Beaded torus

Instead of a continuous tube, the ring is built from n beads strung along the circle of radius R. Each bead is a shaded sphere drawn as a billboard disc on the canvas.

u_k = 2πk/n
P_k = (R cos u_k, R sin u_k, 0)
s_k = s₀·(1 + a·sin(m·u_k))

The sinusoidal size term gives the ring a rhythm: the beads swell and shrink m times per loop, so the eye reads a repeating pulse rather than a uniform necklace. Raise a to exaggerate it, drop it to zero for equal beads.

Beads are depth-sorted and filled with a radial gradient whose highlight centre is pushed along the light direction, which fakes a sphere without any real geometry. The optional dashed circle marks the hidden path the beads travel along.