Skip to main content

Flow Structure based 3D Streamline Placement

  • Chapter
Book cover Topology-Based Methods in Visualization II

Part of the book series: Mathematics and Visualization ((MATHVISUAL))

Summary

Visualizing vector fields using streamlines or some derived applications is still one of the most popular flow visualization methods in use today. Besides the known trade-off between sufficient coverage in the field and cluttering of streamlines, the typical user question is: Where should I start my streamlines to see all important behavior?

In previous work, we define flow structures as an extension of flow topology that permits a partition of the whole flow tailored to the users needs. Based on the skeletal representation of the topology of flow structures, we propose a 3D streamline placement generating a minimal set of streamlines, that on the one hand exactly illustrates the desired property of the flow and on the other hand takes the topology of the specific flow structure into account. We present a heuristic and a deterministic approach and discuss their advantages and disadvantages.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M. Griebel, T. Preusser, M. Rumpf, M.A. Schweitzer, and A. Telea. Flow Field Clustering via Algebraic Multigrid. In IEEE Visualization 2004, pages 35–42, Austin, Texas, 2004.

    Google Scholar 

  2. B Heckel, G.H. Weber, B. Hamann, and K.I. Joy. Construction of Vector Field Hierarchies. In IEEE Visualization 1999, pages 19–25, San Francisco, CA, 1999.

    Google Scholar 

  3. J. L. Helman and L. Hesselink. Visualizing Vector Field Topology in Fluid Flows. IEEE Computer Graphics and Applications, 11(3):36–46, May 1991.

    Article  Google Scholar 

  4. B. Jobard and W. Lefer. Creating evenly-spaced streamlines of arbitrary density. In Visualization in Scientific Computing ′97 (Proceedings of the 8th Eurographics Workshop on Visualization in Scientific Computing ′97, pages 43–55, 1997.

    Google Scholar 

  5. A. Kuba and K. Palagyi. A 3D 6-Subiteration Thinning Algorithm for Extracting Medial Lines. Pattern Recognition Letters, 19(7):613–627, 1998.

    Article  MATH  Google Scholar 

  6. R.S. Laramee, H. Hauser, H. Doleisch, B. Vrolijk, F.H. Post, and Weiskopf D. The State of the Art in Flow Visualization: Dense and Texture Based Techniques. Computer Graphics Forum, 23(2):203–221, 2004.

    Article  Google Scholar 

  7. K. Mahrous, J. Bennett, G. Scheuermann, B. Hamann, and K. I. Joy. Topolog-ical Segmentation of Three-Dimensional Vector Fields. IEEE Transactions on Visualization and Computer Graphics, 10(2):198–205, 2004.

    Article  Google Scholar 

  8. O. Mattausch, T. Theüsl, H. Hauser, and E Gröller. Strategies for Interactive Exploration of 3d Flow Using Evenly-Spaced Illuminated Streamlines. In Proceedin gs of Spri ng Conference on Computer Graphics, pages 213–222, 2003.

    Google Scholar 

  9. F.H. Post, B. Vrolijk, H. Hauser, R.S. Laramee, and H. Doleisch. The State of the Art in Flow Visualization: Feature Extraction and Tracking. 22(4):775–792, 2003.

    Google Scholar 

  10. F. Sadlo, R. Peikert, and E. Parkinson. Vorticity Based Flow Analysis and Visualization for Pelton Turbine Design Optimization. In IEEE Visualization 2004, pages 179–186, Austin, Texas, 2004.

    Google Scholar 

  11. T. Salzbrunn and G. Scheuermann. Streamline Predicates As Flow Topology Generalization. In Topo-I n-Vis P roceedings 2005, 2005.

    Google Scholar 

  12. T. Salzbrunn and G. Scheuermann. Streamline Predicates. IEEE Transactions on Visualization and Computer Graphics, 12(6):1601–1612, 2006.

    Article  Google Scholar 

  13. G. Scheuermann, K.I. Joy, and W. Kollmann. Visualizing Local Vector Field Topology. Journal of Electronic Imaging, 9:356–367, 2000.

    Article  Google Scholar 

  14. D. Sujudi and R. Haimes. Identification of Swirling Flow in 3D Vector Fields. Technical Report AIAA Paper 95–1715, American Institute of Aeronautics and Astronautics, 1995.

    Google Scholar 

  15. A. Telea and J.J. van Wijk. Simplified representation of vector fields. In IEEE Visualization 1999, pages 35–42, San Francisco, CA, 1999.

    Google Scholar 

  16. H. Theisel, T. Weinkauf, H.C. Hege, and H.P. Seidel. Saddle Connectors - An Approach to Visualizing the Topological Skeleton of Complex 3d Vector Fields. In IEEE Visualization 2003, pages 225–232, 2003.

    Google Scholar 

  17. X. Tricoche, T. Wischgoll, G. Scheuermann, and H. Hagen. Topological Tracking for the Visualization of Timedependent Two-Dimensional Flows. Computers & Graphics, 26(2):249–257, 2002.

    Article  Google Scholar 

  18. G. Turk and D. Banks. Image-Guided Streamline Placement. In Computer Graphics Annual Conference Series, pages 453–460, 1996.

    Google Scholar 

  19. V. Verma, D. Kao, and A. Pang. Flow-Guided Streamline Seeding Strategy. In IEEE Visualization 2000, pages 163–170, Salt Lake City, Utah, 2000.

    Google Scholar 

  20. R. Westermann, C. Johnson, and T. Ertl. A Level-Set Method for Flow Visualization. In IEEE Visualization 2000, pages 147–154, Salt Lake City, Utah, 2000.

    Google Scholar 

  21. X. Ye, D. Kao, and A. Pang. Strategy For Seeding 3d Streamlines. In IEEE Visualization 2005, pages 471–478, Minneapolis, MN, 2005.

    Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Salzbrunn, T., Scheuermann, G. (2009). Flow Structure based 3D Streamline Placement. In: Hege, HC., Polthier, K., Scheuermann, G. (eds) Topology-Based Methods in Visualization II. Mathematics and Visualization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88606-8_7

Download citation

Publish with us

Policies and ethics