Abstract
Queries over streaming data offer the potential to provide timely information for modern database applications, such as sensor networks and web services. Isoline-based visualization of streaming data has the potential to be of great use in such applications. Dynamic (real-time) isoline extraction from the streaming data is needed in order to fully harvest that potential, allowing the users to see in real time the patterns and trends – both spatial and temporal – inherent in such data. This is the goal of this paper.
Our approach to isoline extraction is based on data terrains, triangulated irregular networks (TINs) where the coordinates of the vertices corresponds to locations of data sources, and the height corresponds to their readings. We dynamically maintain such a data terrain for the streaming data. Furthermore, we dynamically maintain an isoline (contour) map over this dynamic data network. The user has the option of continuously viewing either the current shaded triangulation of the data terrain, or the current isoline map, or an overlay of both.
For large networks, we assume that complete recomputation of either the data terrain or the isoline map at every epoch is impractical. If n is the number of data sources in the network, time complexity per epoch should be O(log n) to achieve real-time performance. To achieve this time complexity, our algorithms are based on efficient dynamic data structures that are continuously updated rather than recomputed. Specifically, we use a doubly-balanced interval tree, a new data structure where both the tree and the edge sets of each node are balanced.
As far as we know, no one has applied TINs for data terrain visualization before this work. Our dynamic isoline computation algorithm is also new. Experimental results confirm both the efficiency and the scalability of our approach.
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References
Adelson-Velskii, G.M., Landis, E.M.: An algorithm for the organization of information. Soviet Math. Doclady 3, 1259–1263 (1962)
Angel, E.: Interactive Computer Graphics: A Top-Down Approach with OpenGL. Pearson Addison-Wesley (July 2002)
Chiang, Y.-J., Silva, C.T.: I/O Optimal Isosurface Extraction. IEEE Visualization 1997, 293–250 (1997)
Cignoni, P., Marino, P., Montani, C., Puppo, E., Scopigno, R.: Speeding up Isosurface Extraction Using Interval Tree. IEEE Trans. on Visualization and Computer Graphics 3 (April-June 1997)
Devillers, O.: On Deletion in Delaunay Triangulations. In: Proc. 15th Annual Symp. on Computational Geometry, June 1999, pp. 181–188 (1999)
Edelsbrunner: Dynamic Data Structure for Orthogonal Intersection Queries. Tech. Rep. F59, Inst. Informationsverarb. Tech. Univ. Graz, Graz, Austria (1980)
Estrin, D.: Embedded Networked Sensing for Environmental Monitoring: Applications and Challenges. In: DIALM-POMC Joint Workshop on Found. of Mobile Computing, San Diego, CA (September 2003)
Garland, M., Heckbert, P.S.: Fast Polygonal Approximations of Terrains and Height Fields. Tech. Rep. CMU-CS-95-181, Carnegie Mellon Univ. (September 1995)
Guibas, L., Stolfi, J.: Primitives for the Manipulation of General Subdivisions and the Computation of Vorono Diagrams. ACM Trans. on Graphics 4(2), 74–123 (1985)
Heller, M.: Triangulation Algorithms for Adaptive Terrain Modeling. In: Proc. 4th Int’l Symp. of Spatial Data Handling, pp. 163–174 (1990)
Hellerstein, J.M., Hong, W., Madden, S., Stanek, K.: Beyond Average: Towards Sophisticated Sensing with Queries. In: 2nd Int’l Workshop on Information Proc. in Sensor Networks (IPSN 2003) (March 2003)
Larsen, K.S., Soisalon-Soininen, E., Widmayer, P.: Relaxed Balance through Standard Rotations. In: Workshop on Alg. and Data Structures (1997)
Lawson, C.L.: Software for C 1 Surface Interpolation. In: Rice, J.R. (ed.) Mathematical Software III, pp. 161–194. Academic Press, NY (1977)
Mostafavi, M.A., Gold, C., Dakowicz, M.: Delete and Insert Operations in Voronoi / Delaunay Methods and Applications. Computers & Geosciences 29(4), 523–530 (2003)
Shreiner, D., Woo, M., Neider, J., Davis, T.: OpenGL Programming Guide: The Official Guide to Learning OpenGL, Version 1.4, 4th edn. Addison-Wesley, Reading (2003)
van Kreveld, M.: Efficient Methods for Isoline Extraction from a Digital Elevation Model Based on Triangulated Irregular Networks. In: 6th Int’l Symp. on Spatial Data Handling Proc., pp. 835–847 (1994)
van Kreveld, M.: Digital Elevation Models and TIN Algorithms. In: Algorithmic Found. of Geographic Information Systems. LNCS (tutorials), vol. 1340, pp. 37–78. Springer, Berlin (1997)
Watt, A.H.: 3D Computer Graphics. Addison-Wesley, Reading (1999)
Weiss, M.A.: Data Structures and Algorithm Analysis in C. Addison-Wesley, Reading (1997)
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Goldin, D., Gao, H. (2006). Dynamic Isoline Extraction for Visualization of Streaming Data. In: Grigoriev, D., Harrison, J., Hirsch, E.A. (eds) Computer Science – Theory and Applications. CSR 2006. Lecture Notes in Computer Science, vol 3967. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11753728_42
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DOI: https://doi.org/10.1007/11753728_42
Publisher Name: Springer, Berlin, Heidelberg
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