Unduloid

unduloid
Unduloid with varying parameter

Unduloid describes a family of surface of revolution. Let a conics section roll on a line. Its focus traces out a curve. This curve revolved around the line generates the unduloid. The above image shows an unduloid where the rolling curve is an ellipse. It has a mean curvature of 1. If the rolling curve is a parabola, a catenoid will be generated, and has mean curvature of 0.

A soap film is a constant mean curvature surface, if the pressure difference between both sides is constant. (If this constant is zero the surface is called minimal surface)

unduloid st
unduloid st
unduloid sw
unduloid sw
generation of unduloid by rolling an ellipse

Unduloid.pdf