Tubular domains and curves. a) Depicts the tubular co-ordinate system T defined in Eq. (2). b) Depicts a tubular domain with u₃(s) = 0, ∀s. The curves drawn in this domain are curves of constant R and θ values. We see that the curves follow the shape of the tube. b) Depicts a tubular domain with the same axis curve as a), but with u₃(s) ≠ 0 so that the curves of constant (R,θ) value wind internally in the tube.