1. 2D Flow Visualization streamline, pathline, hedges, spotnoise 郭翰琦 陈珩

2. Outline Introduction Data Source Streamline, pathline Spotnoise User interactive

3. Introduction Flow Visualization: In fluid dynamics it is critically important to see the patterns produced by flowing fluids, in order to understand them.

4. Introduction Techniques: Point, Line, Surface, Volume, NPR, LIC, etc. In 2D FlowVis: geo-based, texture-based, etc. The techs we have tried: streamlines, pathlines, hedges, spotnoise.

5. Data Source Using a ‘Navier-Stokes Solver’ in MATLAB, we can get a 2D vector field in a suqare space by assigning boundary conditions. Square meshBoundary conditions 2D field

6. Data Source: interpolation After calculation, we get 2D vector data on thousands of triangles. Then, through interpolation, we get 128×128 mesh on [0,1]×[0,1] square. x 1,v 1 x 3,v 3 x 2,v 2

7. Streamline Streamlines are a family of curves that are instantaneously tangent to the velocity vector of the flow. A streamline is defined as

8. Streamline So, it is a Cauchy problem to integrate a streamline:

9. Streamline We use Runge-Kutta 4 to solve the stream integration: Non-grid points are processed with interpolation

10. Streamline One streamline: Seeds are red~With hedges

11. Streamlines: seeding strategy It is fairy a problem to put the streamlines or select the seeds. Several articles discussed this. (image- guided, even-spaced, etc) We used random seeds and man-select seeds. Random seeds

12. Streamlines: seeding strategy Man-selected seeds may have better effects near the critical points. (also a user-interactive means)

13. Streamline Same seeds with different time-steps:

14. Pathlines Pathlines are the trajectories that individual fluid particles follow. Pathlines are defined as

15. Pathlines It is also a Cauchy problem to integrate a pathline. To simplify the calculation, we use Euler method.

16. Spot Noise Texture is characterized by function f Spot function allows for local control over texture: maps data value (vector) to spot

17. Spot Noise Elliptical spots for visualizing 2D flows – Long axis proportional to |v| – Small axis proportional to 1/|v| 1 seed1000 seeds

18. Spot Noise Shortcomings: SLOW….. It takes 2 minutes to get a spot noise image with 1000 seeds. It may get faster using GPU

19. User interactive right click to choose one mode 8 modes: Streamline Hedge Pathlin Streamline&Hedge Streamline&Pathline Hedge&Pathline Stream&Hedge&Pathline Spotnoise

20. User interactive create a new line create a new path

21. User interactive keyboard: Press any key Pass to the next time step

22. User interactive Spotnoise Number - 10, 20, or 50 click and create spots 10, 20, or 50 each time

23. User interactive different viewpoints in one window overlay two modes color coding 34 colors for streamline and the pathline

24. User interactive

25. Thank you 郭翰琦 陈珩 2009-01-15