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Topology-guided accelerated vector field streamline visualization

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Abstract

Streamline visualization is crucial for understanding 3D vector fields, and seed placement is essential for high-quality streamlines. Current algorithms are either uniform, omitting vital information, or slow due to precalculation. We propose three novel techniques to build a topology-guided accelerated vector field streamline visualization framework. First, we convert the tracing process into an iterative one, dynamically generating seed points based on critical region detection and a cooldown mechanic. Second, we introduce “planar critical points” combined with traditional critical points to identify critical regions, and place new seed points according to their critical point types. During this process, we circumvent complex eigenvalue calculation with determining whether the eigenvalues are real, which is enough for our placement strategies. Third, we offer a fast streamline simplification technique based on global distortion to reduce clutter. Based on the proposed streamline visualization framework and various vector field visualization methods, we develop a CUDA-based application tool called AdaptiFlux, which achieves real-time visualization of vector fields more efficiently than those representative visualization tools.

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Data availability

The datasets used in Sect. 4 are available at https://osf.io/um3xr.

Code availability

The source code of AdaptiFlux is available at https://github.com/42yeah/adaptiflux.

References

  1. Ahrens, J., Geveci, B., Law, C., et al.: 36-paraview: an end-user tool for large-data visualization. In: The Visualization Handbook, vol. 717, pp. 50038–500381. Citeseer (2005)

    MATH  Google Scholar 

  2. Andrysco, N.: A user study contrasting 2d unsteady vector field visualization techniques. Ph.D. thesis, The Ohio State University (2005)

  3. Brambilla, A., Andreassen Ø, Hauser, H.: Integrated multi-aspect visualization of 3d fluid flows. In: VMV, pp. 1–9 (2013)

  4. Bujack, R., Middel, A.: State of the art in flow visualization in the environmental sciences. Environ. Earth Sci. 79(2), 65 (2020)

    Article  MATH  Google Scholar 

  5. Bujack, R., Dutta, S., Zhang, D., et al.: Objective finite-time flow topology from flowmap expansion and contraction. In: Hotz, I., Bin Masood, T., Sadlo, F., et al. (eds.) Topological Methods in Data Analysis and Visualization VI, pp. 111–131. Springer, Cham (2021)

    Chapter  MATH  Google Scholar 

  6. Butcher, J.: Runge–Kutta methods. Scholarpedia 2(9), 3147 (2007)

  7. Cabral, B., Leedom, L.C.: Imaging vector fields using line integral convolution. In: Proceedings of the 20th Annual Conference on Computer Graphics and Interactive Techniques. Association for Computing Machinery, New York, NY, USA, SIGGRAPH ’93, pp 263–270 (1993). https://doi.org/10.1145/166117.166151

  8. Carmo, B.S., Ng, Y.P., Prügel-Bennett, A.: et al A data clustering and streamline reduction method for 3d mr flow vector field simplification. In: Medical Image Computing and Computer-Assisted Intervention–MICCAI 2004: 7th International Conference, Saint-Malo, France, September 26–29, 2004. Proceedings, Part I 7. Springer, pp. 451–458 (2004)

  9. Chao, L., Lingda, W.: Vector field visualization review and prospects. In: 2014 International Conference on Virtual Reality and Visualization, pp. 43–49 (2014). https://doi.org/10.1109/ICVRV.2014.42

  10. Childs, H., Brugger, E., Whitlock, B., et al (2012) Visit: an end-user tool for visualizing and analyzing very large data. In: High Performance Visualization–Enabling Extreme-Scale Scientific Insight. LBNL Publications, pp. 357–372. https://doi.org/10.1201/b12985

  11. Engelke, W., Lawonn, K., Preim, B., et al.: Autonomous particles for interactive flow visualization. Comput. Graph. Forum 38(1), 248–259 (2019). https://doi.org/10.1111/cgf.13528

    Article  MATH  Google Scholar 

  12. Hall, P.: Volume rendering for vector fields. Vis. Comput. 10, 69–78 (1993)

    Article  MATH  Google Scholar 

  13. Hu, X., Weng, J., Chai, J., et al.: A 3d streamline selection algorithm based on comprehensive similarity. In: Third International Conference on Artificial Intelligence and Computer Engineering (ICAICE 2022), pp. 1230–1234. SPIE (2023)

  14. Kong, L.X., Tang, X.A., Li, H., et al.: A view-dependent and physical feature-preservation streamline simplification method for 3d vector field visualization. In: Computers and Information Processing Technologies I, Applied Mechanics and Materials, vol. 571, pp 676–681. Trans Tech Publications Ltd (2014). https://doi.org/10.4028/www.scientific.net/AMM.571-572.676

  15. Kruger, J., Kipfer, P., Konclratieva, P., et al.: A particle system for interactive visualization of 3d flows. IEEE Trans. Vis. Comput. Graph. 11(6), 744–756 (2005). https://doi.org/10.1109/TVCG.2005.87

    Article  MATH  Google Scholar 

  16. Laramee, R.S., Erlebacher, G., Garth, C., et al.: Applications of texture-based flow visualization. Eng. Appl. Comput. Fluid Mech. 2(3), 264–274 (2008)

    MATH  Google Scholar 

  17. Liu, F., Zhou, W., Liu, B., et al.: Flow field description and simplification based on principal component analysis downscaling and clustering algorithms. Front. Earth Sci. 9, 23 (2022). https://doi.org/10.3389/feart.2021.804617

    Article  MATH  Google Scholar 

  18. Max, N.: Progress in scientific visualization. The Visual Computer 21(UCRL-JRNL-208330) (2004)

  19. Nouanesengsy, B., Lee, T.Y., Shen, H.W.: Load-balanced parallel streamline generation on large scale vector fields. IEEE Trans. Vis. Comput. Graph. 17(12), 1785–1794 (2011). https://doi.org/10.1109/TVCG.2011.219

    Article  MATH  Google Scholar 

  20. Peng, B., Wang, W., Li, S.: Data prefetching in streamline visualization of large scale flow field. J. Comput.-Aided Des. Comput. Graph. 28(3), 464–470 (2016)

    MATH  Google Scholar 

  21. Peng, Z., Geng, Z., Laramee, R.S.: Design and implementation of a system for interactive higher dimensional vector field visualization. In: Eurographics (Posters), pp. 13–14 (2011)

  22. Perry, A., Fairlie, B.: Critical points in flow patterns. In: Advances in Geophysics, vol. 18, pp. 299–315. Elsevier (1975)

    MATH  Google Scholar 

  23. Präger, A., Nsonga, B., Scheuermann, G.: Visualizing statistical complexity in 3d turbulent flows using a robust entropy calculation method. In: WSCG 2022 Forum, pp. 28–37 (2022). https://doi.org/10.24132/CSRN.3201.5

  24. Pugmire, D., Childs, H., Garth, C., et al.: Scalable computation of streamlines on very large datasets. In: Proceedings of the Conference on High Performance Computing Networking, Storage and Analysis, pp. 1–12 (2009). https://doi.org/10.1145/1654059.1654076

  25. Salzbrunn, T., Scheuermann, G.: Flow Structure Based 3D Streamline Placement, pp. 89–100. Springer, Berlin (2009). https://doi.org/10.1007/978-3-540-88606-8_7

    Book  MATH  Google Scholar 

  26. Sane, S., Bujack, R., Garth, C., et al.: A survey of seed placement and streamline selection techniques. Comput. Graph. Forum 39(3), 785–809 (2020). https://doi.org/10.1111/cgf.14036

    Article  MATH  Google Scholar 

  27. Schroeder, W., Martin, K., Lorensen, B., et al.: The Visualization Toolkit: An Object-oriented Approach to 3D Graphics. Kitware (2006). https://books.google.co.jp/books?id=rx4vPwAACAAJ

  28. Skala, V., et al.: Classification of critical points using a second order derivative. Procedia Comput. Sci. 108, 2373–2377 (2017)

    Article  MATH  Google Scholar 

  29. Skraba, P., Wang, B., Chen, G., et al.: Robustness-based simplification of 2d steady and unsteady vector fields. IEEE Trans. Vis. Comput. Graph. 21(8), 930–944 (2015). https://doi.org/10.1109/TVCG.2015.2440250

    Article  MATH  Google Scholar 

  30. Skraba, P., Rosen, P., Wang, B., et al.: Critical point cancellation in 3d vector fields: robustness and discussion. IEEE Trans. Vis. Comput. Graph. 22(6), 1683–1693 (2016). https://doi.org/10.1109/TVCG.2016.2534538

    Article  MATH  Google Scholar 

  31. Stalling, D., Hege, H.C.: Fast and resolution independent line integral convolution. In: Proceedings of the 22nd Annual Conference on Computer Graphics and Interactive Techniques. Association for Computing Machinery, New York, NY, USA, SIGGRAPH ’95, pp. 249–256 (1995). https://doi.org/10.1145/218380.218448

  32. Stalling, D., Steinke, T.: Visualization of vector fields in quantum chemistry. Tech. Rep. SC-96-01, ZIB, Takustr. 7, 14195, Berlin (1996)

  33. Storti, D., Yurtoglu, M.: CUDA for Engineers: An Introduction to High-Performance Parallel Computing. Addison-Wesley Professional (2015)

    MATH  Google Scholar 

  34. Sundquist, A.: Dynamic line integral convolution for visualizing streamline evolution. IEEE Trans. Vis. Comput. Graph. 9(3), 273–282 (2003). https://doi.org/10.1109/TVCG.2003.1207436

    Article  MATH  Google Scholar 

  35. Tao, J., Ma, J., Wang, C., et al.: A unified approach to streamline selection and viewpoint selection for 3d flow visualization. IEEE Trans. Vis. Comput. Graph. 19(3), 393–406 (2013). https://doi.org/10.1109/TVCG.2012.143

    Article  MATH  Google Scholar 

  36. Telea, A., Van Wijk, J.: Simplified representation of vector fields. In: Proceedings Visualization ’99 (Cat. No.99CB37067), pp 35–507 (1999). https://doi.org/10.1109/VISUAL.1999.809865

  37. Verma, V., Kao, D., Pang, A.: A flow-guided streamline seeding strategy. In: Proceedings Visualization 2000. VIS 2000 (Cat. No.00CH37145), pp. 163–170 (2000). https://doi.org/10.1109/VISUAL.2000.885690

  38. Wang, C., Han-Wei, S.: Information theory in scientific visualization. Entropy (2011). https://doi.org/10.3390/e13010254

    Article  MATH  Google Scholar 

  39. Wischgoll, T., Scheuermann, G.: Locating closed streamlines in 3d vector fields. In: Proceedings of the Symposium on Data Visualisation 2002. Eurographics Association, Goslar, DEU, VISSYM ’02, p. 227-ff (2002)

  40. Xu, H., Cheng, Z.Q., Martin, R.R., et al.: 3d flow features visualization via fuzzy clustering. Vis. Comput. 27, 441–449 (2011)

    Article  MATH  Google Scholar 

  41. Xu, L., Lee, T.Y., Shen, H.W.: An information-theoretic framework for flow visualization. IEEE Trans. Vis. Comput. Graph. 16(6), 1216–1224 (2010). https://doi.org/10.1109/TVCG.2010.131

  42. Yang, Y., Zhou, H., Peng, W.: Multi-task super resolution method for vector field critical points enhancement. Metaverse 3(1), 8 (2022)

    Article  MATH  Google Scholar 

  43. Ye, X., Kao, D., Pang, A.: Strategy for seeding 3d streamlines. In: VIS 05. IEEE Visualization, 2005., pp. 471–478 (2005). https://doi.org/10.1109/VISUAL.2005.1532831

  44. Zharfa, M., Krueger, P.S.: APS -72nd Annual Meeting of the APS Division of Fluid Dynamics - Event - Critical point identification in 3D velocity fields., in Bulletin of the American Physical Society, American Physical Society. (2019) Available: https://meetings.aps.org/Meeting/DFD19/Session/H12.8. Accessed 8 Apr 2024

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Funding

This work was supported in part by the National Natural Science Foundation of China under Grant (Nos 62072126, 61720164), in part by the Fundamental Research Projects Jointly Funded by Guangzhou Council and Municipal Universities under Grant SL2023A03J00639, and Key Laboratory of Philosophy and Social Sciences in Guangdong Province of Maritime Silk Road of Guangzhou University (GD22TWCXGC15), in part by the PolyU Research Institute for Sports Science and Technology under Grant P0044571.

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Author notes

  1. Hao Zhou and Junjie Yin have contributed equally to this work.

Authors and Affiliations

  1. Metaverse Research Institute, School of Computer Science and Cyber Engineering, Guangzhou University, 230 Wai Huan Xi Road, Guangzhou, 510006, Guangdong, China

    Hao Zhou, Junjie Yin, Yilun Yang & Meie Fang

  2. Department of Computing and the School of Design, The Hong Kong Polytechnic University, 11 Yuk Choi Road, Hung Hom, Hong Kowloon, Hong Kong SAR, China

    Ping Li

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  1. Hao Zhou
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Correspondence to Meie Fang.

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Zhou, H., Yin, J., Yang, Y. et al. Topology-guided accelerated vector field streamline visualization. Vis Comput 41, 709–722 (2025). https://doi.org/10.1007/s00371-024-03357-8

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