onduloid

An unduloid, also called an onduloid, is a surface of revolution with constant nonzero mean curvature. It is a roulette obtained from the path described by the foci of a conic section when rolled on a line. This curve then generates an unduloid when revolved about the line. These curves are special cases of the shapes assumed by soap film spanning the gap between prescribed boundaries. The unduloid of a parabola gives a catenoid.

calculus of variations | catenoid | roulette | surface of revolution