A Ruled Surface is called a generalized cone if it can be parameterized by , where is a fixed point which can be regarded as the vertex of the cone. A generalized cone is a Regular Surface wherever . 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.