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 cone over a cardioid. A generalized cone is a developable surface and is sometimes called "conical surface."
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ReferencesGray, A. Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca Raton, FL: CRC Press, pp. 439-441, 1997.Kern, W. F. and Bland, J. R. "Conical Surfaces." §23 in Solid Mensuration with Proofs, 2nd ed. New York: Wiley, p. 57, 1948.
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Weisstein, Eric W. "Generalized Cone." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/GeneralizedCone.html