Contour-slice torus

The ring is cut into S horizontal slabs and the slabs are pulled apart a little, so the solid reads like a topographic model. The gaps let you see straight through to the hollow centre.

z_k = −r + (k + ½)·2r/S
ρ_k = √(r² − z_k²)
t = (2r/S)·(1 − gap)

Slab k spans z_k ± t/2, and there its torus cross-section is a washer with outer radius R + ρ_k and inner radius R − ρ_k. Near the top of the tube ρ is small, so the washer is a narrow ring; at the equator the washer is at its widest.

Each washer is meshed as a top annulus, a bottom annulus and inner and outer cylinder walls, all flat-shaded from their own face normals. Viewed from directly above, the washers nest into concentric annuli and the silhouette fills out to a flat ring spanning R − r to R + r; the wireframe modes are what make the individual circles legible.