Surface of Delaunay

A surface of Delaunay is a Surface of revolution to average Courbure constant (nonnull).

Its Génératrice is the curve followed by the hearth of a ellipse or a hyperbole when this one rolls without slipping on a line (the axis of revolution of surface). In the case of an ellipse, the generator does not have an car-intersection; surface obtained is called a onduloïde. In the case of a hyperbole, the generator has car-intersections; surface obtained is called a nodoïde.

The Sphere and the Cylindre of revolution are borderline cases of onduloïdes.

Surfaces of Delaunay are only surfaces with nonnull curve average constant which are also of revolution. The Caténoïde (null average curve) is also a borderline case of onduloïde and nodoïde.

Physical application: a filament of water has as a form a surface of Delaunay.

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