  In a recent article (Auer et al, Algorithmica 2016) it was claimed that every
outer-1-planar graph has a planar visibility representation of area $O(n\log
n)$. In this paper, we show that this is wrong: There are outer-1-planar graphs
that require $\Omega(n^2)$ area in any planar drawing. Then wegive a
construction (using crossings, but preserving a given outer-1-planar embedding)
that results in an orthogonal box-drawing with O(n log n) area and at most two
bends per edge.
