vortex fluid structure for smoke control

Vortex Fluid StructureVortex Fluid StructureFor Smoke ControlFor Smoke Control

SCA 2006SCA 2006

Alexis Angelidis Alexis Angelidis (1)

Fabrice Neyret Fabrice Neyret (2)

Karan Singh Karan Singh (1)

Derek Nowrouzezahrai Derek Nowrouzezahrai (1)

(1): DGP, U of Toronto(2): Evasion-GRAVIR / IMAG-INRIA

MotivationMotivation• Fluid Animation: Fluid Animation: smokesmoke, clouds, fire, explosion, splashes, sea…, clouds, fire, explosion, splashes, sea…

• Simulation vs AnimationSimulation vs Animation

[ Areté Entertainment, inc. 96][ Areté Entertainment, inc. 96] [ [ LOTRLOTR ] ]

MotivationMotivation• Fluid Animation: Fluid Animation: smokesmoke, clouds, fire, explosion, splashes, sea…, clouds, fire, explosion, splashes, sea…

• Simulation vs AnimationSimulation vs Animation

• Approaches to control:Approaches to control:– Phenomenological, limitedPhenomenological, limited– Fake forcesFake forces– Control by keyframing ‘shapes’Control by keyframing ‘shapes’

[ Areté Entertainment, inc. 96][ Areté Entertainment, inc. 96] [ [ LotRLotR ] ]

MotivationMotivation

Most related workMost related work• Density field given at keyframesDensity field given at keyframes• Solver between framesSolver between frames

What we wantWhat we want• No hand-drawn smokeNo hand-drawn smoke• Natural controlNatural control

[Treuille [Treuille et al.et al.03],[McNamara 03],[McNamara et al.et al.04],[Fattal 04],[Fattal et al.et al.04]04]

[McNamara [McNamara et al.et al.04]04]

key1 key2

Background Background [AN05][AN05]

EulerianEulerian

VorticityVorticityVelocityVelocity

LagrangianLagrangian

movingmovingquantityquantity

representationrepresentation

ourourmethodmethod

v ω

‘‘‘‘Chart of methods for numerical fluid simulation’’Chart of methods for numerical fluid simulation’’

popularpopular

BackgroundBackground

EulerianEulerian




ourourmethodmethod

v ωrepresentationrepresentation

velocity velocity vv

translation in translation in m sm s-1-1 Rotation in Rotation in rad srad s-1-1

vorticity vorticity ω

popularpopular

3D3Dfield field

vω CurlCurl


EulerianEulerian




ourourmethodmethod


velocity velocity vv vorticityvorticity ω

popularpopular

dx

xpxp

34)(

ωv

BIOT-SAVARTBIOT-SAVART


EulerianEulerian




ourourmethodmethod


velocity velocity vv vorticityvorticity ω

popularpopular


EulerianEulerian





ourourmethodmethod

v ω

EulerianEulerian


The flow modifies quantitiesThe flow modifies quantitiesheld at static positionsheld at static positions

The flow carries floaters thatThe flow carries floaters thathold the quantitieshold the quantities

Dynamics :Dynamics :

popularpopular


EulerianEulerian





ourourmethodmethod

v ω

dtd

t v

)(

LagrangianLagrangianEulerianEulerianv v v

at particleat particlein gridin grid

popularpopular


EulerianEulerian




popularpopular

ourourmethodmethod

v ω

ijkv

0

1)( 2

v

gvvvv p

t

NAVIER-STOKESNAVIER-STOKES

( incompressible )( incompressible )



EulerianEulerian




ourourmethodmethod

v ω


gvvvv

2 1)(

p

t

popularpopular


EulerianEulerian




ourourmethodmethod

v ω

VORTICITY EQUATIONVORTICITY EQUATION

vωω )( dtd


( inviscid )( inviscid )

popularpopular


EulerianEulerian




ourourmethodmethod


popularpopular

Easy boundary conditionsEasy boundary conditionsEasy extra differential eqnEasy extra differential eqn……

No diffusionNo diffusionImplicit incompressibilityImplicit incompressibility compactcompactUnboundedUnbounded……

ω


EulerianEulerian




ourourmethodmethod

v ω

VORTICITY EQUATIONVORTICITY EQUATION

vωω )( dtd


popularpopular

Vorticity:Vorticity:Vortex particle advected,Vortex particle advected, vector stretched vector stretchedω

vorticity moves as vorticity moves as material linesmaterial lines


EulerianEulerian




ourourmethodmethod


popularpopular

Vorticity:Vorticity:Our primitive = curvesOur primitive = curves = tangent= tangentω


EulerianEulerian




ourourmethodmethod


Density: Density: a quantity at nodesa quantity at nodes

Density:Density: Dedicated particlesDedicated particles - passive floaters- passive floaters - for rendering- for rendering - only where smoke is- only where smoke is

popularpopular

Lagrangian primitivesLagrangian primitives

• Curves carry the Curves carry the vorticityvorticity

• Each local Each local vortexvortex induces a weighted rotation induces a weighted rotation

dlxpxp

34

)(ωv

dx

xpxp

34)(

ωv

Method of simulationMethod of simulation• Vortex particlesVortex particles (for motion) (for motion)

organized as curves. = tangent organized as curves. = tangent • Smoke particlesSmoke particles (for visualisation) (for visualisation)

• Curves carry vorticesCurves carry vortices• Vortices induce a velocity fieldVortices induce a velocity field• velocity field deforms curves & smokevelocity field deforms curves & smoke

At every step:At every step: • Advect the curvesAdvect the curves• Stretch Stretch • Advect the smokeAdvect the smoke

ω

ω

Method of simulationMethod of simulation• Vortex particles (for motion)Vortex particles (for motion)

organized as curves. = tangent organized as curves. = tangent • Smoke particles (for visualisation)Smoke particles (for visualisation)

• Curves carry vorticesCurves carry vortices• Vortices induce a velocity fieldVortices induce a velocity field• velocity field deforms curves & smokevelocity field deforms curves & smoke

At every step:At every step: • Advect the curvesAdvect the curves• Stretch Stretch • Advect the smokeAdvect the smoke

ω

ω

• A A new representationnew representation of vortex curves of vortex curvesCompact, stable, controlable motion primitivesCompact, stable, controlable motion primitives

• Controls Controls of the motion primitivesof the motion primitives

• Fast ‘‘Fast ‘‘noisenoise’’ for fake turbulence details’’ for fake turbulence details

ContributionsContributions

Deformation of curves Deformation of curves previous approach previous approach [AN05][AN05]

If refined:If refined:too complextoo complex

PolygonPolygonIf not refined:If not refined:

undersamplingundersampling

Strategy to control complexityStrategy to control complexity

New representationNew representation• Solution: Solution: harmonic analysisharmonic analysis of coordinates of coordinates

xx= in = in yy

zz

• Reference frame: Reference frame: best ellipsoid best ellipsoid

a a pair of coefficientspair of coefficients for each harmonic for each harmonic

• Curves described by :Curves described by :– Frame Frame o eo exx e eyy e ezz

– FrequenciesFrequencies <c <cxx c cyy c czz>>1..N1..N

SynthesisSynthesisAdvectionAdvectionAnalysisAnalysis

Complexity controlComplexity control

……

New representationNew representation• Solution: Solution: harmonic analysisharmonic analysis of coordinates of coordinates

xx= in = in yy

zz

• Reference frame: Reference frame: best ellipsoid best ellipsoid

a a pair of coefficientspair of coefficients for each harmonic for each harmonic

• Curves described by :Curves described by :– Frame Frame o eo exx e eyy e ezz

– FrequenciesFrequencies <c <cxx c cyy c czz>>1..N1..N

SynthesisSynthesisAdvectionAdvectionAnalysisAnalysis

Complexity controlComplexity controleexx

eeyyeezz

oo

……

Meaning of descriptionMeaning of description

• eezz points towards moving direction points towards moving direction

eexx

eeyyeezz

oo

• FrFrequenciesequencies c cxx c cyy c czz give give texture texture to the flowto the flow

……

• ThicknessThickness

Video: representationVideo: representation

• directiondirection: : alignalign e ezz with tangent with tangent

• TargetsTargets::

• TwistingTwisting smoke: smoke: spin vortices around spin vortices around eezz

• Edit, delete …Edit, delete …

• Modulate Modulate ccxx c cyy c czz to to texturetexture the flowthe flow

ControlControl

without with

eexx

eeyyeezzoo ……

<cx cy cz>1..N

++

How to controlHow to control

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

eexx

eeyyeezz

oo

• Solution: Solution: paddlepaddle (servoing )(servoing ) ω

Video: controlVideo: control

[AN05]:[AN05]: noise = extra vortex particles noise = extra vortex particles advected in the flow, no stretchadvected in the flow, no stretch• Costly (needs a lot)Costly (needs a lot)• Source, samplingSource, sampling

Tiled vortex noise:Tiled vortex noise:noise layer =noise layer =• separate simulation, in toroidal spaceseparate simulation, in toroidal space• Tiled in spaceTiled in space• Additional evolving velocity fieldAdditional evolving velocity field

Noise: fake turbulence detailsNoise: fake turbulence details

Video: noiseVideo: noise




• Velocity cache, renderingVelocity cache, rendering


Octree cacheOctree cache

• Velocity computed at Velocity computed at every every smoke particlesmoke particle & & every every vorticity curve samplevorticity curve sample

• Velocity computed at Velocity computed at octree leavesoctree leaves + + inbetween interpolationinbetween interpolation

RenderingRendering• Thick smoke: plain particlesThick smoke: plain particles• Thin smoke: adaptive particlesThin smoke: adaptive particles [AN05][AN05]

– accumulate stretchingaccumulate stretching

01nTOT JJJJ ...

RenderingRendering• Thin smoke behaves like a surfaceThin smoke behaves like a surface

[ William Brennan ][ William Brennan ]

ee

nnll

eJJn 1T

Results - videoResults - video

fpsfps Forest fire Genie&lamp Walkthrough Fly Forest fire Genie&lamp Walkthrough Fly Modeler qualityModeler quality 55 12 12 5 18 5 18Final rendering qualityFinal rendering quality 0.540.54 0.2 1. 0.2 1. 0.37 0.37

Vorticity filaments:Vorticity filaments:• Compact, high-res, fastCompact, high-res, fast• Good handles to manipulate a fluidGood handles to manipulate a fluid• Can be manipulated Can be manipulated interactivelyinteractively or or postpost--

Future work:Future work:• Split/mergeSplit/merge• High-quality collisionsHigh-quality collisions• 2-phase, buoyancy, …2-phase, buoyancy, …

ConclusionConclusion

Coupling with gridsCoupling with grids

Thanks!Thanks!

Video: collisionsVideo: collisions

Video: thicknessVideo: thickness


eJJn 1T Diffuse offDiffuse off Diffuse onDiffuse on

ee

nnll

Lagrangian primitivesLagrangian primitives

• Curves carry the Curves carry the vorticityvorticity

• Each Each vortexvortex induces a weighted rotation induces a weighted rotation

Effect of one vortex on aEffect of one vortex on ashape :shape :

dlxpxp

34

)(ωv

dx

xpxp

34)(

ωv

Control currentsControl currents

• Without controlWithout control • With controlWith control

LL

eezz

LL

CheckpointCheckpoint• With controlWith control

vortex fluid structure for smoke control

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