Two selected filaments illustrate the fitting of the velocity gradient. Upper panels: velocity gradients are fit in the ranges defined by the vertical dashed red lines, and straight lines show the linear fitting results. Lower panels: dotted blue and red lines show the normalized velocity and intensity, respectively. The orange circles mark the intensity peaks of ¹³CO (3–2) emission associated with ATLASGAL clumps. For other filaments, see Figs. A.4–A.8.