Orthogonal 3-D Graph Drawing

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. Communicated by G. Di Battista and P. Mutzel. Submitted: February 1998. Revised: November 1998. The authors gratefully thank N.S.E.R.C. for financial assistance. The conference version of this paper appeared in the proceedings of Graph Drawing ’97. These joint results were also presented as part of the Ph.D. thesis of T. Biedl at Rutgers University. This work was done while the fourth author was on sabbatical leave at McGill University. 

• Type: Conference
• Year: 1997
• Where: GD
• Authors: Therese C. Biedl, Thomas C. Shermer, Sue Whitesides, Stephen K. Wismath
• Keywords: Asymptotic Lower Bounds, Computer Graphics, Edge Route, GD 1997, Orthogonal Grid Drawings