Elliptical torus

A circular tube is swept along an elliptical centreline. Its cross-section stays perpendicular to that centreline, rather than being stretched with the whole object.

C(u) = (a cos u, b sin u, 0)
P(u,v) = C(u) + r cos v N(u) + r sin v (0,0,1)

N is the normalized outward ellipse normal. The tube radius is limited below the minimum centreline curvature radius to avoid a folded surface.