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Visualizing Stochastic Vector Fields: Enhancing Error Representation in 2D and 3D

This project focuses on generating plausible streamlines and estimating their density from vector fields containing random errors. With the increasing importance of accurately visualizing errors in both experimental and simulated data, this research aims to create effective representations that incorporate uncertainty. Through various examples, including evenly spaced streamlines and multiple draggers, we demonstrate integration techniques and visualization methods to handle randomness within vector fields. Future enhancements will include improved error generation and dataset handling.

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Visualizing Stochastic Vector Fields: Enhancing Error Representation in 2D and 3D

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  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 R3 ( x1(t), x2(t), x3(t) ) • Mean:  x(t)  = 0 • Uncorrelated:  x(s) x(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

  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, 2001 • [2] C.R. Johnson and A.R. Sanderson, A Next Step: Visualizing Errors and Uncertainty, 2003

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