In octilinear drawings of planar graphs, every edge is drawn as an
alternating sequence of horizontal, vertical and diagonal (45∘)
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(n2)×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