This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Generation of Accurate Integral Surfaces in Time-Dependent Vector Fields
November/December 2008 (vol. 14 no. 6)
pp. 1404-1411
ASCII Text
x 
 
Christoph Garth, Han Krishnan, Xavier Tricoche, Tom Tricoche, Kenneth I. Joy, "Generation of Accurate Integral Surfaces in Time-Dependent Vector Fields," IEEE Transactions on Visualization and Computer Graphics, vol. 14, no. 6, pp. 1404-1411, November/December, 2008.
 
 
BibTex
x
 
@article{ 10.1109/TVCG.2008.133,
author = {Christoph Garth and Han Krishnan and Xavier Tricoche and Tom Tricoche and Kenneth I. Joy},
title = {Generation of Accurate Integral Surfaces in Time-Dependent Vector Fields},
journal ={IEEE Transactions on Visualization and Computer Graphics},
volume = {14},
number = {6},
issn = {1077-2626},
year = {2008},
pages = {1404-1411},
doi = {http://doi.ieeecomputersociety.org/10.1109/TVCG.2008.133},
publisher = {IEEE Computer Society},
address = {Los Alamitos, CA, USA},
}
 
 
RefWorks Procite/RefMan/Endnote
x 
 
TY - JOUR
JO - IEEE Transactions on Visualization and Computer Graphics
TI - Generation of Accurate Integral Surfaces in Time-Dependent Vector Fields
IS - 6
SN - 1077-2626
SP1404
EP1411
EPD - 1404-1411
A1 - Christoph Garth,
A1 - Han Krishnan,
A1 - Xavier Tricoche,
A1 - Tom Tricoche,
A1 - Kenneth I. Joy,
PY - 2008
KW - Index Terms—3D vector field visualization
KW - flow visualization
KW - time-varying and time-series visualization
KW - surface extraction
VL - 14
JA - IEEE Transactions on Visualization and Computer Graphics
ER -
 
Christoph Garth, University of California, Davis
Han Krishnan, University of California, Davis
Xavier Tricoche, Purdue University
Tom Tricoche, University of Kaiserslauterns
Kenneth I. Joy, University of California, Davis
We present a novel approach for the direct computation of integral surfaces in time-dependent vector fields. As opposed to previous work, which we analyze in detail, our approach is based on a separation of integral surface computation into two stages: surface approximation and generation of a graphical representation. This allows us to overcome several limitations of existing techniques. We first describe an algorithm for surface integration that approximates a series of time lines using iterative refinement and computes a skeleton of the integral surface. In a second step, we generate a well-conditioned triangulation. Our approach allows a highly accurate treatment of very large time-varying vector fields in an efficient, streaming fashion. We examine the properties of the presented methods on several example datasets and perform a numerical study of its correctness and accuracy. Finally, we investigate some visualization aspects of integral surfaces.

[1] A. A. Andronov, Qualitative Theory of Second-Order Dynamic Systems. John Wiley & Sons, 1973.
[2] U. Dallmann, Topolo gical Structures of Three-Dimensional Flow Separations. Technical Report 221-82 A 07, Deutsche Forschungs- und Versuchsanstalt fuer Luft- und Raumfahrt, 1983.
[3] C. Garth, X. Tricoche, T. Salzbrunn, and G. Scheuermann, Surface techniques for vortex visualization. In Proceedings Eurographics - IEEE TCVG Symposium on Visualization, May 2004.
[4] I. Gladwell, L. F. Shampine, L. S. Baca, and R. W. Brankin, Practical aspects of interpolation in runge-kutta codes. SIAM J. Sci. Stat. Comput., 8 (3): 322–341, 1987.
[5] J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Springer-Verlag, 1983.
[6] E. Hairer, S. P. Nørsett, and G. Wanner, Solving Ordinary Differential Equations I, second edition, volume 8 of Springer Series in Comput. Mathematics. Springer-Verlag, 1993.
[7] J. P. M. Hultquist, Constructing stream surfaces in steady 3d vector fields. In A. E. Kaufman and G. M. Nielson, editors, Proceedings of IEEE Visualization 1992, pages 171 – 178, Boston, MA, 1992.
[8] 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.
[9] R. S. Laramee, C. Garth, J. Schneider, and H. Hauser, Texture advection on stream surfaces: A novel hybrid visualization applied to cfd simulation results. In Data Visualization, Proceedings of the Joint EUROGRAPHICS - IEEE VGTC Symposium on Visualization (EuroVis 2006), 2006.
[10] H. Löffelmann, L. Mroz, E. Gröller, and W. Purgathofer, Stream arrows: enhancing the use of stream surfaces for the visualization of dynamical systems. The Visual Computer, 13 (8): 359 – 369, 1997.
[11] G. M. Nielson, Dual marching cubes. In VIS '04: Proceedings of the conference on Visualization '04, pages 489–496, Washington, DC, USA, 2004. IEEE Computer Society.
[12] P. J. Prince and J. R. Dormand, High order embedded runge-kutta formulae. Journal of Computational and Applied Mathematics, 7 (1), 1981.
[13] T. Schafhitzel, E. Tejada, D. Weiskopf, and T. Ertl, Point-based stream surfaces and path surfaces. In GI '07: Proceedings of Graphics Interface 2007, pages 289–296, New York, NY, USA, 2007. ACM.
[14] G. Scheuermann, T. Bobach, H. Hagen, K. Mahrous, N. Hahman, and K. Joy, A tetrahedra-based stream surface algorithm. In IEEE Visualization Proceedings, 2001.
[15] L. F. Shampine, Interpolation for runge-kutta methods. SIAM J. Numer. Anal., 5, 1985.
[16] D. Stalling, Fast Texture-Based Algorithms for Vector Field Visualization. PhD thesis, Freue Universität Berlin, 1998.
[17] J. van Wijk, Implicit stream surfaces. In Proceedings of IEEE Visualization '93 Conference, pages 245–252, 1993.
[18] J. J. van Wijk, Rendering surface particles. In IEEE Visualization Proceedings, pages 54 – 61, 1992.

Index Terms:
Index Terms—3D vector field visualization, flow visualization, time-varying and time-series visualization, surface extraction
Citation:
Christoph Garth, Han Krishnan, Xavier Tricoche, Tom Tricoche, Kenneth I. Joy, "Generation of Accurate Integral Surfaces in Time-Dependent Vector Fields," IEEE Transactions on Visualization and Computer Graphics, vol. 14, no. 6, pp. 1404-1411, Nov.-Dec. 2008, doi:10.1109/TVCG.2008.133
Usage of this product signifies your acceptance of the Terms of Use.