Elliptical Torus

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This Demonstration shows a torus for which both the tube and the cross section of the tube are elliptical.

Contributed by: Erik Mahieu (July 2015)
Open content licensed under CC BY-NC-SA

Snapshots

The parametric equation of an elliptical ring torus with an elliptical cross section is obtained as follows.

The ring ellipse has parametric equation in the - plane, where and are the semimajor and semiminor axes.

Using the Mathematica function FrenetSerretSystem, define the normal and binormal vectors and :

This gives the parametric equation of the elliptical torus:

where and are the semimajor and semiminor axes of the cross-sectional ellipse.

Expanded, this becomes:


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