Abstract
In this paper we investigate some applications of the concept of tolerance to graph drawing. Given a geometric structure, the tolerance is a measure of how much the set of points can be arbitrarily changed while preserving the structure. Then, if we have a layout of a graph and we want to redraw the graph while preserving the mental map (captured by some proximity graph of the set of nodes), the tolerance of this proximity graph can be a useful tool. We present an optimal O(n log n) algorithm for computing the tolerance of the Delaunay triangulation of a set of points and propose some variations with applications to interactive environments.
Partially supported by CICYT grant TIC 93-0747-C02
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
M. Abellanas, J. García, G. Hernández, F. Hurtado, O. Serra, J. Urrutia: Updating polygonizations, Computer Graphics Forum, vol.12, n.3 (1993), pp.143–152.
M. Abellanas, F. Hurtado, P. Ramos: Tolerance of geometric structures, Proc. 6th Canadian Conference on Computational Geometry (1994).
P.J. Agarwal, M. Sharir, S. Toledo: Applications of parametric searching in geometric optimization, Proc. 3rd ACM-SIAM Symposium on Discrete Algorithms (1992), pp.72–82.
F. Aurenhammer: Improved algorithms for discs and balls using power diagrams, Journal of Algorithms 9 (1988), pp.151–161.
K.Q. Brown: Geometric transforms for fast geometric algorithms, Ph.D. thesis, Rep. CMU-CS-80-101, Dept. of Computer Science, Carnegie-Mellon Univ., Pittsburgh (1980).
P. Eades, R. Tamassia: Algorithms for drawing graphs: An annotated bibliography, Technical report, Dept. of Computer Science, Brown Univ., Providence, Rhode Island (1989).
P. Eades, W. Lai, K. Misue, K. Sugiyama: Preserving the Mental Map of a Diagram Research Report IIAS-RR-91-16E, International Institute for Advanced Study of Social Information Science, Fujitsu Laboratories Ltd., 17–25, Shinkamata 1-chome, Ohta-ku, Tokyo 144, Japan, August 1991.
K.A. Lyons: Cluster Busting in Anchored Graph Drawing Ph.D. thesis, Queen's University (1994).
K.A. Lyons, H. Meijer, D. Rappaport: Properties of the Voronoi Diagram Cluster Buster Proc. 1993 CAS Conference (CASCON'93) Vol. II, A. Gawman, W.M. Getleman, E. Kidd, P. Larson, J. Slonim, Eds, IBM Canada Ltd. Laboratory Center for Advanced Studies and NRC Canada, Toronto (Canada), October 24–28 1993, pp. 1148–1163.
P. Ramos: Tolerancia de Estructuras Geométricas y Combinatorias Ph.D. Thesis (in Spanish), in preparation.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1995 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Abellanas, M., Hurtado, F., Ramos, P.A. (1995). Redrawing a graph within a geometric tolerance. In: Tamassia, R., Tollis, I.G. (eds) Graph Drawing. GD 1994. Lecture Notes in Computer Science, vol 894. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58950-3_376
Download citation
DOI: https://doi.org/10.1007/3-540-58950-3_376
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-58950-1
Online ISBN: 978-3-540-49155-2
eBook Packages: Springer Book Archive