Geodesic
Extension of the 'Villarceau-Section' to Surfaces of Revolution with a Generating Conic
Journal for geometry and graphics, Tome 6 (2002) no. 2, pp. 121-132.

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When a surface of revolution with a conic as meridian is intersected with a double tangential plane, then the curve of intersection splits into two congruent conics. This decomposition is valid whether the surface of revolution intersects the axis of rotation or not. It holds even for imaginary surfaces of revolution. We present these curves of intersection in different cases and we also visualize imaginary curves. The arguments are based on geometrical reasoning. But we also give in special cases an analytical treatment. Keywords: Villarceau-section, ring torus, surface or revolution with a generating conic, double tangential plane. Classification1: 51N05. 
@article{JGG_2002_6_2_a1,
     author = {A. Hirsch},
     title = {Extension of the {'Villarceau-Section'} to {Surfaces} of {Revolution} with a {Generating} {Conic}},
     journal = {Journal for geometry and graphics},
     pages = {121--132},
     publisher = {mathdoc},
     volume = {6},
     number = {2},
     year = {2002},
     url = {http://geodesic.mathdoc.fr/item/JGG_2002_6_2_a1/}
}
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A. Hirsch. Extension of the 'Villarceau-Section' to Surfaces of Revolution with a Generating Conic. Journal for geometry and graphics, Tome 6 (2002) no. 2, pp. 121-132. http://geodesic.mathdoc.fr/item/JGG_2002_6_2_a1/