torus-plane intersection

A toric section is a curve obtained by slicing a torus (generally a horn torus) with a plane. A spiric section is a special case of a toric section in which the slicing plane is perpendicular to both the midplane of the torus and to the plane x = 0. Consider a torus with tube radius a. For a cutting plane parallel to the x y-plane, the toric section is either a single circle (for left bracketing bar z right bracketing bar = a) or two concentric circles (for 0<= left bracketing bar z right bracketing bar <=a). For planes containing the z-axis, the section is two equal circles.

Cassini ovals | conic section | cross section | cylindric section | ellipsoidal section | lemniscate | spheric section | spheroidal section | spiric section | torus