Distribution of backbone mass between non-parallel lines

We determine the backbone mass distributions for bond percolation between two lines of arbitrary orientations in three dimensions. All simulations were performed at the percolation threshold pc. The slope of the power law regime of the backbone mass distribution is dependent upon the angle between the lines, θ, but the characteristic backbone mass is only weakly affected by θ. We propose new scaling functions that reproduce the θ dependence of the characteristic backbone mass found in the simulations.