Elliptical Cross-section:

If the axis of rotation does not pass through the center of a total circle or ellipse, then rotation around the axis generates a torus along with a circular or elliptical cross section as appropriate. Noting that the parametric equation of a non-origin-centered ellipse in the xy plane is

x = h + a cos θ                         0  ≤θ ≤ 2π

y = k + b sin θ

here (h, k) are the x and y coordinates of the center of the ellipse. The parametric equation for a particular point on the torus is

Q (θ, φ) = [h + a cos θ (k + b sin θ) cos φ   (k + b sin θ) sin φ]