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RULED SURFACE WHITH A STRAIGHT DIRECTRIX

Studied by Barré in 1916, Buhl in 1944. |

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