A forming device for gathering the width of a traveling web is disclosed. The forming device includes opposing arrays of flute-forming bars that can be interlaced to define therebetween a longitudinal flute-forming labyrinth effective to reduce the width of a web traveling therethrough by a preselected take-up ratio. The flute-forming bars are curved beginning at an entry end of the forming device such that they converge in a lateral direction as they proceed in the machine direction. In this manner, individual elements of the web traveling between the respective arrays in the machine direction follow contour lines along the curved bars or between adjacent ones of the curved bars so that no such element crosses any flute-forming bar in the cross-machine direction as the web travels and is fluted. A corrugating die for introducing a near-net shape to the intermediate-fluted web is also disclosed, as are a corrugating line incorporating these operations and methods for its operation.