Scientific Visualization
CIS 5930

Spring 2004
Tuesday/Thursday 02:00pm
499 Dirac Science Library
Dr. David C. Banks

Course
  course webpage
  assignment webpage
  students webpages

Contents
  home

Homework
  hw.00
  hw.01
  hw.02
  hw.03
  hw.04
  hw.05
  hw.06
  hw.07
  hw.08
  hw.09

Info.
  Yoshihito Yagi
  yagi@cs.fsu.edu

Project: Stochastic Vector Field

        In this project, I wrote a program and visualized vectorfields which contain errors. I put multiple draggers as seed points in a scene and generate several streamlines from them.


    Paper : project.pdf

    Presentation : presentation.ppt


    Basic Idea
  • Apr 16 - 21
      Integration : normal vector field
      
      Integration : stochastic vector field
      
      
      Tornado Vector Field : mean(x,y,z) = (cos(t)*x-sin(t)*y, a, sin(t)*x+cos(t)*y), t=0.23*2*PI, a=0.012
      evenly spaced
      
      
      single dragger - generates tubes forward and backward [left: 10, middle: 100, right: 200]
      
      
      multiple draggers - each one generates 10 tubes
      
      animation
      
      big tube
      
      transparency
      
      
      density by amira - isosurface
      
      
  • Apr 13 - 15
      tornado
      
      

  • Apr 6 - 12
      
      
      
      
      [left] sigma=1.0 [middle] sigma=2.0 [right] sigma=3.0
      
      
      
      

    A big tube covers all stochastic tubes.
      
      

  • Apr 1 - 5
        C(t) = C(0) + | mean * dt + | sigma * noise * dt

      First Order Approximation:
        if mean and sigma are constant, then
        C(t) = C(0) + mean(0) * t + sigma(0) * Z(t)
        Z(h) = sqrt(h) * Y
        Y = N(0,1)
        =>
        C(t) = C(0) + mean(0) * t + sigma(0) * sqrt(h) * N(0,1)

      Higher Order Approximation:
        
        | mu(C(t))dt = | [mu0 + mu'(C(t) - C(0)]dt
         = mu0*h + 1/2*mu0'mu0*h^2 + mu'sigma0*| Z(t)dt
        | sigma(C(t))*s(t)dt = [sigma0 + sigma0'(C(t) - C(0))]*s(t)dt
         = sigma0*Z(h) + mu0*sigma0'[h*Z(h) - Z(t)dt] + 1/2*sigma0sigma0'*Z^2(h)

  • Mar 27 - 31
    [0] V(x,y,z) = (0,0,0)
        Pk+1 <- Pk + V(Pk) * h + (drand48(),drand48(),drand48()) * sqrt(h) : change step size h and step number H
        
        
        [left] h=5 H=90 [middle] h=10 H=45 [right] h=15 H=30 : vector field 100x100x100 : seed (0.0, 0.0, 0.0)
    [1] V(x,y,z) = (0,0,0)
        Pk+1 <- Pk + V(Pk) * h + N(0,sigma) * sqrt(h) : change step size h and step number H
        
        
         [left] h=5 H=90 [middle] h=10 H=45 [right] h=15 H=30 : sigma=1.0 : vector field 100x100x100 : seed (0.0, 0.0, 0.0)
    [2] V(x,y,z) = (1,0,0)
         Pk+1 <- Pk + V(Pk) * h + N(0,sigma) * sqrt(h) : change sigma
        
        
        [left] sigma=1.0 [middle] sigma=2.0 [right] sigma=3.0 : vector field 100x100x100 : seed (0.0, 0.0, 0.0) : h 2.0
    [3] V(x,y,z) = (-y,x,0)
        Pk+1 <- Pk + V(Pk) * h + N(0,sigma) * sqrt(h) : change sigma
        
        
        [left] sigma=1.0 [middle] sigma=2.0 [right] sigma=3.0 : vector field 100x100x100 : seed (15.0, 0.0, 0.0) : h 0.2
    [4] V(x,y,z) = (1,0,0)
        Pk+1 <- Pk + V(Pk) * h + N(0,x) * sqrt(h) : change x
        
        vector field 10x10x10 : seed (0.1, 0.0, 0.0) : h 0.2

    *** Submit Abstract on Wednesday ***
    I gave up submitting a paper this semester, but I like to complete this project before the end of semester.
    link : abstract

  • Mar 22 - 26
    I am creating animation and adding textures.
    I will calculate density.
    I rendered ivfile by Pane.


  • Mar 13 - 21
    5. Evenly-Spaced Streamlines
    Reference: Creating Evenly-Spaced Streamlines of Arbitrary Density

    vector field 100x100x100, v = ( z,-x, y)
    [left] minmum distance = 20.0, # of streamlines = 45
    [middle] minmum distance = 10.0, # of streamlines = 228
    [right] minmum distance = 5.0, # of streamlines = 1328

    Stochastic Streamlines
    I created multiple draggers.


  • Spring Break:
      Mar 6 - Mar 12
    1. Random Walk


    2. Add Streamline


    3. Add QuadMesh


    4. Add Vector Field

    Vector Field [left] v = (-z, 0, x), [right] v = ( z,-x, y)

    5. Evenly-Spaced Streamlines
    Coming Soon.

    Stochastic Streamlines


  • Homework07: Demo and paper
      Feb 26 - Mar 03
  • Homework06: Example images
      Feb 19 - Feb 25
  • Homework05: Bibliography
      Feb 12 - Feb 18
  • Homework03: First meeting
      Jan 29 - Feb 04