  An octilinear drawing of a planar graph is one in which each edge is drawn as
a sequence of horizontal, vertical and diagonal at 45 degrees line-segments.
For such drawings to be readable, special care is needed in order to keep the
number of bends small. As the problem of finding planar octilinear drawings of
minimum number of bends is NP-hard, in this paper we focus on upper and lower
bounds. From a recent result of Keszegh et al. on the slope number of planar
graphs, we can derive an upper bound of 4n-10 bends for 8-planar graphs with n
vertices. We considerably improve this general bound and corresponding previous
ones for triconnected 4-, 5- and 6-planar graphs. We also derive non-trivial
lower bounds for these three classes of graphs by a technique inspired by the
network flow formulation of Tamassia.
