This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Fast, Memory-Efficient Cell Location in Unstructured Grids for Visualization
November/December 2010 (vol. 16 no. 6)
pp. 1541-1550
Christoph Garth, University of California, Davis
Kenneth I. Joy, University of California, Davis
Applying certain visualization techniques to datasets described on unstructured grids requires the interpolation of variables of interest at arbitrary locations within the dataset's domain of definition. Typical solutions to the problem of finding the grid element enclosing a given interpolation point make use of a variety of spatial subdivision schemes. However, existing solutions are memory- intensive, do not scale well to large grids, or do not work reliably on grids describing complex geometries. In this paper, we propose a data structure and associated construction algorithm for fast cell location in unstructured grids, and apply it to the interpolation problem. Based on the concept of bounding interval hierarchies, the proposed approach is memory-efficient, fast and numerically robust. We examine the performance characteristics of the proposed approach and compare it to existing approaches using a number of benchmark problems related to vector field visualization. Furthermore, we demonstrate that our approach can successfully accommodate large datasets, and discuss application to visualization on both CPUs and GPUs.

[1] N. Andrysco, X. Tricoche, Matrix *trees. Computer Graphics Forum, 29 (3) 2010 (to appear).
[2] K. Bürger, F. Ferstl, H. Theisel, and R. Westermann, Interactive streak surface visualization on the gpu. IEEE Transactions on Visualization and Computer Graphics, 15: 1259–1266, 2009.
[3] K. Burger, P. Kondratieva, J. Kriiger, and R. Westermann, Importance-driven particle techniques for flow visualization. In Proceedings of IEEE VGTC Pacific Visualization Symposium, 2008.
[4] K. Bürger, J. Schneider, P. Kondratieva, J. Kriiger, and R. Westermann, Interactive visual exploration of instationary 3D-flows. In Eurographics/IEEE VGTC Symposium on Visualization (EuroVis), to appear, 2007.
[5] G. F. Carey and J. T. Oden, Finite Elements: A Second Course. Prentice-Hall, Englewood Cliffs, NJ, 1983.
[6] H. Childs, E. S. Brugger, K. S. Bonnell, J. S. Meredith, M. Miller, B. J. Whitlock, and N. Max, A contract-based system for large data visualization. In Proceedings of IEEE Visualization 2005 pages 190–198, 2005.
[7] P. Fischer, J. Lottes, D. Pointer, and A. Siegel, Petascale algorithms for reactor hydrodynamics. Journal of Physics: Conference Series, 125: 1–5, 2008.
[8] C. Garth, H. Krishnan, X. Tricoche, T. Tricoche, and K. I. Joy, Generation of accurate integral surfaces in time-dependent vector fields. IEEE Transactions on Visualization and Computer Graphics, 14 (6): 1404–1411, 2008.
[9] J. Goldsmith and J. Salmon, Automatic creation of object hierarchies for ray tracing. IEEE Computer Graphics and Applications, 7 (5): 14–20, 1987.
[10] V. Havran, Heuristic Ray Shooting Algorithms. PhD thesis, Czech Technical University, Prague, 2001.
[11] A. Henderson, ParaView Guide. A Parallel Visualization Application. Kitware Inc., 2007.
[12] M. Langbein, G. Scheuermann, and X. Tricoche, An efficient point location method for visualization in large unstructured grids. In Proceedings of Vision, Modeling, Visualization, 2003.
[13] P. J. Prince and J. R. Dormand, High order embedded runge-kutta formulae. Journal of Computational and Applied Mathematics, 7 (1), 1981.
[14] F. Sadlo and R. Peikert, Visualizing lagrangian coherent structures and comparison to vector field topology. In Topology-Based Methods in Visualization II, Mathematics and Visualization, pages 15–29. Springer, Berlin Heidelberg, 2007.
[15] M. Schirski, C. Bischof, and T. Kuhlen, Interactive Particle Tracing on Tetrahedral Grids Using the GPU. In Proceedings of Vision, Modeling, and Visualization (VMV) 2006, pages 153–160, 2006.
[16] W Schroeder, K. Martin, and B. Lorensen, The Visualization Toolkit: An Object-Oriented Approach to 3D Graphics. Prentice Hall, 1997.
[17] W von Funck, T. Weinkauf, H. Theisel, and H.-P. Seidel, Smoke surfaces: An interactive flow visualization technique inspired by real-world flow experiments. IEEE Transactions on Visualization and Computer Graphics, 14 (6): 1396–1403, 2008.
[18] C. Wächter and A. Keller, Instant ray tracing: The bounding interval hierarchy. In Proceedings of the 17th Eurographics Symposium on Rendering, 2006.
[19] D. Weiskopf and T. Ertl, GPU-Based 3D Texture Advection for the Visualization of Unsteady Flow Fields. In In WSCG 2004 Conference Proceedings, Short Papers, pages 259–266, 2004.
[20] A. Wiebel, C. Garth, M. Hlawitschka, T. Wischgoll, and G. Scheuermann, Fantom - lessons learned from design, implementation, administration, and use of a visualization system for over 10 years. In In Refactoring Visualization from Experience (ReVisE) 2009, co-located with IEEE Visualization, 2009.
[21] J. Wilhelms and A. van Gelder, Octrees for faster isosurface generation. ACM Transactions of Graphics, 11 (3): 201–227, 1992.
[22] G. Zachmann, Minimal hierarchical collision detection. In Proc. ACM Symposium on Virtual Reality Software and Technology (VRST), pages 121–128, Hong Kong, China, Nov. 11–13 2002.

Index Terms:
unstructured grids, cell location, interpolation, vector field visualization
Citation:
Christoph Garth, Kenneth I. Joy, "Fast, Memory-Efficient Cell Location in Unstructured Grids for Visualization," IEEE Transactions on Visualization and Computer Graphics, vol. 16, no. 6, pp. 1541-1550, Nov.-Dec. 2010, doi:10.1109/TVCG.2010.156
Usage of this product signifies your acceptance of the Terms of Use.