Join of 2 Tori

join two tori 001
Join Two Tori

These surfaces are the level surfaces of a function. For small values the levels are tubes around two circles. For larger values a connection (called “handle”) between the tubes makes the level into a torus. For even larger values the holes of the torus disappear.

join2tori decorated
Surface with a geodesic grid and a pair of curvature circles.
join2tori geodesic
Surface with two closed geodesics.