72. Building surface sweeps

In the manufacture of various structures and products from sheet material, the construction of surface scans is of great importance. If one imagines a surface as a flexible non-stretchable film, then some of them can be combined with a plane without bending and deformations by bending. Such surfaces refer to developable ones, and the flat figure obtained as a result of surface deployment is called the development of this figure. Those surfaces that can not be combined without breaks and deformations are non-deployable (see § 45).

In practice, it becomes necessary to manufacture from sheet iron not only developable planes. Theoretically, only faceted surfaces, torsos, conical or cylindrical surfaces are accurately developed. When deploying conical and cylindrical surfaces of general form in practice, they are approximated by inscribed faceted surfaces. In this case, the more edges the inscribed surface contains, the more accurate its unfolding. Surface scans constructed in this way are called approximate.

To construct the sweepings of non-expandable surfaces, these surfaces are broken into pieces that can be approximately replaced by developable surfaces. After that, the sweep of these parts is built, which together give a conditional scan of the non-deployable surface.