Generalized Cone

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

See also Cone

References

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