1. Project: Visualization of Stochastic Vector Fields Yoshihito Yagi http://www.csit.fsu.edu/~yagi/visualization/project/ Expertise : Dr. Banks, Dr. Srivastava

2. Goal and Motivation Goal : – generate plausible streamlines and estimate their density from given a vector field that contains errors. Motivation : – “Majority of 2D graphs represent errors within the experimental or simulated data.”[2] – “It’s equally important to represent error and uncertainty in 2D and 3D visualization.”[2]

3. Stochastic Vector fields Vector fields contain random errors. White (Uncorrelated) Noise: – In R 3 (  1 (t),  2 (t),  3 (t) )  (t) = 0 – Mean:   (t)  = 0  (s)  (t) =  (t-s) – Uncorrelated:   (s)  (t)  =  (t-s)

4. Integration Normal Vector Field Stochastic Vector Field

5. Integration First Order Approximation

6. Integration First Order Approximation – Assume mean and sigma are constants

7. Example1: evenly spaced vectors. “ Creating Evenly-Spaced Streamlines of Arbitrary Density ” – Bruno Jobard, Wilfrid Lefer Bruno JobardWilfrid Lefer

8. Example2: single dragger Generate streamlines from a dragger. Use timer and recreate streamlines.

9. Example3: multiple draggers Generate streamlines from multiple draggers.

10. Example4: big tube One big tube covers all possible streamlines.

11. Example5: transparency Apply transparency.

12. Example6: density by amira When streamlines are generated, their position are recorded. Amira shows isosurface.

13. Future Works Better implementation. Use better function which creates random errors. Read dataset.

14. Thanks. Reference: – [1] D.C. Banks and A. Srivastava, Rendering Stochastic Flows, 2001Rendering Stochastic Flows – [2] C.R. Johnson and A.R. Sanderson, A Next Step: Visualizing Errors and Uncertainty, 2003A Next Step: Visualizing Errors and Uncertainty