I am looking for a way to create Unduloids from elliptic catenaries. They look like reasonably simple surfaces to generate with Rhino/Grasshopper, but sadly I lack the maths skills to implement what is described on these Wikipedia pages.
no math needed, just read the bolt words and ignore the rest:
In geometry, an unduloid, or onduloid, is a surface with constant nonzero mean curvature obtained as a surface of revolution of an elliptic catenary: that is, by rolling an ellipse along a fixed line, tracing the focus, and revolving the resulting curve around the line. In 1841 Delaunay proved that the only surfaces of revolution with constant mean curvature were the surfaces obtained by rotating the roulettes of the conics. These are the plane, cylinder, sphere, the catenoid, the unduloid and no…
yellow line: representing an elipse, but for explanation purposes, this will do. mentionned as elliptic catenary above.
fixed line above. axis around which the yellow curve is revolved.(revolution above)
not used in practice, but represents the way the yellow line is moved around the axis to obtain the surface. in an abstract way this can represent the revolution itself.
hope thats a bit more clear for you. you can find the command _-revolve in rhino and follow the instructions in the command line and you’ll easily understand.