Vortex%20Fluid%20Structure%20For%20Smoke%20Control

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Vortex Fluid StructureFor Smoke Control
SCA 2006

• Alexis Angelidis (1)
• Fabrice Neyret (2)
• Karan Singh (1)
• Derek Nowrouzezahrai (1)
• (1) DGP, U of Toronto
• (2) Evasion-GRAVIR / IMAG-INRIA

2
Motivation

• Fluid Animation smoke, clouds, fire, explosion,
  splashes, sea
• Simulation vs Animation

Areté Entertainment, inc. 96
LOTR
3
Motivation

• Fluid Animation smoke, clouds, fire, explosion,
  splashes, sea
• Simulation vs Animation
• Approaches to control
• Phenomenological, limited
• Fake forces
• Control by keyframing shapes

Areté Entertainment, inc. 96
LotR
4
Motivation

• Most related work
• Density field given at keyframes
• Solver between frames
• What we want
• No hand-drawn smoke
• Natural control

Treuille et al.03,McNamara et al.04,Fattal
et al.04
key2
key1
McNamara et al.04
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Background AN05
Vorticity
Velocity
moving quantity
representation
popular
Eulerian
our method
Lagrangian
Chart of methods for numerical fluid
simulation
6
Background
Vorticity
Velocity
moving quantity
representation
popular
Eulerian
our method
Lagrangian
velocity v
3D field
Rotation in rad s-1
translation in m s-1
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Background
Vorticity
Velocity
moving quantity
representation
popular
Eulerian
our method
Lagrangian
velocity v
Curl
8
Background
Vorticity
Velocity
moving quantity
representation
popular
Eulerian
our method
Lagrangian
velocity v
BIOT-SAVART
9
Background
Vorticity
Velocity
moving quantity
representation
popular
Eulerian
our method
Lagrangian
Dynamics
Eulerian
The flow modifies quantities held at static
positions
Lagrangian
The flow carries floaters that hold the quantities
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Background
Vorticity
Velocity
moving quantity
representation
popular
Eulerian
our method
Lagrangian
Lagrangian
Eulerian
at particle
in grid
11
Background
Vorticity
Velocity
moving quantity
representation
popular
Eulerian
our method
Lagrangian
NAVIER-STOKES
( incompressible )
12
Background
Vorticity
Velocity
moving quantity
representation
popular
Eulerian
our method
Lagrangian
13
Background
Vorticity
Velocity
moving quantity
representation
popular
Eulerian
our method
Lagrangian
VORTICITY EQUATION
( inviscid )
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Background
Vorticity
Velocity
moving quantity
representation
popular
Eulerian
our method
Lagrangian
No diffusion Implicit incompressibility
compact Unbounded
Easy boundary conditions Easy extra differential
eqn
15
Background
Vorticity
Velocity
moving quantity
representation
popular
Eulerian
our method
Lagrangian
Vorticity Vortex particle advected, vector
stretched
vorticity moves as material lines
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Background
Vorticity
Velocity
moving quantity
representation
popular
Eulerian
our method
Lagrangian
Vorticity Our primitive curves
tangent
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Background
Vorticity
Velocity
moving quantity
representation
popular
Eulerian
our method
Lagrangian
Density Dedicated particles - passive
floaters - for rendering - only where smoke
is
Density a quantity at nodes
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Lagrangian primitives

• Curves carry the vorticity
• Each local vortex induces a weighted rotation

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Lagrangian primitives

• Curves carry the vorticity
• Each local vortex induces a weighted rotation

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Method of simulation

• Vortex particles (for motion) organized
  as curves. tangent
• Smoke particles (for visualisation)
• Curves carry vortices
• Vortices induce a velocity field
• velocity field deforms curves smoke
• At every step
• Advect the curves
• Stretch
• Advect the smoke

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Method of simulation

• Vortex particles (for motion) organized
  as curves. tangent
• Smoke particles (for visualisation)
• Curves carry vortices
• Vortices induce a velocity field
• velocity field deforms curves smoke
• At every step
• Advect the curves
• Stretch
• Advect the smoke

22
Method of simulation

• Vortex particles (for motion) organized
  as curves. tangent
• Smoke particles (for visualisation)
• Curves carry vortices
• Vortices induce a velocity field
• velocity field deforms curves smoke
• At every step
• Advect the curves
• Stretch
• Advect the smoke

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Contributions

• A new representation of vortex curves
• Compact, stable, controlable motion primitives
• Controls of the motion primitives
• Fast noise for fake turbulence details

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Contributions

• A new representation of vortex curves
• Compact, stable, controlable motion primitives
• Controls of the motion primitives
• Fast noise for fake turbulence details

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Deformation of curves previous approach AN05
If not refined undersampling
Polygon
If refined too complex
Strategy to control complexity
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New representation

• Solution harmonic analysis of coordinates

x in y z
a pair of coefficients for each harmonic

• Reference frame best ellipsoid

Complexity control

• Curves described by
• Frame o ex ey ez
• Frequencies ltcx cy czgt1..N

Synthesis Advection Analysis
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New representation

• Solution harmonic analysis of coordinates

x in y z
a pair of coefficients for each harmonic
ez
ey

• Reference frame best ellipsoid

o
ex
Complexity control

• Curves described by
• Frame o ex ey ez
• Frequencies ltcx cy czgt1..N

Synthesis Advection Analysis
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New representation

• Solution harmonic analysis of coordinates

x in y z
a pair of coefficients for each harmonic
ez
ey

• Reference frame best ellipsoid

o
ex
Complexity control

• Curves described by
• Frame o ex ey ez
• Frequencies ltcx cy czgt1..N

Synthesis Advection Analysis
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New representation

• Solution harmonic analysis of coordinates

x in y z
a pair of coefficients for each harmonic
ez
ey

• Reference frame best ellipsoid

o
ex
Complexity control

• Curves described by
• Frame o ex ey ez
• Frequencies ltcx cy czgt1..N

Synthesis Advection Analysis
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Meaning of description

• ez points towards moving direction

• Frequencies cx cy cz give texture to the flow

• Thickness

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Video representation
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Contributions

• A new representation of vortex curves
• Compact, stable, controlable motion primitives
• Controls of the motion primitives
• Fast noise for fake turbulence details

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Control

• direction align ez with tangent
• Targets
• Twisting smoke spin vortices around ez
• Edit, delete
• Modulate cx cy cz to texture the flow

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Control

• direction align ez with tangent
• Targets
• Twisting smoke spin vortices around ez
• Edit, delete
• Modulate cx cy cz to texture the flow

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Control

• direction align ez with tangent
• Targets
• Twisting smoke spin vortices around ez
• Edit, delete
• Modulate cx cy cz to texture the flow

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How to control

• One cannot just translate the curves the smoke
  does not follow

• Solution paddle (servoing )

ez
ey
o
ex
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Video control
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Contributions

• A new representation of vortex curves
• Compact, stable, controlable motion primitives
• Controls of the motion primitives
• Fast noise for fake turbulence details

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Noise fake turbulence details

• AN05
• noise extra vortex particles
• advected in the flow, no stretch
• Costly (needs a lot)
• Source, sampling
• Tiled vortex noise
• noise layer
• separate simulation, in toroidal space
• Tiled in space
• Additional evolving velocity field

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Noise fake turbulence details

• AN05
• noise extra vortex particles
• advected in the flow, no stretch
• Costly (needs a lot)
• Source, sampling
• Tiled vortex noise
• noise layer
• separate simulation, in toroidal space
• Tiled in space
• Additional evolving velocity field

41
Noise fake turbulence details

• AN05
• noise extra vortex particles
• advected in the flow, no stretch
• Costly (needs a lot)
• Source, sampling
• Tiled vortex noise
• noise layer
• separate simulation, in toroidal space
• Tiled in space
• Additional evolving velocity field

42
Video noise
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Contributions

• A new representation of vortex curves
• Compact, stable, controlable motion primitives
• Controls of the motion primitives
• Fast noise for fake turbulence details
• Velocity cache, rendering

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Octree cache

• Velocity computed at every smoke particle
  every vorticity curve sample

• Velocity computed at octree leaves inbetween
  interpolation

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Octree cache

• Velocity computed at every smoke particle
  every vorticity curve sample

• Velocity computed at octree leaves inbetween
  interpolation

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Rendering

• Thick smoke plain particles
• Thin smoke adaptive particles AN05
• accumulate stretching

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Rendering

• Thin smoke behaves like a surface

William Brennan
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Results - video
fps Forest fire Genielamp
Walkthrough Fly
Modeler quality 5 12
5 18 Final rendering
quality 0.54 0.2 1.
0.37
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Conclusion

• Vorticity filaments
• Compact, high-res, fast
• Good handles to manipulate a fluid
• Can be manipulated interactively or post-
• Future work
• Split/merge
• High-quality collisions
• 2-phase, buoyancy,

Coupling with grids
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Thanks!
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Video collisions
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Video thickness
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Rendering

• Thin smoke behaves like a surface

Diffuse off
Diffuse on
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Rendering

• Thin smoke behaves like a surface

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Lagrangian primitives

• Curves carry the vorticity
• Each vortex induces a weighted rotation

Effect of one vortex on ashape
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Control currents

• Without control

• With control

ez
t
L
L
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Checkpoint

• With control