Roulettes of Conics

Profile curves of Delaunay surfaces

The roulette of a conic, traced out by its focus, is the profile curve of a Delaunay surface [1]. Roulettes of ellipses make unduloids, and those of hyperbola make nodoids. The major and minor axes of the conic determine the neck and bulge sizes of the Delaunay surface. The roulettes in these flipbooks are traced out at constant speed.

Roulette of an ellipse. (Drag mouse on image.)

Roulette of a hyperbola. (Drag mouse on image.)

References

M. Kilian, On the associated family of Delaunay surfaces, Proc. Amer. Math. Soc. 132 (2004), no. 10, 3075—3082 [2063129].