A ruled surface parameterization 
is called noncylindrical if 
is nowhere 
. A noncylindrical ruled surface always has a parameterization
of the form
 |
where 
and 
,
where 
is called the striction curve of 
and 
the director curve.
Noncylindrical Ruled Surface
See also
Distribution Parameter, Ruled Surface, Striction CurveExplore with Wolfram|Alpha
References
Gray, A. "Noncylindrical Ruled Surfaces." §19.4 in Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca Raton, FL: CRC Press, pp. 445-448, 1997.Referenced on Wolfram|Alpha
Noncylindrical Ruled SurfaceCite this as:
Weisstein, Eric W. "Noncylindrical Ruled Surface." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/NoncylindricalRuledSurface.html