Left: maps of the visual extinction A_V derived from the sub-mm dust opacity from Planck Collaboration XI (2014) at the 15′ resolution of our analysis for the Taurus molecular cloud (top), and the Chamaeleon molecular complex including the Musca filament (bottom). The vectors tracing the magnetic field orientation, computed from and , are plotted with a fixed length. Right: corresponding maps of the relative orientation between matter structures and magnetic field quantified by cos2Θ for the selected structures (Sect. 4). This figure shows coherent structures where the cosine is either positive or negative, corresponding to a magnetic field aligned with, or perpendicular to the structures.