6.3 Halo effect
6.3.2 Shading with LIC
Limb darkening can also be utilized when visualizing LIC textures. When using a volume renderer with support for trilinear interpolation1, some of the halo effect automatically occur in the rendered image. The reason is when Line Integral Convolution is applied to a sparse input texture, the resulting field lines in the LIC texture are mostly covered by very “low” values, and interpolations between these values and the core values, results in a darker layer around the core of the field lines, see figure 5.13 on page 45. By using proper color and opacity tables, we are then able to create a reasonable limb darkening (see figure 6.6).
To emphasize the effect we have tried two different techniques. In the first technique we made the spot sizes in the input texture bigger by assigning lower values in neighboring voxels of the originally chosen cells. This works well if the integrated lines from the modified spots have somewhat similar directions. But in places where the field lines diverge from one another we lose the effect.
To avoid the problem above, we propose an improvement of the shading effect by convolv-ing the LIC texture with a Ù:ÙD convolution matrixF . Convolution leads to a smearing of the field lines and makes the strokes thicker and the 3D shape more clear. We have achieved good result using a convolution matrix F , where ÌÔÔc¸ and the rest of the entries are set to
² 92 .
Both these techniques reduces aliasing present in the output texture. Figure 5.14 on page 45 demonstrates the effect of the convolution applied to a texture computed by the Seed LIC.
The “natural” halo effect caused by the interpolation, is stronger in fast-LIC than in Seed LIC. This is because the fast-LIC algorithm already leads to a smearing of the individual field
1Both Viz and Volumizer 2 have support for trilinear interpolation.
Figure 6.6: Limb darkening used to visualize field lines in a LIC texture. Left: By letting the alphachange from zero to higher opacity values and thevalue ë go from dark to bright, we obtain a three-dimensional look. Right: If a constantvalue(ë ) is applied to all the voxels in the LIC volume, this will lead to a more flat appearance.
to determine the color. This method is useful for conveying information about related scalar quantities obtained from a simulation.
As an example of the first approach, we have in figure 6.7 visualized both the enstrophy
((Ë ø&ÿÙvÅø
) and a LIC texture displaying the vorticity field. The visualized data are obtained from [17]. To obtain smooth field lines, we have oversampled the textures by a factor of three before computing the Seed LIC, and then convolved the output texture obtained from the Seed LIC. In order to compare the two data sets, we oversampled the enstrophy scalar field by a factor of three. This was achieved by trilinearly interpolating the data.
The latter approach can be used to display additional scalar variables over a 3D flow. This can be achieved by letting the scalar values from the LIC texture define the opacity, and a related scalar quantity, like temperature or the vorticity magnitude, define the color. In figure 6.8, color is used to indicate vector magnitude across the synthetic vector field defined on page 13.
Since the LIC texture only determine the opacity, shading of the field lines with limb dark-ening becomes difficult2. To improve the clarity of the depth relations among the field lines, we therefore employ a black background. For sparse LIC textures, the use of a black background makes it easier to differentiate the individual lines.
6.4.1 “Polkagris” visualization
Finally, we will present a variation of the two field visualization technique to depict the behavior of the vorticity field inside vortex tubes obtained from [17]. In this method, which we have calledpolkagris3 visualization, the enstrophy is used to define the opacity while the voxel set obtained from LIC (applied to the vorticity field) is used to define the color. Since enstrophy expresses the vortical structures of the flow, we get images of vortex tubes colored by the LIC texture conveying the directional structure of the vorticity field. The reason for naming the technique “polkagris visualization”, can be seen in figure 6.9. The field lines of the vorticity field twists around the vortices, resulting in “objects” very similar to the candy “humbug” or
“candy cane”. Figure 6.10 shows the color table used to visualize the “candy canes” in figure 6.9. The “low” values in the sparse LIC texture are set to white, while the field lines are colored red. Examples of the polkagris technique are shown in figures 6.11, 6.12, 6.13 and 6.14.
2To achieve shading of the field lines with limb darkening, both theopacityand thevaluein the HSVA color model have to be defined by the LIC texture.
3Polkagris is a Swedish candy similar to the English “humbug” or the American “candy cane”.
Figure 6.7: Two field visualization, using two independent sets of color and opacity tables.
Top: The enstrophy field is displayed by assigning low opacity values to the LIC texture. The color varies from yellow to red with increasing enstrophy value. Middle: The vorticity field is displayed by assigning low opacity to the enstrophy field. Bottom: Both fields displayed in the same image. The visualized data are obtained from [17]. The resolution of the textures are
93äÙÌcÙ3 .
Figure 6.8: Visualization of two fields simultaneously. The opacity is defined by the LIC texture and the color is defined by vector magnitude. The color varies from red to blue with increasing vector magnitude.
Figure 6.9: Polkagris visualization.
Figure 6.10: The color table for the visualization of the LIC texture shown in figure 6.9.
Figure 6.11: Polkagris visualization used on the same subset as visualized in figure 6.7. The opacity is defined by enstrophy, and the color is defined by a LIC texture conveying the direc-tional structures of a vorticity field inside the vortices.
Figure 6.12: Visualization of two scalar fields simultaneously. The opacity is defined by enstro-phy, and the color is defined by a LIC texture conveying the directional structures of a vorticity field inside the vortices.
Figure 6.13: Visualization of two scalar fields simultaneously using clip plane. The opacity is defined by enstrophy, and the color is defined by a LIC texture conveying the directional structures of a vorticity field inside the vortices.
Figure 6.14: Visualization of two scalar fields simultaneously. The opacity is defined by enstro-phy, and the color is defined by a LIC texture conveying the directional structures of a vorticity field inside the vortices.
effectively visualizing 3D vector fields with volume LIC and we have shown that it is a viable tool for this purpose.
We have shown how hardware assisted volume rendering using 3D textures can provide interactive visualization and produce images of high quality. We have also demonstrated how interactive modification of color and opacity values and the use of clip planes can simplify the exploration of LIC textures. Both these functionalities should be supported by a volume renderer application.
We have also seen how the application of input textures, consisting of a sparse set of points, may improve the visualization of vector fields. The application of sparse input textures can be used as an alternative to the manipulation of the opacity value, to reveal the structures of the field. The LIC texture is dependent on the choice of input texture. In order to make an appropriate input texture, some insight in the data is needed.
We have applied statistical methods for distributing the points in the input texture. Best results were achieved when requiring a minimum distance between the selected points. By doing this, and at the same time limiting the length of the field lines, we can prevent the field lines in the LIC texture from getting too close. We have also achieved good results by increasing the resolution of the input and output texture. Then the details of the vector fields can be more easily seen.
For large 3D data sets, the fast-LIC algorithm proposed by Stalling and Hege [12] is very compute intensive. We have developed a faster method called Seed LIC for visualizing 3D vector fields, which exploits the sparsity of the input texture. With a proper input texture this technique result in images that clearly and effectively reveal the directional structure of a vector field.
The Seed LIC algorithm makes it possible to generate LIC textures at a much more interac-tive rate. Instead of a computation time of several hours, we can reduce the computation time to minutes or even seconds. The Seed LIC algorithm therefore has a great potential as an interac-tive tool to depict the directional information of a vector field in a volume renderer application.
Earlier, 3D LIC have been thought of as a tool only to visualize vector fields in those instances where high image quality is desired and the ability to generate images at an interactive rate is not required.
We have not optimized the Seed LIC algorithm, so our algorithm have still room for
perfor-Finally, we have demonstrated how direct volume rendering together with volume LIC, can be used to display additional information about related scalar quantities when visualizing vector fields. This is used to enhance the visual information describing a vector field.
7.1 Future work
Future work includes implementing the Seed LIC algorithm in a volume renderer application, such as the VoluViz, and further explore its use as an interactive tool to depict the directional information of a vector field. In order for this technique to become more useful for practical applications, the Seed LIC algorithm should be extended to also handle unstructured grids.
Finally, an interesting topic of further research is to investigate methods for efficiently gen-erating animations of the 3D LIC textures.
[3] J. P. M. HULTQUIST. Interactive numerical flow visualization using stream surfaces.
Computing Systems in Engineering, 1(2-4):349–353, 1990.
[4] N. MAX, B. BECKER, and R. CRAWFIS. Flow volumes for interactive vector field visualization. InProceedings of Visualization ’93, pages 19–24, October, 1993.
[5] B. CABRAL and C. LEEDOM. Imaging Vector Fields Using Line Integral Convolution.
InComputer Graphics Proceedings, volume 27 ofAnnual Conference Series, pages 263–
270, July 1993.
[6] P. K. KUNDU. Fluid Mechanics. Academic Press, 1990.
[7] J. E. MARSDEN and A. J. TROMBA. Vector Calculus. W. H. Freeman and Company, 4th edition, 1996.
[8] D. KINCAID and W. CHENEY. Numerical Analyses. Brooks/Cole Publishing Company, 2nd edition, 1996.
[9] D. STALLING, M. ZÖCKLER, and H.-C. HEGE. Fast display of illuminated field lines.
InIEEE transactions on visualization and computer graphics, volume 3, pages 118–128, 1997.
[10] J. J. VAN WIJK. Spot noise-texture synthesis for data visualization. InComputer Graphics Proceedings, volume 25 ofAnnual Conference Series, pages 309–318, Juli-August 1991.
[11] W. C. DE LEEUW and J. J. VAN WIJK. Enhanced Spot Noise for Vector Field Visualiza-tions. InProceedings of Visualization ’95, pages 233–239, 1995.
[12] D. STALLING and H.-C. HEGE. Fast and Resolution Independent Line Integral Convo-lution. In Computer Graphics Proceedings, Annual Conference Series, pages 249–256, August 1995.
[13] V. INTERRANTE and C. GROSCH. Recent Advances in Visualizing 3D Flow with LIC. ICASE Report No. 98-26, NASA Langley Research Center, July 1998.
http://citeseer.nj.nec.com/interrante98recent.html.
ing of the International Conference on Godunov Methods, pages 549–556, 1999.
[17] J. WERNE and D. C. FRITTS. Stratified shear turbulence: Evolution and statistic. Geo-physical research letters, 26(4):439–442, February 1999.
[18] B. TOM. Atmospheric Waves. Halsted press, 1974.
[19] H. TENNEKES and J. L. LUMLEY. A first course in turbulence. The MIT Press, 1972.
[20] A. VINCENT and M. MENEGUZZI. The spatial structure and statistical properties of homogeneous turbulence. J. Fluid Mech., 225:1–20, 1991.
[21] Y. DUBIEF and F. DELCAYRE. On coherent-vortex identification in turbulence.Journal of Turbulence, 1:11–32, December 2000. http://jot.iop.org.
[22] J. JEONG and F. HUSSAIN. On the identification of a vortex.Journal of Fluid Mechanics, 285:64–94, 1995.
[23] HDF webpage. http://hdf.ncsa.uiuc.edu.
[24] Qt webpage. http://www.trolltech.com.
[25] O. ANDREASSEN. Seminar in data visualization: UNIK-VAVD.
[26] Silicon Graphics. Onyx2 Reality and Onyx2 InfiniteReality Technical Report. Technical report, Silicon Graphics, inc, Oktober 1996.
[27] K. JONES. OpenGL Volumizer\ 2 Programmer’s Guide. Silicon Graphics.
http://www.sgi.com/software/volumizer/documents.html.
[28] W. E. LORENSEN and H. E. CLINE. MARCHING CUBES: A High Resolution 3D Sur-face Construction Algorithm. InComputer Graphics Proceedings, volume 21 ofAnnual Conference Series, pages 163–169, July 1987.
[29] C. MONTANI, R. SCATENI, and R. SCOPIGNI. Discretized Marching Cubes. In Visualization ’94 Proceedings, pages 281–287. IEEE Computer Society Press, 1994.
http://citeseer.nj.nec.com/montani94discretized.html.
[30] H. SHEN and C. JOHNSON. Sweeping simplicies: A Fast Isosurface Extraction Algo-rithm for Unstructured Grids. InProceedings of Visualization ’95, pages 143–150, 1995.
In Proceedings of the 1992 Workshop on Volume Rendering, pages 91–98, 1992.
http://citeseer.nj.nec.com/denskin92fast.html.
[34] M. LEVOY. Efficient Ray Tracing of Volume Data. ACM Transactions on Graphics, 9(3):245–261, July 1990.
[35] S. PARKER, M. PARKER, Y. LIVNAT, P. P. SLOAN, C. HANSEN, and P. SHIRLEY.
Interactive Ray Tracing for Volume Visualization. IEEE Transactions on Visualization and Computer Graphics, 5(3):238–250, July-September 1999.
[36] I. WALD, C. BENTHIN, M. WAGNER, and P. SLUSALLEK. Interactive Rendering with Coherent Ray Tracing. In Computer Graphics Forum (Proceedings of EUROGRAPH-ICS 2001", volume 20. Blackwell Publishers, Oxford, 2001. http://graphics.cs.uni-sb.de/ wald/Publications.
[37] B. CABRAL, N. CAM, and J. FORAN. Accelerated Volume Rendering and Tomographic Reconstruction Using Texture Mapping Hardware. In Proceedings 1994 Symposium on Volume Visualization, pages 91–98, Oktober 1994.
[38] T. J. CULLIP and U. NEUMANN. Accelerated Volume Reconstruction with 3D Tex-ture Mapping Hardware. Technical Report TR93-027, Department of Computer Sci-ence,University of North Carolina, Mai 1994.
[39] M. WOO, J. NEIDER, T. DAVIS, and D. SHREINER. OpenGL Programming Guide.
Addison-Wesley, third edition, 1999.
[40] M. WEILER, R. WESTERMANN, C. HANSEN, K. ZIMMERMANN, and T. ERTL.
Level-Of-Detail Volume Rendering via 3D Textures. InProceedings of Volume Visualiza-tion and Graphics Sympsium 2000, pages 7–13. IEEE, 2000.
[41] Viz. Information and software. Available on the web at the URL, ftp://ftp.ffi.no/spub/stsk/viz/features.html.
[42] M. ZÖCKLER, D. STALLING, and H.-C. HEGE. Parallel Line Integral Convolution. In Proceedings First Eurographics Workshop on Parallel Graphics and Visualization, Annual Conference Series, pages 249–256, September 1996.
[43] L. FORSELL. Visualizing Flow Over Curvelinear Grid Surfaces Using Line Integral Con-volution. InProceedings of Visualization 94, pages 240–247, Oktober 1994.
[44] H.-W. SHEN, C. R. JOHNSON, and K.-L. MA. Visualizing Vector Fields Using Line Integral Convolution and Dye Advection. InProceedings of the 1996 Volume Visualization Symposium, pages 63–70, Oktober 1996.