Rounded-square torus
Geometry
A rounded square centreline carries a circular tube. The centreline is a superellipse, |x/a|^n + |y/b|^n = 1, traced parametrically as x = a sgn(cos u)|cos u|^(2/n), y = b sgn(sin u)|sin u|^(2/n). At n = 2 this is an ellipse; larger n pushes material into the four corners.
P(u,v) = C(u) + r cos v N(u) + r sin v (0,0,1)
N is the numerical outward normal, N = normalize(Ty, −Tx) with T = C(u+ε) − C(u−ε), ε = 0.001, so the cross-section stays circular and square to the centreline rather than being stretched with the shape. The tube radius is capped at 0.8 × the smallest centreline curvature radius, sampled over 200 positions, so the surface never folds through itself.
The porcelain-white surface is left plain: light falls on the broad faces and the inner edge of the ring darkens on its own, which is what gives the form its quiet edge.