Using PVsolve to analyze and locate positions of parallel vectors

IEEE Transactions on Visualization and Computer Graphics

Volumn 15, Issue 4, 2009, Pages 682-695

  Van Gelder, Allen ^a   Pang, Alex ^a  

^a University of California Santa Cruz   (United States)

Author keywords

Adjugate matrix; Dimensionless projection vector; Feature flow field; Flow visualization; Newton Raphson root finding; Parallel vectors; PVsolve; Vortex core

Indexed keywords

ADJUGATE MATRIX; DIMENSIONLESS PROJECTION VECTOR; FEATURE FLOW FIELD; NEWTON-RAPHSON ROOT FINDING; PARALLEL VECTORS; PVSOLVE; VORTEX CORE;

FLOW FIELDS; FLOW VISUALIZATION; FLUID DYNAMICS; MATHEMATICAL OPERATORS; VORTEX FLOW;

VECTORS;

EID: 67649336780     PISSN: 10772626     EISSN: None     Source Type: Journal    
DOI: 10.1109/TVCG.2009.11     Document Type: Article

References (23)

1. D.C. Banks and B.A. Singer, "Vortex Tubes in Turbulent Flows: Identification, Representation, Reconstruction," Proc. IEEE Visualization Conf. '94, pp. 132-139, 1994.
2. D.C. Banks and B.A. Singer, "A Predictor-Corrector Technique for Visualizing Unsteady Flow," IEEE Trans. Visualization and Computer Graphics, vol. 1, no. 2, pp. 151-163, June 1995.
3. C. Garth, R.S. Laramee, X. Tricoche, J. Schneider, and H. Hagen, "Extraction and Visualization of Swirl and Tumble Motion from Engine Simulation Data," Topology-Based Methods in Visualization, H. Hauser, H. Hagen, and H. Theisel, eds., pp. 121-135, Springer, 2007.
4. G.H. Golub and C.F. Van Loan, Matrix Computations, third ed.Johns Hopkins University Press, 1996.
5. A.J. Hanson, Geometry for N-Dimensional Graphics, P. Heckbert, ed.,pp. 149-170, Academic Press, 1994.
6. M.W. Hirsch and S. Smale, Differential Equations, Dynamical Systems, and Linear Algebra. Academic Press, 1974.
7. R. Hooke and T.A. Jeeves, "'Direct Search' Solution of Numerical and Statistical Problems," J. ACM, vol. 8, no. 2, pp. 212-229, 1961.
8. J. Jeong and F. Hussain, "On the Identification of a Vortex,"J. Fluid Mechanics, vol. 285, pp. 69-94, 1995.
9. Kitware, ParaView Guide, Kitware, Version 3, http://www.paraview. org, Feb. 2008.
10. M. Marcus and H. Minc, Introduction to Linear Algebra. MacMillan,1969.
11. W.S. Massey, "Cross Products of Vectors in Higher Dimensional Euclidean Spaces," Am. Math. Monthly, vol. 90, pp. 697-701, 1983.
12. G.M. Nielson and I.-H. Jung, "Tools for Computing Tangent Curves for Linearly Varying Vector Fields over Tetrahedral Domains," IEEE Trans. Visualization and Computer Graphics,vol. 5, no. 4, pp. 360-372, Oct.-Dec. 1999.
13. R. Peikert and M. Roth, "The Parallel Vector Operator-A Vector Field Visualization Primitive," Proc. IEEE Visualization Conf. '99,pp. 263-270, 1999.
14. M. Roth, "Automatic Extraction of Vortex Core Lines and Other Line-Type Features for Scientific Visualization," PhD thesis, ETH Zurich, Inst. of Scientific Computing, Diss. ETH No. 13673, 2000.
15. L.F. Shampine and M.W. Reichelt, "The Matlab ODE Suite," SIAM J. Scientific Computing, vol. 18, pp. 1-22, 1997.
16. S. Stegmaier, U. Rist, and T. Ertl, "Opening The Can of Worms: An Exploration Tool for Vortical Flows," Proc. IEEE Visualization Conf. '05, pp. 463-470, 2005.
17. G.W. Stewart, "On the Adjugate Matrix," Linear Algebra and Its Applications, vol. 283, pp. 151-164, 1998.
18. J. Sukharev, X. Zheng, and A. Pang, "Tracing Parallel Vectors," Proc. SPIE Visual Data Analysis and Exploration, 2006.
19. H. Theisel, J. Sahner, T. Weinkauf, H.-C. Hege, and H.-P. Seidel,"Extraction of Parallel Vector Surfaces in 3D Time-Dependent Fields and Application to Vortex Core Line Tracking," Proc.Visualization Conf. 05, pp. 631-638, 2005.
20. H. Theisel and H.-P. Seidel, "Feature Flow Fields," Proc. Joint Eurographics-IEEE TCVG Symp. Visualization (VisSym'03), pp. 141-148, 2003.
21. A. Van Gelder, "Report on Relaxed Jordan Canonical Form for Computer Animation and Visualization," technical report, Univ. of California, Santa Cruz, http://www.cse.ucsc.edu/ ~avg/Papers/rjcfTR.pdf, Jan. 2009.
22. T. Weinkauf, "Extraction of Topological Structures in 2D and 3D Vector Fields," PhD thesis, Otto von Guericke Univ. of Magdeburg, Germany, 2008.
23. T. Weinkauf, J. Sahner, H. Theisel, H.-C. Hege, and H.-P. Seidel,"A Unified Feature Extraction Architecture," Active Flow Control,R. King, ed., pp. 119-133, Springer, 2007.