“Image-guided streamline placement” by Turk and Banks

Accurate control of streamline density is key to producing several effective forms of visualization of two-dimensional vector fields. We introduce a technique that uses an energy function to guide the placement of streamlines at a specified density. This energy function uses a low-pass filtered version of the image to measure the difference between the current image and the desired visual density. We reduce the energy (and thereby improve the placement of streamlines) by (1) changing the positions and lengths of streamlines, (2) joining streamlines that nearly abut, and (3) creating new streamlines to fill sufficiently large gaps. The entire process is iterated to produce streamlines that are neither too crowded nor too sparse. The resulting streamlines manifest a more hand-placed appearance than do regularly- or randomly-placed streamlines. Arrows can be added to the streamlines to disambiguate flow direction, and flow magnitude can be represented by the thickness, density, or intensity of the lines.

1. Bertin, Jacques, Semiology of Graphics, translated from French, The University of Wisconsin Press 1983.
2. Bryson, Steve and Creon Levit, “The Virtual Wind Tunnel: An Environment for the Exploration of Three-Dimensional Unsteady Flows,” Proceedings Visualization ’91, San Diego, California, October 22-25, pp. 17-24.
3. Cabral, Brian and Leith (Casey) Leedom, “Imaging Vector Fields Using Line Integral Convolution,” Computer Graphics Proceedings, Annual Conference Series (SIGGRAPH ’93), pp. 263-270.
4. Crawfis, Roger and Nelson Max, “Direct Volume Visualization of Three Dimensional Vector Fields,” Proceedings of the 1992 Workshop on Volume Visualization, pp. 55-60.
5. de Leeuw, Willem C., and Jarke van Wijk, “Enhanced Spot Noise for Vector Field Visualization,” Proceedings Visualization ’95, Atlanta, Georgia, Oct. 29 – Nov. 3, pp. 233-239.
6. Delmarcelle, Thierry and Lambertus Hesselink, “The Topology of Symmetric, Second-Order Tensor Fields,” Proceedings Visualization ’94, Washington, D.C., October 17-21, pp. 140-147.
7. Dovey, Don, “Vector Plots for Irregular Grids,” Proceedings Visualization ’95, Atlanta, Georgia, Oct. 29 – Nov. 3, pp. 248-253.
8. Feibush, Eliot, Marc Levoy and Robert Cook, “Synthetic Texturing Using Digital Filters,” Computer Graphics Proceedings, Annual Conference Series (SIGGRAPH ’80), pp. 294- 301.
9. Feynman, Richard R, Robert B. Leighton and Matthew Sands, The Feynman Lectures on Physics, Addison-Wesley, Reading, Massachusetts, 1964.
10. Forsell, Lisa K., “Visualizing Flow over Curvalinear Grid Surfaces Using Line Integral Convolution,” Proceedings Visualization ’94, Washington, D.C., October 17-21, pp. 240-247.
11. Fowler, David and Colin Ware, “Strokes for Representing Univariate Vector Field Maps,” Graphics Interface ’89, London, Ontario, June 19-23, 1989, pp. 249-253.
12. Globus, A., C. Levit and T. Lasinski, “A Tool for Visualizing the Topology of Three-Dimensional Vector Fields,” Proceedings Visualization ’91, San Diego, California, October 22- 25, pp. 33-40.
13. Helman, J. L. and L. Hesselink, “Visualization of Vector Field Topology in Fluid Flows,” IEEE Computer Graphics and Applications, Vol. 11, No. 3, pp. 36-46.
14. Hoppe, Hugues, Tony DeRose, Tom Duchamp, John McDonald and Werner Stuetzel, “Mesh Optimization,” Computer Graphics Proceedings, Annual Conference Series (SIGGRAPH ’93), pp. 19-26.
15. Kundu, Pijush K., Fluid Mechanics, Academic Press, Inc., San Diego, 1990.
16. Max, Nelson, Roger Crawfis and Charles Grant, “Visualizing 3D Velocity Fields Near Contour Surfaces,” Proceedings Visualization’ 94, Washington, D.C., October 17-21, pp. 248- 255.
17. Saito, Takafumi and Tokiichiro Takahashi, “Comprehensible Rendering of 3-D Shapes,” Computer Graphics, Vol. 24, No. 4 (SIGGRAPH ’90), pp. 197-206.
18. Salisbury, Michael R, Sean E. Anderson, Ronen Barzel and David H. Salesin, “Interactive Pen-and-Ink Illustration’, Computer Graphics Proceedings, Annual Conference Series (SIGGRAPH ’94), pp. 101-108.
19. Stalling, Detlev and Hans-Christian Hege, “Fast and Resolution Independent Line Integral Convolution,” Computer Graphics Proceedings, Annual Conference Series (SIGGRAPH ’95), pp. 249-256.
20. Turk, Greg, “Generating Textures on Arbitrary Surfaces Using Reaction-Diffusion,” Computer Graphics, Vol. 25, No. 4 (SIGGRAPH ’91), pp. 289-298.
21. van Wijk, Jarke J., “Spot Noise: Texture Synthesis for Data Visualization,” Computer Graphics, Vol. 25, No. 4 (SIGGRAPH ’91), pp. 309-318.
22. Winkenbach, Georges and David H. Salesin, “Computer-Generated Pen-and-Ink Illustrations,” Computer Graphics Proceedings, Annual Conference Series (SIGGRAPH ’94), pp. 91-98.
23. Witkin, Andrew and Paul Heckbert, “Using Particles to Sample and Control Implicit Surfaces,” Computer Graphics Proceedings, Annual Conference Series (SIGGRAPH 94), pp. 269-277.