We study the problem of drawing a graph-theoretic path where each edge is assigned an axis-parallel direction in 3D. Di Battista et al.[3] gives a combinatorial characterization for such path drawings that start at the origin and reach a point in an octant. In this paper, we consider the drawability question for such paths that start at the origin and reach a point in a quadrant or an axis. We show that neither the necessity nor the sufficiency of the characterization given in [3] extends immediately to handle these cases. Furthermore, we give necessary conditions for such reachability, and also give examples to show they are not sufficient.
['Ethan Kim', 'Sue Whitesides', 'Giuseppe Liotta']
A note on drawing direction-constrained paths in 3D