This is regarding the fundamental group computation of the complement of a toral knot in $S^3$ in Hatcher's algebraic topology book. See page 48. I have understood till the stage where the cross section of the torus minus the knot deformation-retracts to the radial segments as the arrows indicate. What is not clear is "Letting $x$ vary, these radial segments then trace out a copy of the mapping cylinder $X_m$ in the first solid torus."
I tried imagining this with a simple cases like the trefoil knot, but can't fathom this statement. Any help would be greatly appreciated!