Orthogonal Drawings of Cycles in 3D Space (Extended Abstract)

Let C be a directed cycle, whose edges have each been assigned a desired direction in 3D (East, West, North, South, Up, or Down) but no length. We say that C is a shape cycle. We consider the following problem. Does there exist an orthogonal drawing $\Gamma$ of C in 3D such that each edge of $\Gamma$ respects the direction assigned to it and such that $\Gamma$ does not intersect itself? If the answer is positive, we say that C is simple. This problem arises in the context of extending orthogonal graph drawing techniques and VLSI rectilinear layout techniques from 2D to 3D. We give a combinatorial characterization of simple shape cycles that yields linear time recognition and drawing algorithms