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Flow Visualization Flow Visualization
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Fluid Simulation a
Looking at vector fields… g
how?
Bolz et al. Laidlaw et al.
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Flow Visualization Flow Visualization CS 176 Spring 2011 1 Fluid - - PowerPoint PPT Presentation
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
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Field Visualization V a a
Stalling et al. Cabral et al. Stalling et al.
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Methods
Physical analogies y g
particle advection
static or dynamic static or dynamic
ink advection
Issues:
Bolz et al.
Issues:
missing important detail
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Texture Methods x r
Advection
advect texture coordinates with
velocity; display regular grid with velocity; display regular grid with
- riginal texture
next time step: use previous texture next time step: use previous texture blend with exponential decay
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Line Integral Convltn. ra v
Continuous version
integral curves of the flow particles in flow follow one traj.
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Integrate Along Flow ra A w
Integrate nois noise g
output pixel: high correlation along flow
noise texture
high correlation along flow low correlation orthogonal to flow
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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
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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
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Animation A a
Slide integration along streamline g g
blend multiple images with different
phases phases
contrast and brightness (renormalize)
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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)
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(g )
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What Image? W a a
Issues to consider
aliasing in time and space
pink not white noise pink, not white noise
contrast, boundaries
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Nice Example xa
van Wijk’s ibfv program j p g
testbed for visualization
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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
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Shaded Lines a
What normal?
standard model
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Implementation a
Shading is function of L, T, V g , ,
texture lookup inner products via texture xform inner products via texture xform
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Details a
Implementation p
shading too bright: for diffuse add transparency: “wispy” tails
h d
how to seed stream lines?
user driven Monte Carlo; Voronoi divergence… (reseed)
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g
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Papers a r
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