Orthogonal 3-D graph drawing
This paper studies 3-D orthogonal grid drawings for graphs of arbitrary degree, Kn in particular, with vertices drawn as boxes. It establishes an asymptotic lower bound for the volume of the bounding box of such drawings and exhibits a construction that achieves this bound. No edge route in this unconstrained construction bends more than three times.
For drawings constrained to have at most k bends on any edge route, simple constructions are given for k = 1 and k = 2. The unconstrained construction handles the k ≥ 3 cases, while for k = 0 (no bends), it is proved here that not all graphs can be drawn.
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