  We examine semi-bar visibility graphs in the plane and on a cylinder in which
sightlines can pass through k objects. We show every semi-bar k-visibility
graph has a (k+2)-quasiplanar representation in the plane with vertices drawn
as points in convex position and edges drawn as segments. We also show that the
graphs having cylindrical semi-bar k-visibility representations with semi-bars
of different lengths are the same as the (2k+2)-degenerate graphs having
edge-maximal (k+2)-quasiplanar representations in the plane with vertices drawn
as points in convex position and edges drawn as segments.
