For surfaces of directrix Oz : Differential cylindrical caracterisation: . Cylindrucal equation: . Cartesian paramétrisation: .

A ruled surface is said to be with straight directrix if its generators all pass through a fixed line.

Examples :
 - cones (case where the directrix is reduced to a point), 
 - conoids (of which the hyperbolic paraboloid), case where there is also a director plane, 
 - conoidal surfaces (of wich the milk cartoon), case where there are two straight directrices
 - closed ruled helicoids (of which the right helicoid), .

See also the ruled surfaces with a director plane.
 

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© Robert FERRÉOL  2020