, Volume 17, Issue 2, pp 199208
First online:
Threedimensional graph drawing
 R. F. CohenAffiliated withDepartment of Computer Science, University of Newcastle
 , P. EadesAffiliated withDepartment of Computer Science, University of Newcastle
 , Tao LinAffiliated withCSIRO DIT
 , F. RuskeyAffiliated withDepartment of Computer Science, University of Victoria
Rent the article at a discount
Rent now* Final gross prices may vary according to local VAT.
Get AccessAbstract
Graph drawing research has been mostly oriented toward twodimensional drawings. This paper describes an investigation of fundamental aspects of threedimensional graph drawing. In particular we give three results concerning the space required for threedimensional drawings.
We show how to produce a grid drawing of an arbitrarynvertex graph with all vertices located at integer grid points, in ann×2n×2n grid, such that no pair of edges cross. This grid size is optimal to within a constant. We also show how to convert an orthogonal twodimensional drawing in anH×V integer grid to a threedimensional drawing with\(\left\lceil {\sqrt H } \right\rceil \times \left\lceil {\sqrt H } \right\rceil \times V\) volume. Using this technique we show, for example, that threedimensional drawings of binary trees can be computed with volume\(\left\lceil {\sqrt n } \right\rceil \times \left\lceil {\sqrt n } \right\rceil \times \left\lceil {\log n} \right\rceil \). We give an algorithm for producing drawings of rooted trees in which thezcoordinate of a node represents the depth of the node in the tree; our algorithm minimizes thefootprint of the drawing, that is, the size of the projection in thexy plane.
Finally, we list significant unsolved problems in algorithms for threedimensional graph drawing.
Key Words
Graph drawing Algorithms Threedimensional Title
 Threedimensional graph drawing
 Journal

Algorithmica
Volume 17, Issue 2 , pp 199208
 Cover Date
 199702
 DOI
 10.1007/BF02522826
 Print ISSN
 01784617
 Online ISSN
 14320541
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Graph drawing
 Algorithms
 Threedimensional
 Industry Sectors
 Authors

 R. F. Cohen ^{(1)}
 P. Eades ^{(1)}
 Tao Lin ^{(2)}
 F. Ruskey ^{(3)}
 Author Affiliations

 1. Department of Computer Science, University of Newcastle, University Drive, 2308, Callaghan, New South Wales, Australia
 2. CSIRO DIT, GPO Box 664, 2601, Camberra, ACT, Australia
 3. Department of Computer Science, University of Victoria, V8W 3P6, Victoria, B.C., Canada