A ruled surface is called a generalized cylinder if it can be parameterized by , where is a fixed point. A generalized cylinder is a regular
surface wherever . The above surface is a generalized cylinder over
a cardioid. A generalized cylinder is a developable
surface and is sometimes called a "cylindrical surface" (Kern and Bland
1948, p. 32) or "cylinder surface" (Harris and Stocker 1998, p. 102).

A generalized cylinder need not be closed (Kern and Bland 1948, p. 32).

Kern and Bland (1948, p. 32) define a cylinder as a solid bounded by a generalized cylinder and two parallel planes. However, when
used without qualification, the term "cylinder" generally refers to the
particular case of a right circular cylinder.