C¹⁸O distribution histogram of the oriented angles of the column density (top row) and velocity gradients (middle row) in the Horsehead nebula from the reference decomposition DO (left), decomposition Dl (middle) and decomposition D2 (right), respectively. Last row: histograms of the relative orientation between column density and velocity. Data with are shown in cyan, in blue, in blue-violet, in purple, and in fuchsia. The colored bars at 10° show the error bars of the histograms.