How to make curved line into torus?

  1. Greetings,

    I am trying to figure out how to modify the equations for a trefoil knot to make it toroidal.

    A trefoil knot is:
    x = (2 + cos 3t)cos 2t
    y = (2 + cos 3t)sin 2t
    z = sin 3t

    A torus is:
    x(u, v) = (R + r cos v) cos u
    y(u, v) = (R + r cos v) sin u
    z(u,v) = r sin v


    u, v are in the interval [0, 2π),
    R is the distance from the center of the tube to the center of the torus,
    r is the radius of the tube.

  2. jcsd
  3. A comparison of the equations suggests that we set R=2, r=1 & (u,v) =(2t,3t).
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