Contour-line torus

The tube is sampled as a meridians × parallels grid: u runs around the ring, v around the tube, so meridians sit at fixed u and parallels at fixed v.

P(u,v) = ((R + r cos v) cos u, (R + r cos v) sin u, r sin v)
N(u,v) = (cos v cos u, cos v sin u, sin v)

Nothing is filled — every grid edge is a separate stroke. Vertices and normals are rotated by the same yaw/pitch, and each segment takes the mean view-space normal n_z of its two ends: alpha = 0.06 + 0.9 (1−|n_z|)^p and width = w0 (0.6 + 1.4 (1−|n_z|)^p).

Weight therefore rises toward the silhouette: marks are boldest where the surface turns edge-on and thinnest where it meets the eye frontally, so line density increases near the edges. Volume is implied by mark weight alone, and the exponent p tunes how aggressively the bold passes give way.