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Issue No.06 - November/December (2010 vol.16)
pp: 1569-1577
Florian Ferstl , Technische Universität München
Kai Bürger , Technische Universität München
Holger Theisel , University of Magdeburg
Rüdiger Westermann , Technische Universität München
ABSTRACT
Streak surfaces are among the most important features to support 3D unsteady flow exploration, but they are also among the computationally most demanding. Furthermore, to enable a feature driven analysis of the flow, one is mainly interested in streak surfaces that show separation profiles and thus detect unstable manifolds in the flow. The computation of such separation surfaces requires to place seeding structures at the separation locations and to let the structures move correspondingly to these locations in the unsteady flow. Since only little knowledge exists about the time evolution of separating streak surfaces, at this time, an automated exploration of 3D unsteady flows using such surfaces is not feasible. Therefore, in this paper we present an interactive approach for the visual analysis of separating streak surfaces. Our method draws upon recent work on the extraction of Lagrangian coherent structures (LCS) and the real-time visualization of streak surfaces on the GPU. We propose an interactive technique for computing ridges in the finite time Lyapunov exponent (FTLE) field at each time step, and we use these ridges as seeding structures to track streak surfaces in the time-varying flow. By showing separation surfaces in combination with particle trajectories, and by letting the user interactively change seeding parameters such as particle density and position, visually guided exploration of separation profiles in 3D is provided. To the best of our knowledge, this is the first time that the reconstruction and display of semantic separable surfaces in 3D unsteady flows can be performed interactively, giving rise to new possibilities for gaining insight into complex flow phenomena.
INDEX TERMS
Unsteady flow visualization, feature extraction, streak surface generation, GPUs
CITATION
Florian Ferstl, Kai Bürger, Holger Theisel, Rüdiger Westermann, "Interactive Separating Streak Surfaces", IEEE Transactions on Visualization & Computer Graphics, vol.16, no. 6, pp. 1569-1577, November/December 2010, doi:10.1109/TVCG.2010.169
REFERENCES
[1] G. Benettin, L. Galgani, A. Giorgilli, and J. M. Strelcyn, Lyapunov characteristic exponent for smooth dynamical systems and hamiltonian systems; a method for computing all of them. Mechanica, 15 (1): 9–20, 1980.
[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 (6): 1259–1266, November-December 2009.
[3] K. Bürger, P. Kondratieva, J. Krüger, and R. Westermann, Importance-Driven Particle Techniques for Flow Visualization. In Proceedings of IEEE VGTC Pacific Visualization Symposium 2008, pages 71–78, 2008.
[4] K. Bürger, J. Schneider, P. Kondratieva, J. Krüger, and R. Westermann, Interactive Visual Exploration of Instationary 3D-Flows. In Eurographics/IEEE VGTC Symposium on Visualization (EuroVis), pages 251–258, 2007.
[5] D. Eberly, R. Gardner, B. Morse, S. Pizer, and C. Scharlach, Ridges for image analysis. J. Math. Imaging Vis., 4 (4): 353–373, 1994.
[6] O. Frederich, E. Wassen, and F. Thiele, Flow Simulation around a Finite Cylinder on Massively Parallel Computer Architecture. In International Conference on Parallel Computational Fluid Dynamics, pages 85–93, 2005.
[7] C. Garth, F. Gerhardt, X. Tricoche, and H. Hagen, Efficient Computation and Visualization of Coherent Structures in Fluid Flow Applications. IEEE Transactions on Visualization and Computer Graphics, 13: 1464–1471, 2007.
[8] C. Garth, H. Krishnan, X. Tricoche, T. Bobach, 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] C. Garth, G. Li, X. Tricoche, C. Hansen, and H. Hagen, Visualization of Coherent Structures in Transient 2D Flows. In Topology-Based Methods in Visualization II (Proceedings of TopoInVis 2007), pages 1–14, 2009.
[10] S. Guthe, S. Gumhold, and W. Strasser, Interactive visualization of volumetric vector fields using texture based particles. In Proceedings of WSCG, volume 10, pages 33–41, 2002.
[11] G. Haller, Distinguished material surfaces and coherent structures in three-dimensional fluid flows. Phys. D, 149 (4): 248–277, 2001.
[12] G. Haller, Lagrangian coherent structures from approximate velocity data. Physics of Fluids, 14 (6): 1851–1861, 2002.
[13] G. Haller and G. Yuan, Lagrangian coherent structures and mixing in two-dimensional turbulence. Phys. D, 147 (3–4): 352–370, 2000.
[14] R. M. Haralick, Ridges and valleys on digital images. Computer Vision, Graphics, and Image Processing, 22 (1): 28–38, 1983.
[15] J. P.M. Hultquist, Constructing stream surfaces in steady 3D vector fields. pages 171–178, 1992.
[16] J. Kasten, C. Petz, I. Hotz, B. Noack, and H.-C. Hege, Localized finite-time lyapunov exponent for unsteady flow analysis. In M. Magnor, B. Rosenhahn, and H. Theisel editors, , Vision Modeling and Visualization, volume 1, pages 265–274. Universitat Magdeburg, Inst. f. Simulation u. Graph., 2009.
[17] G. L. Kindlmann, R. S.J. Estépar, S. M. Smith, and C.-F. Westin, Sampling and visualizing creases with scale-space particles. IEEE Trans. Visualization and Computer Graphics, 15 (6): 1415–1424, Nov/Dec 2009.
[18] P. Kondratieva, J. Kriiger, and R. Westermann, The Application of GPU Particle Tracing to Diffusion Tensor Field Visualization. 0: 10, 2005.
[19] H. Krishnan, C. Garth, and K. Joy, Time and Streak Surfaces for Flow Visualization in Large Time-Varying Data Sets. IEEE Transactions on Visualization and Computer Graphics, 15: 1267–1274, 2009.
[20] J. Krüger, P. Kipfer, P. Kondratieva, and R. Westermann, A Particle System for Interactive Visualization of 3D Flows. IEEE Transactions on Visualization and Computer Graphics, 11 (6): 744–756, 2005.
[21] F. Lekien, C. Coulliette, A. J. Mariano, E. H. Ryan, L. K. Shay, G. Haller, and J. Marsden, Pollution release tied to invariant manifolds: A case study for the coast of florida. Phys. D, 210 (1), 2005.
[22] T. Lindeberg, Edge detection and ridge detection with automatic scale selection. Int. J. Comput. Vision, 30 (2): 117–156, 1998.
[23] D. Lipinski and K. Mohseni, A ridge tracking algorithm and error estimate for efficient computation of lagrangian coherent structures. Chaos: An Interdisciplinary Journal of Nonlinear Science, 20 (1): 017504, 2010.
[24] T. McLoughlin, R. Laramee, R. Peikert, F. Post, and M. Chen, Over Two Decades of Integration-Based, Geometric Flow Visualization. In Computer Graphics Forum, (to appear), 2010.
[25] D. Merhof, M. Sonntag, F. Enders, C. Nimsky, and G. Greiner, Hybrid visualization for white matter tracts using triangle strips and point sprites. IEEE Transactions on Visualization and Computer Graphics, 12 (5): 1181–1188, 2006.
[26] K. Palgyi and A. Kuba, A parallel 3d 12-subiteration thinning algorithm. Graphical Models and Image Processing, 61 (4): 199 – 221, 1999.
[27] R. Peikert and F. Sadlo, Height Ridge Computation and Filtering for Visualization. In Proceedings of IEEE VGTC Pacific Visualization Symposium 2008, pages 119–126, 2008.
[28] F. H. Post, B. Vrolijk, H. Hauser, R. S. Laramee, and H. Doleisch, The state of the art in flow visualisation: Feature extraction and tracking. Computer Graphics Forum, 22 (4): 775–792, 2003.
[29] M. Roerdink, The watershed transform: definitions, algorithms, and parallellization strategies. Fundamenta Informaticae, 41 (1): 187–228, 2000.
[30] F. Sadlo and R. Peikert, Efficient Visualization of Lagrangian Coherent Structures by Filtered AMR Ridge Extraction. IEEE Transactions on Visualization and Computer Graphics, 13 (6): 1456–1463, 2007.
[31] F. Sadlo and R. Peikert, Visualizing lagrangian coherent structures and comparison to vector field topology. In Topology-Based Methods in Visualization II (Proceedings of TopoInVis 2007), pages 15–30, March 2009.
[32] F. Sadlo, A. Rigazzi, and R. Peikert, Time-Dependent Visualization of Lagrangian Coherent Structures by Grid Advection. In Proceedings of TopoInVis 2009 (to appear). Springer, 2009.
[33] F. Sadlo and D. Weiskopf, Time-Dependent 2D Vector Field Topology: An Approach Inspired by Lagrangian Coherent Structures. Computer Graphics Forum, 29 (1): 88–100, 2010.
[34] J. Sahner, T. Weinkauf, N. Teuber, and H.-C. Hege, Vortex and Strain Skeletons in Eulerian and Lagrangian Frames. IEEE Transactions on Visualization and Computer Graphics, 13 (5): 980–990, September - October 2007.
[35] S. Camarri, M. Salvetti, M. Buffoni, and A. Iollo, Simulation of the three-dimensional flow around a square cylinder between parallel walls at moderate Reynolds numbers. In Proceedings of XVII Congresso di Meccanica Teorica ed Applicata, 2005.
[36] T. Schafhitzel, E. Tejada, D. Weiskopf, and T. Ertl, Point-based Stream Surfaces and Path Surfaces. In Proceedings of Graphics Interface 2007, pages 289–296, 2007.
[37] T. Schafhitzel, J. E. Vollrath, J. P. Gois, D. Weiskopf, A. Castelo, and T. Ertl, Topology-preserving λ2-based vortex core line detection for flow visualization. Computer Graphics Forum, 27 (3): 1023–1030, 2008.
[38] G. Scheuermann, T. Bobach, H. H.K. Mahrous, B. Hamann, K. Joy, and W. Kollmann, A Tetrahedra-based Stream Surface Algorithm. pages 151–158, 2001.
[39] M. Schirski, C. Bischof, and T. Kuhlen, Interactive particle tracing on tetrahedral grids using the GPU. In Vision Modeling and Visualization, 2006.
[40] M. Schirski, A. Gerndt, T. van Reimersdahl, T. Kuhlen, P. Adomeit, O. Lang, S. Pischinger, and C. H. Bischof, ViSTA FlowLib: A Framework for Interactive Visualization and Exploration of Unsteady Flows in Virtual Environments. In 7th International Workshop on Immersive Projection Technology, 9th Eurographics Workshop on Virtual Enviroments, pages 77–86, 2003.
[41] M. Schirski, T. Kuhlen, M. Hopp, P. Adomeit, S. Pischinger, and C. Bischof, Efficient visualization of large amounts of particle trajectories in virtual environments using virtual tubelets. In VRCAI `04: Proceedings of the 2004 ACM SIGGRAPH international conference on Virtual Reality continuum and its applications in industry, pages 141–147, 2004.
[42] D. Schneider, A. Wiebel, and G. Scheuermann, Smooth Stream Surfaces of Fourth Order Precision. In Eurographics/IEEE VGTC Symposium on Visualization (EuroVis), pages 871–878, 2009.
[43] T. Schultz, H. Theisel, and H.-P. Seidel, Crease Surfaces: From Theory to Extraction and Application to Diffusion Tensor MRI. IEEE Transactions on Visualization and Computer Graphics, 16: 109–119, 2010.
[44] S. C. Shadden, F. Lekien, and J. E. Marsden, Definition and properties of lagrangian coherent structures from finite-time lyapunov exponents in two-dimensional aperiodic flows. Phys. D, 212 (7): 271–304, 2005.
[45] S. C. Shadden, F. Lekien, J. D. Paduan, F. P. Chavez, and J. E. Marsden, The correlation between surface drifters and coherent structures based on high-frequency radar data in monterey bay. Deep Sea Research Part II: Topical Studies in Oceanography, 56 (3-5): 161–172, 2009. AOSNII: The Science and Technology of an Autonomous Ocean Sampling Network.
[46] H.-W. Shen, G.-S. Li, and U. D. Bordoloi, Interactive Visualization of Three-Dimensional Vector Fields with Flexible Appearance Control. IEEE Transactions on Visualization and Computer Graphics, 10 (4): 434–445, 2004.
[47] C. Sigg, T. Weyrich, M. Botsch, and M. Gross, GPU-Based Ray Casting of Quadratic Surfaces. In Proceedings of the Eurographics/IEEE VGTC Symposium on Point-Based Graphics, pages 59–65, 2006.
[48] D. Stalling, Fast Texture-based Algorithms for Vector Field Visualization. PhD thesis, FU Berlin, Department of Mathematics and Computer Science, 1998.
[49] J. J. van Wijk, Implicit Stream Surfaces. pages 245–252, 1993.
[50] 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.
[51] M. Weldon, T. Peacock, G. B. Jacobs, M. Helu, and G. Haller, Experimental and numerical investigation of the kinematic theory of unsteady separation. Journal of Fluid Mechanics, 611: 1–11, 2008.
[52] A. Wiebel, D. Schneider, H. Jaenicke, X. Tricoche, and G. Scheuermann, Generalized Streak Lines: Analysis and Visualization of Boundary Induced Vortices. IEEE Transactions on Visualization and Computer Graphics, 13 (6): 1735–1742, 2007.
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