A noncylindrical ruled surface is a ruled surface parameterization such that 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.
More things to try:
Weisstein, Eric W. "Noncylindrical Ruled Surface." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/NoncylindricalRuledSurface.html
such that 
is nowhere 
.
A noncylindrical ruled surface always has a parameterization of
the form
and 
, where 
is called the striction
curve of 
and 
the director curve.
