Using Graph Layout to Visualize Train Interconnection Data
We are concerned with the problem of visualizing interconnections in railroad systems. The real-world systems we have to deal with contain connections of thousands of trains. To visualize such a system from a given set of time tables a so-called train graph is used. It contains a vertex for each station met by any train, and one edge between every pair of vertices connected by some train running from one station to the other without halting in between.
In visualizations of train graphs, positions of vertices are predetermined, since each station has a given geographical location. If all edges are represented by straight-lines, the result is visual clutter with many overlaps and small angles between pairs of lines. We here present a non-uniform approach using different representations for edges of distinct meaning in the exploration of the data. Only edges of certain type are represented by straight-lines, whereas so-called transitive edges are rendered using Bézier curves. The layout problem then consists of placing control points for these curves. We transform it into a graph layout problem and exploit the generality of random field layout models for its solution.
KeywordsLayout Problem Graph Layout Minimal Edge Visual Clutter Layout Model
- Pierre Bézier. Numerical Control. John Wiley, 1972.Google Scholar
- Ulrik Brandes, Patrick Kenis, Jörg Raab, Volker Schneider, and Dorothea Wagner. Explorations into the visualization of policy networks. To appear in Journal of Theoretical Politics.Google Scholar
- Ulrik Brandes and Dorothea Wagner. A Bayesian paradigm for dynamic graph layout. Proceedings of Graph Drawing’ 97. Springer, Lecture Notes in Computer Science, vol. 1353, pages 236–247, 1997.Google Scholar
- Ulrik Brandes and Dorothea Wagner. Random field models for graph layout. Konstanzer Schriften in Mathematik und Informatik 33, University of Konstanz, 1997.Google Scholar
- Toshiyuki Masui. Evolutionary learning of graph layout constraints from examples. Proceedings of the ACM Symposium on User Interface Software and Technology. ACM Press, pages 103–108, 1994.Google Scholar
- Xavier MendonÇa and Peter Eades. Learning aesthetics for visualization. Anais do XX Seminário Integrado de Software e Hardware, Florianópolis, Brazil, pages 76–88, 1993.Google Scholar
- Marcello Pelillo and Edwin R. Hancock (eds.). Energy Minimization Methods in Computer Vision and Pattern Recognition, Springer, Lecture Notes in Computer Science, vol. 1223, 1997.Google Scholar
- Gerhard Winkler. Image Analysis, Random Fields and Dynamic Monte Carlo Methods, vol. 27 of Applications of Mathematics. Springer, 1995.Google Scholar