  In octilinear drawings of planar graphs, every edge is drawn as an
alternating sequence of horizontal, vertical and diagonal ($45^\circ$)
line-segments. In this paper, we study octilinear drawings of low edge
complexity, i.e., with few bends per edge. A $k$-planar graph is a planar graph
in which each vertex has degree less or equal to $k$. In particular, we prove
that every 4-planar graph admits a planar octilinear drawing with at most one
bend per edge on an integer grid of size $O(n^2) \times O(n)$. For 5-planar
graphs, we prove that one bend per edge still suffices in order to construct
planar octilinear drawings, but in super-polynomial area. However, for 6-planar
graphs we give a class of graphs whose planar octilinear drawings require at
least two bends per edge.
