# To Approach Cylindrical Coordinates to Represent Multivariable Spatio-temporal Data

• Phuoc Vinh Tran
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7654)

## Abstract

Data representing a moving object include the data of time, position, and attributes. The data of positions and attributes of a moving object, which change over time may be recorded asynchronously because of the difference of sampling methods. Mathematically, these data may be synchronized over time by space-time conversions to constitute the data tuples at various time moments. In this article, we proposed the concept of data plane to represent data according to each tuple at each time moment. Subsequently, we integrated the data planes into the dimensions of a cylindrical coordinate system to represent the movement of objects in a space-time cylinder (STCy). In a space-time cylinder, positions of moving objects are indicated on the data planes which are constituted by the cylinder axis employed as the cylindrical axis of the cylindrical coordinate system, and the polar vectors of the cylindrical coordinate system. Each data plane indicates the data of objects at a time moment. The position of a moving object at a time moment is indicated by its coordinates on the data plane and the time moment by the angular coordinate of this plane. The attributes of moving objects are represented on data planes as the attribute bars parallel to the cylinder axis. The space-time path of a moving object surrounds the cylinder axis. Hence, the space-time cylinder is consistent with the representation of cyclic movements.

## Keywords

space-time cylinder spatio-temporal data movement data visualization

## References

1. 1.
Andrienko, N., Andrienko, G.: Visual analytics of movement: an overview of methods, tools, and procedures (2012)Google Scholar
2. 2.
Andrienko, G., Andrienko, N., Bak, P., Keim, D., Kisilevich, S., Wrobel, S.: A conceptual framework and taxonomy of techniques for analyzing movement. Journal of Visual Languages and Computing 23, 213–232 (2011)
3. 3.
Andrienko, G., Andrienko, N., Keim, D., MacEachren, A.M., Wrobel, S.: Challenging problems of geospatial visual analytics. Editorial/Journal of Visual Languages and Computing 22, 251–256 (2011)
4. 4.
Andrienko, G., Andrienko, N., Demsar, U., Dransch, D., Dykes, J., Fabrikant, S.I., Jern, M., Kraak, M.J., Schumann, H., Tominski, C.: Space, time and visual analytics. International Journal of Geographical Information Science 24(10), 1577–1600 (2010)
5. 5.
Andrienko, G., Andrienko, N.: Dynamic Time Transformation for Interpreting Clusters of Trajectories with Space-Time Cube. In: IEEE Symposium on Visual Analytics Science and Technology, Poster (2010)Google Scholar
6. 6.
Andrienko, G., Andrienko, N.: Visual Analytics for Geographic Analysis, Exemplified by Different Types of Movement Data. In: Information Fusion and Geographic Information Systems, Part 1. Lecture Notes in Geoinformation and Cartography, pp. 3–17 (2009)Google Scholar
7. 7.
Andrienko, N., Andrienko, G., Pelekis, N., Spaccapietra, S.: Basic concepts of movement data. In: Giannotti, F., Pedreschi, D. (eds.) Mobility, Data Mining and Privacy, Geographic Knowledge Discovery, pp. 15–38. Springer (2008)Google Scholar
8. 8.
Andrienko, N., Andrienko, G., Gatalsky, P.: Exploratory spatio-temporal visualization: an analytical review. Journal of Visual Languages and Computing, Special Issue on Visual Data Mining 14(6), 503–541 (2003)Google Scholar
9. 9.
Dodge, S., Weibel, R., Lautenschütz, A.-K.: Towards a Taxonomy of Movement Patterns. Information Visualization 2008(7), 240–252 (2008)
10. 10.
Gatalsky, P., Andrienko, N., Andrienko, G.: Interactive Analysis of Event Data Using Space-Time Cube. In: Proceedings of the Eighth International Conference on Information Visualisation (IV 2004). IEEE Computer Society (2004)Google Scholar
11. 11.
Hagerstrand, T.: What about people in regional science? Papers of Ninth European Congress of Regional Science Association, vol. 24, pp. 7–21 (1970)Google Scholar
12. 12.
Kraak, M.J.: The Space-Time Cube Revisited from a Geovisualization Perspective. In: Proceedings of the 21st International Cartographic Conference (ICC) “Cartographic Renaissance”, pp. 1988–1996 (2003)Google Scholar
13. 13.
Keim, D.A., Andrienko, G., Fekete, J.-D., Görg, C., Kohlhammer, J., Melançon, G.: Visual Analytics: Definition, Process, and Challenges. In: Kerren, A., Stasko, J.T., Fekete, J.-D., North, C. (eds.) Information Visualization. LNCS, vol. 4950, pp. 154–175. Springer, Heidelberg (2008)
14. 14.
Li, X., Kraak, M.J.: New views on multivariable spatiotemporal data: the space time cube expanded. In: International Symposium on Spatio-temporal Modelling, Spatial Reasoning, Analysis, Data Mining and Data Fusion, vol. XXXVI, pp. 199–201 (2005)Google Scholar
15. 15.
Willems, N., van Hage, W.R., de Vries, G., Janssens, J.H.M., Malais, V.: An integrated approach for visual analysis of a multi-source moving objects knowledge base. International Journal of Geographical Information Science 24(9), 1–16 (2010)Google Scholar
16. 16.
Peuquet, D.J.: It’s About Time: A Conceptual Framework for the Representation of Temporal Dynamics in Geographic Information Systems. Annals of the Association of American Geographers 84(3), 441–461 (1994)
17. 17.
Peuquet, D.J.: Representations of Space and Time. Guilford, New York (2002)Google Scholar
18. 18.
Tominski, C., Schulze-Wollgast, P., Schumann, H.: 3D Information Visualization for Time Dependent Data on Maps. In: Proceedings of the International Conference on Information Visualization (IV), pp. 175–181. IEEE Computer Society (2005)Google Scholar
19. 19.
Phuoc, T.V., Hong, N.T.: An Integrated Space-Time-Cube as a Visual Warning Cube. In: Proceedings of 3rd International Conference on Machine Learning and Computing, vol. 4, pp. 449–453. IEEE (2011)Google Scholar
20. 20.
Phuoc, T.V., Hong, N.T.: Visualization Cube for Tracking Moving Object. In: Proceedings of Computer Science and Information Technology, Information and Electronics Engineering, vol. 6, pp. 258–262. IACSIT Press (2011)Google Scholar
21. 21.
Li, X., Kraak, M.-J.: A temporal visualization concept: A new theoretical analytical approach for the visualization of multivariable spatio-temporal data. In: 18th International Conference on Geoinformatics, pp. 1–6 (2010), doi: 10.1109/GEOINFORMATICS.2010.5567529Google Scholar
22. 22.
Song, Y., Miller, H.J.: Exploring traffic flow databases using space-time plots and data cubes. Transportation 39(2), 215–234 (2012)