Eccentric-aperture torus

Two circles that do not share a centre. The outer contour is a circle of radius Ro about the origin; the hole is a circle of radius Ri about H = (e, 0). A ray leaving H at angle u meets the outer circle at distance d(u) = −e cos u + √(e² cos²u + Ro² − e²).

M(u) = H + ((Ri + d)/2)(cos u, sin u)
rt(u) = (d(u) − Ri)/2
P(u,v) = M(u) + rt(u)(cos v (cos u, sin u) + sin v (0,0,1))

At v = 0 the surface sits exactly on the outer circle and at v = π exactly on the hole, so the wall interpolates between the two off-centre circles and the outer contour stays a perfect circle. The wall is thickest where the circles are farthest apart and thinnest on the opposite side.

The controls always keep Ri + e < Ro − 0.25, so the aperture never breaks the rim; the status line reports the thick : thin ratio that results.