Abstract
We present two algorithms for orthogonal graph drawing in three dimensional space. For graphs of maximum degree six, the 3-D drawing is produced in linear time, has volume at most 4.66n 3 and each edge has at most three bends. If the degree of the graph is arbitrary, the vertices are represented by solid 3-D boxes whose surface is proportional to their degree. The produced drawing has two bends per edge. Both algorithms guarantee no crossings and can be used under an interactive setting (i.e., vertices arrive and enter the drawing on-line), as well.
Research supported in part by NIST, Advanced Technology Program grant number 70NANB5H1162.
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
T. Biedl and G. Kant, A Better Heuristic for Orthogonal Graph Drawings, Proc. 2nd Ann. European Symposium on Algorithms (ESA '94), Lecture Notes in Computer Science, vol. 855, pp. 24–35, Springer-Verlag, 1994.
M. Brown and M. Najork, Algorithm animation using 3D interactive graphics, Proc. ACM Symp. on User Interface Software and Technology, 1993, pp. 93–100.
I. Bruss and A. Frick, Fast Interactive 3-D Visualization, Proc. of Workshop GD '95, Lecture Notes in Comp. Sci. 1027, Springer-Verlag, 1995, pp. 99–110.
R. Cohen, P. Eades, T. Lin, F. Ruskey, Three Dimensional Graph Drawing, Proc. of DIMACS Workshop GD '94, Lecture Notes in Comp. Sci. 894, Springer-Verlag, 1994, pp. 1–11.
I. Cruz and J. Twarog, 3D Graph Drawing with Simulated Annealing, Proc. of Workshop GD '95, Lecture Notes in Comp. Sci. 1027, Springer-Verlag, 1995, pp. 162–165.
G. Di Battista, P. Eades, R. Tamassia and I. Tollis, Algorithms for Drawing Graphs: An Annotated Bibliography, Computational Geometry: Theory and Applications, vol. 4, no 5, 1994, pp. 235–282. Also available via anonymous ftp from ftp.cs.brown.edu, gdbiblio.tex.Z and gdbiblio.ps.Z in /pub/papers/compgeo.
P. Eades, C. Stirk, S. Whitesides, The Techniques of Kolmogorov and Bardzin for Three Dimensional Orthogonal Graph Drawings, TR 95-07, Dept. of Computer Science, University of Newcastle, Australia, 1995. Also to appear in Information Processing Letters.
P. Eades, A. Symvonis, S. Whitesides, Two Algorithms for Three Dimensional Orthogonal Graph Drawing, Proc. of Workshop GD '96, Lecture Notes in Comp. Sci. 1190, Springer-Verlag, 1996, pp. 139–154.
A. Garg and R. Tamassia, GIOTT03D: A System for Visualizing Hierarchical Structures in 3D, Proc. of Workshop GD '96, Lecture Notes in Comp. Sci. 1190, Springer-Verlag, 1996, pp. 193–200.
Goos Kant, Drawing Planar Graphs Using the Canonical Ordering, Algorithmica, vol. 16, no. 1, 1996, pp. 4–32.
A. N. Kolmogorov and Y. M. Bardzin, About Realization of Sets in 3-dimensional Space, Problems in Cybernetics, 1967, pp. 261–268.
J. MacKinley, G. Robertson, S. Card, Cone Trees: Animated 3d visualizations of hierarchical information, In Proc. of SIGCHI Conf. on Human Factors in Computing, pp. 189–194, 1991.
A. Papakostas and I. G. Tollis, Algorithms for Area-Efficient Orthogonal Drawings, Technical Report UTDCS-06-95, The University of Texas at Dallas, 1995.
A. Papakostas and I. G. Tollis, Issues in Interactive Orthogonal Graph Drawing, Proc. of Workshop GD '95, Lecture Notes in Comp. Sci, 1027, Springer-Verlag, 1995, pp. 419–430.
A. Papakostas and I. G. Tollis, A Pairing Technique for Area-Efficient Orthogonal Drawings, Proc. of Workshop GD '96, Lecture Notes in Comp. Sci. 1190, Springer-Verlag, 1996, pp. 355–370.
A. Papakostas, J. Six and I. G. Tollis, Experimental and Theoretical Results in Interactive Graph Drawing, Proc. of Workshop GD '96, Lecture Notes in Comp. Sci. 1190, Springer-Verlag, 1996, pp. 371–386.
A. Papakostas and I. G. Tollis, Incremental Orthogonal Graph Drawing in Three Dimensions, Technical Report UTDCS-02-97, The University of Texas at Dallas, 1997. (available through www.utdallas.eduttollis)
S. Reiss, An engine for the 3D visualization of program information, J. Visual Languages and Computing, vol. 6, no. 3, 1995.
Markus Schäffter, Drawing Graphs on Rectangular Grids, Discr. Appl. Math. 63 (1995) pp. 75–89.
R. Tamassia and I. Tollis, Planar Grid Embeddings in Linear Time, IEEE Trans. on Circuits and Systems CAS-36 (1989), pp. 1230–1234.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1997 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Papakostas, A., Tollis, I.G. (1997). Incremental orthogonal graph drawing in three dimensions. In: DiBattista, G. (eds) Graph Drawing. GD 1997. Lecture Notes in Computer Science, vol 1353. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63938-1_50
Download citation
DOI: https://doi.org/10.1007/3-540-63938-1_50
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-63938-1
Online ISBN: 978-3-540-69674-2
eBook Packages: Springer Book Archive