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