An Advanced Evenly-Spaced Streamline Placement Algorithm
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This paper presents an advanced evenly-spaced streamline placement algorithm for fast, high-quality, and robust layout of flow lines. A fourth-order Runge-Kutta integrator with adaptive step size and error control is employed for rapid accurate streamline advection. Cubic Hermite polynomial interpolation with large sample-spacing is adopted to create fewer evenly-spaced samples along each streamline to reduce the amount of distance checking. We propose two methods to enhance placement quality. Double queues are used to prioritizetopological seeding and to favor long streamlines to minimize discontinuities. Adaptive distance control based on the local flow variance is explored to reduce cavities. Furthermore, we propose a universal, effective, fast, and robust loop detection strategy to address closed and spiraling streamlines. Our algorithm is an order-of-magnitude faster than Jobard and Lefer?s algorithm [8] with better placement quality and over 5 times faster than Mebarki et al.?s algorithm [9] with comparable placement quality, but with a more robust solution to loop detection.
[1] 965 J. J. van Wijk, "Spot Noise: Texture Synthesis for Data Visualization," Proc. ACM SIGGRAPH '91, pp. 309–318, 1991.
[2] B. Cabral and L. Leedom, "Imaging Vector Fields Using Line Integral Convolution," Proc. ACM SIGGRAPH '93, pp. 263–270, 1993.
[3] D. Stalling and H.-C. Hege, "Fast and Resolution Independent Line Integral Convolution," Proc. ACM SIGGRAPH '95, pp. 249–256, 1995.
[4] H.-W. Shen and D. L. Kao, "A New Line Integral Convolution Algorithm for Visualizing Time-Varying Flow Fields," IEEE Trans. Visualization and Computer Graphics, vol.. 4, no. 2, pp. 98–108, 1998.
[5] Z. Liu and R. J. Moorhead II, "Accelerated Unsteady Flow Line Integral Convolution," IEEE Trans. Visualization and Computer Graphics, vol. 11, no. 2, pp. 113–125, 2005.
[6] B. Jobard, G. Erlebacher, and M. Y. Hussaini, "Lagrangian-Eulerian Advection of Noise and Dye Textures for Unsteady Flow Visualization," IEEE Trans. Visualization and Computer Graphics, vol. 8, no. 3, pp. 211–222, 2002.
[7] J. J. van Wijk, "Image Based Flow Visualization," Proc. ACM SIGGRAPH '02, pp. 745–754, 2002.
[8] B. Jobard and W. Lefer, "Creating Evenly-Spaced Streamlines of Arbitrary Density," Proc. Eighth Eurographics Workshop on Visualization in Scientific Computing, pp. 45–55, 1997.
[9] A. Mebarki, P. Alliez, and O. Devillers, "Farthest Point Seeding for Efficient Placement of Streamlines," Proc. IEEE Visualization '05, pp. 479–486, 2005.
[10] G. Turk and D. Banks, "Image-Guided Streamline Placement," Proc. ACM SIGGRAPH '96, pp. 453–460, 1996.
[11] X. Mao, Y. Hatanaka, H. Higashida, and A. Imamiya, "Image-Guided Streamline Placement on Curvilinear Grid Surfaces," Proc. IEEE Visualization '98, pp. 135–142, 1998.
[12] B. Jobard and W. Lefer, "Unsteady Flow Visualization by Animating Evenly-Spaced Streamlines," Proc. Eurographics '00, pp. 21–31, 2000.
[13] B. Jobard and W. Lefer, "Multiresolution Flow Visualization," Proc. Ninth International Conf. in Central Europe on Computer Graphics, Visualization, and Computer Vision (WSCG '01), pp. 33–37, 2001.
[14] O. Mattausch, T. Theubl, H. Hauser, and E. Groller, "Strategies for Interactive Exploration of 3D Flow Using Evenly-Spaced Illuminated Streamlines," Proc. Nineteenth Spring Conf. on Computer Graphics, pp. 213–222, 2003.
[15] V. Verma, D. Kao, and A. Pang, "A Flow-Guided Streamlines Seeding Strategy," Proc. IEEE Visualization '00, pp. 163–170, 2000.
[16] X. Ye, D. Kao, and A. Pang, "Strategy for Seeding 3D Streamlines," Proc. IEEE Visualization '05, pp. 471–478, 2005.
[17] T. Wischgoll and G. Scheuermann, "Detection and Visualization of Closed Streamlines in Planar Flows," IEEE Trans. Visualization and Computer Graphics, vol. 7, no. 2, pp. 165–172, 2001.
[18] H. Theisel, T. Weinkauf, H.-C. Hege, and H.-P. Seidel, "Grid-Independent Detection of Closed Streamlines in 2D Vector Fields," Proc. Ninth International Fall Workshop on Vision, Modeling, and Visualization (VMV'04), pp.421–428, 2004.
[19] A. Mebarki, "Demo Executable" http://www-sop.inria.fr/geometrica/teamAbdelkrim.Mebarki.
[20] D. Higham, "Highly Continuous Runge-Kutta Interpolants," ACM Trans. Mathematical Software, vol. 17, no. 3, pp. 368–386, 1991.
Index Terms:
Flow visualization, evenly-spaced streamlines, streamline placement, seeding strategy, closed streamlines.
Citation:
Zhanping Liu, Robert Moorhead, Joe Groner, "An Advanced Evenly-Spaced Streamline Placement Algorithm," IEEE Transactions on Visualization and Computer Graphics, vol. 12, no. 5, pp. 965-972, Sept. 2006, doi:10.1109/TVCG.2006.116
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