Representation of the orbit (in green) of the compact object around its stellar companion (in blue) for Vela X-1 (top panel) and Cygnus X-1 (bottom panel) as seen from Earth, where the eccentricity of the orbit has been neglected. Only a fraction of the clumps susceptible to contribute to the column density along the orbit have been represented (in semi-opaquegrey). The black cross indicates the point of inferior conjunction on the orbit.