At the page https://www.lucamoroni.it/toric-sections/ there is a new article about toric sections, their geoemetry and their math.
The article goes together with a Geogebra simulation that can be seen at the page Intersection of a torus with a plane (simulation)
The curve of intersection of a torus with a plane is called toric section. Even if both surfaces are rather simple to define and are described by rather simple equations, the toric section has a rather complicated equation and can assume rather interesting shapes.
In this article I’ll discuss some properties of this curve, investigate its differences with the most renowned conic section, show how to build its general quartic equation, how a toric section can also be generated by intersecting a cylinder with a cone and finally describe how it is possible to represent it in the 3D Graphics view of Geogebra…