I know I can create a toroidal knot ribbon: If B is the binormal to the curve, adding uB to the parametrization for some u between -1 and 1 should do it. You get a surface described by r(t,u). However, this ribbon will always be tangent to the surface of the torus and not "hug" it.
How can I create the equations that describe a toroidal knot patch that wraps on the surface of the torus? (I envision this as the portion of the torus surface between two knots that are exactly the same, only offset from each other by some amount).