Elliptic Torus

A generalization of the ring Torus produced by stretching or compressing in the $z$ direction. It is given by the parametric equations

$$x(u,v) = (a+b\cos v)\cos u$$

$$y(u,v) = (a+b\cos v)\sin u$$

$$z(u,v) = c\sin v.$$

See also Torus

References

Gray, A. ``Tori.'' §11.4 in Modern Differential Geometry of Curves and Surfaces. Boca Raton, FL: CRC Press, pp. 218-220, 1993.