Abstract—Predicates are functions that return Boolean values. They are an essential tool in computer science. A close look at flow feature definitions reveals that they can be seen as point predicates that tell if a specific feature exists at a certain point. Besides the information about features, scientists and engineers like to know the overall behavior of all streamlines in the flow, typically in the connection with the important features in their application domain. We call this a structure definition for the flow. A successful example for a structure definition is flow topology. In this paper, we present streamline predicates as functions that tell the user about the connection between streamlines and features selected by the user. This means answers to questions like: Which streamlines flow through a given vortex, separation bubble, or shock wave? It can be shown that streamline predicates may refine flow topology so that it also reveals questions about vortices in 3D.
[1] 1601 J. Blaas, C.P. Botha, B. Peters, F.M. Vos, and F.H. Post, “Fast and Reproducible Fiber Bundle Selection in DTI Visualization,” Proc. IEEE Visualization Conf., pp. 59-64, 2005.
[2] H. Doleisch, M. Gasser, and H. Hauser, “Interactive Feature Specification for Focus+Context Visualization of Complex Simulation Data,” Proc. Fifth Joint IEEE TCVG—EUROGRAPHICS Symp. Visualization (VisSym '03), pp. 239-248, 2003.
[3] J.R. Dormand and P.J. Prince, “Dopri 5—A Family of Embedded Runge-Kutta Formulae,” J. Computational and Applied Math., vol. 6, pp. 19-26, 1980.
[4] M. Griebel, T. Preusser, M. Rumpf, M.A. Schweitzer, and A. Telea, “Flow Field Clustering via Algebraic Multigrid,” Proc. IEEE Visualization Conf., pp. 35-42, 2004.
[5] B Heckel, G.H. Weber, B Hamann, and K.I. Joy, “Construction of Vector Field Hierarchies,” Proc. IEEE Visualization Conf., pp. 19-25, 1999.
[6] J.L. Helman and L. Hesselink, “Visualizing Vector Field Topology in Fluid Flows,” IEEE Computer Graphics and Applications, vol. 11, no. 3, pp. 36-46, May 1991.
[7] J. Jeong and F. Hussain, “On the Identification of a Vortex,” J.Fluid Mechanics, vol. 285, pp. 69-94, 1995.
[8] M. Jiang, R. Machiraju, and D.S. Thompson, “Geometric Verification of Swirling Features of Flow Fields,” Proc. IEEE Visualization Conf., pp. 307-314, 2002.
[9] K.-L. Ma, J. van Rosendale, and W. Vermeer, “3D Shock Wave Visualization on Unstructured Grids,” Proc. Symp. Volume Visualization, pp. 87-94, 1996.
[10] K. Mahrous, J. Bennett, G. Scheuermann, B. Hamann, and K.I. Joy, “Topological Segmentation of Three-Dimensional Vector Fields,” IEEE Trans. Visualization and Computer Graphics, vol. 10, no. 2, pp.198-205, Mar.-Apr. 2004.
[11] G.M. Nielson, “Dual Marching Cubes,” Proc. IEEE Visualization Conf., pp. 489-496, 2004.
[12] H.-G. Pagendarm and B. Seitz, “An Algorithm for Detection and Visualization of Discontinuities,” Scientific Visualization—Advanced Software Techniques, P. Palamidese, ed., pp. 161-177. Ellis Horwood Ltd., 1993.
[13] R. Peikert and M. Roth, “The Parallel Vectors Operator—A Vector Field Visualization Primitive,” Proc. IEEE Visualization Conf., pp.263-270, 1999.
[14] L.M. Portela, “Identification and Characterization of Vortices in the Turbulent Boundary Layer,” PhD thesis, Stanford Univ., 1997.
[15] F.H. Post, B. Vrolijk, H. Hauser, R.S. Laramee, and H. Doleisch, “The State of the Art in Flow Visualization: Feature Extraction and Tracking,” Proc. Computer Graphics Forum 22, vol. 4, pp. 775-792, 2003.
[16] T. Preusser and M. Rumpf, “Anisotropic Nonlinear Diffusion in Flow Visualization,” Proc. IEEE Visualization Conf., pp. 325-332, 1999.
[17] S.K. Robinson, “Coherent Motions in the Turbulent Boundary Layer,” Ann. Rev. Fluid Mechanics, vol. 23, pp. 601-639, 1991.
[18] M. Roth, “Automatic Extraction of Vortex Core Lines and Other Line-Type Features for Scientific Visualization,” PhD thesis, ETH Zürich, 2000.
[19] I.A. Sadarjoen, F.H. Post, B. Ma, D.C. Banks, and H.G. Pagendarm, “Selective Visualization of Vortices in Hydrodynamic Flows,” Proc. IEEE Visualization Conf., pp. 419-422, 588, 1998.
[20] T. Salzbrunn and G. Scheuermann, “Streamline Predicates as Flow Topology Generalization,” Topo-in-Vis Proc. (under review), 2005.
[21] G. Scheuermann, I.J. Kenneth, and W. Kollmann, “Visualizing Local Vector Field Topology,” J. Electronic Imaging, vol. 9, pp. 356-367, 2000.
[22] A. Sherbondy, D. Akers, R. Mackenzie, R. Dougherty, and B. Wandell, “Exploring Connectivity of the Brain's White Matter with Dynamic Queries,” IEEE Trans. Visualization and Computer Graphics, vol. 11, no. 4, pp. 419-430, July/Aug. 2005.
[23] D. Sujudi and R. Haimes, “Identification of Swirling Flow in 3D Vector Fields,” Technical Report AIAA Paper 95-1715, Am. Inst. of Aeronautics and Astronautics, 1995.
[24] A. Telea and J.J. van Wijk, “Simplified Representation of Vector Fields,” Proc. IEEE Visualization Conf., pp. 35-42, 1999.
[25] H. Theisel, T. Weinkauf, H.C. Hege, and H.P. Seidel, “Saddle Connectors—An Approach to Visualizing the Topological Skeleton of Complex 3d Vector Fields,” Proc. IEEE Visualization Conf., pp. 225-232, 2003.
[26] X. Tricoche, T. Wischgoll, G. Scheuermann, and H. Hagen, “Topological Tracking for the Visualization of Timedependent Two-Dimensional Flows,” Computers & Graphics, vol. 26, no. 2, pp.249-257, 2002.
[27] T. van Walsum, F.H. Post, D. Silver, and F.J. Post, “Feature Extraction and Iconic Visualization,” IEEE Trans. Visualization and Computer Graphics, vol. 2, no. 2, pp. 111-119, 1996.
Index Terms:
Flow visualization, feature detection.
Citation:
Tobias Salzbrunn, Gerik Scheuermann, "Streamline Predicates," IEEE Transactions on Visualization and Computer Graphics, vol. 12, no. 6, pp. 1601-1612, Nov./Dec. 2006, doi:10.1109/TVCG.2006.104
PURCHASE ARTICLE: $19
IEEE Xplore Subscribers
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb