Project: Visualization of Stochastic Vector Fields Yoshihito Yagi Expertise : Dr. Banks, Dr. Srivastava

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]

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)

Integration Normal Vector Field Stochastic Vector Field

Integration First Order Approximation

Integration First Order Approximation – Assume mean and sigma are constants

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

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

Example3: multiple draggers Generate streamlines from multiple draggers.

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

Example5: transparency Apply transparency.

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

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

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