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Elliptic Torus

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

$\displaystyle x(u,v)$ $\textstyle =$ $\displaystyle (a+b\cos v)\cos u$  
$\displaystyle y(u,v)$ $\textstyle =$ $\displaystyle (a+b\cos v)\sin u$  
$\displaystyle z(u,v)$ $\textstyle =$ $\displaystyle c\sin v.$  

See also Torus


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

© 1996-9 Eric W. Weisstein