Bounds For Orthogonal 3-D Graph Drawing
Thérèse Biedl, Thomas Caton Shermer, Sue H. Whitesides, Stephen Wismath · Journal of Graph Algorithms and Applications · 1999
This paper studies 3-D orthogonal grid drawings for graphs of arbitrary degree, in particular Kn, with vertices drawn as boxes. It establishes asymptotic lower bounds for the volume of the bounding box and the number of bends of such drawings and exhibits a construction that achieves these bounds. No edge route in this 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.