Generalized Cylinder

A Ruled Surface is called a generalized cylinder if it can be parameterized by ${\bf x}(u,v)=v {\bf p}+{\bf y}(u)$, where ${\bf p}$ is a fixed point. A generalized cylinder is a Regular Surface wherever ${\bf y}'\times{\bf p} \not={\bf0}$. The above surface is a generalized cylinder over a Cardioid. A generalized cylinder is a Flat Surface.

See also Cylinder

References

Gray, A. Modern Differential Geometry of Curves and Surfaces. Boca Raton, FL: CRC Press, pp. 341-342, 1993.