and by understanding the process of developing a shape by triangulation.
The auxiliary view is, of course, another way to solve for true length and shape. It works best on small objects or portions of a setting. Because askew planes in scenery are usually large in size and often not complete objects, the rotation method provides an accurate solution with the least amount of additional drawing.
Finding the true length of a line, like any graphic solution, begins with the information provided in two or more views or projections of the line and their relationship to the folding line. The folding line (FL), which represents the intersection of the vertical and horizontal planes of projection, is omitted though understood in the normal orthographic projection. It is easier, however, to show a line segment or single plane in space if the folding line is indicated with the conventional reference line symbol.
The draftsman can recognize a line parallel to one of the principal planes of projection by noting whether one of the line's projections is parallel to the folding line or not. When one projection of the line is parallel to FL the opposite view is seen in true length (TL). Similarly, if the top and front views are perpendicular to FL, the side view of the line is in true length. When a line is askew to all the principal planes of projection it has to be rotated into a parallel position with one of the planes to solve for true length.
1. With the line segment AB as an example, it is evident from its top and front view that it is askew in space and not parallel to either the vertical or horizontal plane of projection. Working in the top view, it is possible to rotate B to a position parallel to (FL) by using A as a center and AB as the radius of the arc.
2. The new position of B brings the line