Flow Visualization Flow Visualization CS 176 Spring 2011 1 Fluid - PowerPoint PPT Presentation

Flow Visualization Flow Visualization CS 176 Spring 2011 1

Fluid Simulation a Looking at vector fields… g  how? Bolz et al. Laidlaw et al. CS 176 Spring 2011 2

Field Visualization V a a Stalling et al. Cabral et al. Stalling et al. CS 176 Spring 2011 3

Methods Physical analogies y g  particle advection  static or dynamic  static or dynamic  ink advection Bolz et al. Issues: Issues:  missing important detail CS 176 Spring 2011 4

Texture Methods x r Advection  advect texture coordinates with velocity; display regular grid with velocity; display regular grid with original texture  next time step: use previous texture  next time step: use previous texture  blend with exponential decay CS 176 Spring 2011 5

Line Integral Convltn. ra v Continuous version  integral curves of the flow  particles in flow  follow one traj. CS 176 Spring 2011 6

Integrate Along Flow ra A w Integrate nois g noise  output pixel: noise texture  high correlation along flow  high correlation along flow  low correlation orthogonal to flow CS 176 Spring 2011 7

Making it Fast ak a Pixels along path are correlated g p  curve tracing for each output pixel far to expensive far to expensive  step along curve!  accumulate results in pixels crossed  renormalize at end CS 176 Spring 2011 8

Details a Streamline integration g  high order integrator recommended  may make LARGE steps  may make LARGE steps  need to interpolate along path  aliasing…  step size 1/2 of texture cell p  path length: 1/10 image size CS 176 Spring 2011 9

Animation A a Slide integration along streamline g g  blend multiple images with different phases phases  contrast and brightness (renormalize) CS 176 Spring 2011 10

Image Based Flow Viz a a w V Treat images as basic primitive g p  LIC as blending of advected images  setup mesh with advected texture  setup mesh with advected texture coordinates  render and blend; repeat  render and blend; repeat  what image?  random noise (gives standard LIC) (g ) CS 176 Spring 2011 11

What Image? W a a Issues to consider  aliasing in time and space  pink not white noise  pink, not white noise  contrast, boundaries CS 176 Spring 2011 12

Nice Example xa van Wijk’s ibfv program j p g  testbed for visualization CS 176 Spring 2011 13

Direct Visualization r V a a Integral curves as shaded lines g  “hair” like analogy  how to shade lines?  how to shade lines?  usually objects co-D 1 New shading model  objects of co D 2  objects of co-D 2  think cylinders of infinitesimal size CS 176 Spring 2011 14

Shaded Lines a What normal?  standard model CS 176 Spring 2011 15

Implementation a Shading is function of L, T, V g , ,  texture lookup  inner products via texture xform  inner products via texture xform CS 176 Spring 2011 16

Details a Implementation p  shading too bright: for diffuse  add transparency: “wispy” tails  how to seed stream lines? h d  user driven  Monte Carlo; Voronoi  divergence… (reseed) g CS 176 Spring 2011 17

Papers a r CS 176 Spring 2011 18