  A directed path whose edges are assigned labels "up", "down", "right", or
"left" is called \emph{four-directional}, and \emph{three-directional} if at
most three out of the four labels are used. A \emph{direction-consistent
embedding} of an \mbox{$n$-vertex} four-directional path $P$ on a set $S$ of
$n$ points in the plane is a straight-line drawing of $P$ where each vertex of
$P$ is mapped to a distinct point of $S$ and every edge points to the direction
specified by its label. We study planar direction-consistent embeddings of
three- and four-directional paths and provide a complete picture of the problem
for convex point sets.
