Four HFs structures used to demonstrate the velocity gradient fitting. The beamsize is ~0.34 pc. In the first row, the background is the integrated intensity map of ¹³CO (3-2); orange and cyan lines are the filaments identified by the filfinder algorithm. The background images were re-gridded, in contrast to those shown in Fig. 2. The two rows below show the velocity and intensity profiles extracted along the orange filaments. In panel a, velocity gradients are fitted in the ranges defined by the vertical dashed red lines in panel b. Straight lines show the linear fitting results. In panel b, dotted blue and red lines show the normalized velocity and intensity, respectively.