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Transcript of Qyu Defense
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a Ph.D. Defense by
Qizhi YuUnder the Advisements ofDr. Fabrice NeyretDr. Eric Bruneton
November 17, 2008
Grenoble Institute of Technology (INPG)
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Introduction
Previous work
Strategy overview
Contributions
Conclusion
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RiversHydrology
Hydraulics Geomorphology
Ecology
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RiversHydraulics
Hydrology
Computergraphics
Geomorphology
Ecology
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ObjectiveSynthesize visually convincing rivers
Study contentModeling River shape & surface details
Animating Water motion in rivers.
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Many applications, need more studies
EA: CrysisGoogle Earth
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Multi-scaleGeometry
Kilometer-scale lengthmillimeter-scale waves
Water motion Kilometer-scale mean flow
millimeter-scale fluctuation
Complicated physicsTurbulence Surface phenomena
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Modeling and animating rivers
ConstraintsReal-timeScalabilityControllability
Realism
25 fps or more
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Modeling and animating rivers
ConstraintsReal-timeScalabilityControllability
Realism
Very long or unbounded riversCamera moves arbitrarily
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Modeling and animating rivers
ConstraintsReal-timeScalabilityControllability
Realism Intuitive handles for controllingappearance and behavior of rivers
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Modeling and animating rivers
ConstraintsReal-timeScalabilityControllability
RealismAnimated surface detailswith temporal and spatial continuity
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Modeling and animating rivers
ConstraintsReal-timeScalabilityControllability
Realism
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Introduction
Previous work
Strategy overview
Contributions
Conclusion
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3D Navier-Stokes simulation
2D depth-averaged simulation
2D simulation
Surface wave models (2D)
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3D Navier-Stokes simulation
2D depth-averaged simulation
2D simulation
Surface wave models (2D)
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Incompressible Navier-Stokes equationsMomentum conservation
Volume conservation
Boundary conditions
Computational Fluid Dynamics (CFD)Numerical methods
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CFD CG fluid animationStable solver [stam99]
Two approachesEulerian : defines quantities at fixed pointLagrangian: defines quantities at particles
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Water animation [EMF02]Solve NSE numerically on a grid to get velocities
Use level-set to track water-air interface
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Pouring water in a glass
[EMF02]15 minutes per frame
55 x 120 x55 grids
Computationally expensive!
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Poorly scalableCG (stable solver): O(N^3)
Difficult to control for artistsWater Behavior Initial values, boundary conditionsNo intuitive relation
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Smoothed Particle Hydrodynamics (SPH) [MCG03]Solve NSE in the Lagrangian formalism
Compared with Eulerian approachEasier adaptive to complex domainDifficult to reconstructa smooth surface
For our purposeSimilar problemsas Eulerian approach
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2200 particles5 fps
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3D Navier-Stokes simulation
2D depth-averaged simulation
2D simulation
Surface wave models (2D)
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2D Shallow Water model [Mol95]Commonly used in Hydraulics for simulating riversAssumptions Hydrostatic approximation
No vertical water motionIntegrate the NS equations along vertical directionUnknowns:
depth-averaged velocity & elevation of water surface
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PropertiesA lot faster than 3D N-S simulation
Loss some 3D surface features (e.g. overturning )Shallow waves ( wavelength >> depth)
For our purposeStill too expensive, especially for large riversBounded domain (like other simulation).
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Linear wave equation [KM90]Simplified from shallow water model
Assumptions constant water depth, no advection term
Properties Fast, cant simulate river flow
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[Irving et al. 06]
20 processors25 minutes per frame
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3D Navier-Stokes simulation
2D depth-averaged simulation
2D simulation
Surface wave models (2D)
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Simulate 2D velocity by solving 2D N-Sno surface elevation simulated
Use tricks for surface elevationPressure [CdVL95]Noise [TG01]
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3D Navier-Stokes simulation
2D depth-averaged simulation
2D simulation
Surface wave models (2D)
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AssumptionDeep water: wave length
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AssumptionHeight field
A procedural methodParticles on surfaces, advected with a fixed speedEach carries a wave shape functionSuperpose all particles height field
PropertiesImitate object-water interactionNo water flow
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Superpose sine waves [FR86, Pea86]Dynamic wave tracing [GS00]Ship wave [Gla02]
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[Gla02] [GS00] [Pea86]
Not for river flow
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Many work on water or wave animation (CG),river simulation (Hydraulics)
None for river animation under ourconstrains:
Real-time
ScalabilityControllability
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Introduction
Previous work
Strategy overview
Contributions
Conclusion
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Model river aspects in three scales, fromcoarse to fine
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Model river aspects in three scalesMacro-scale: river shape & mean water surface
Meso-scale: individual & structured waves
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Model river aspects in three scalesMacro-scale: river shape & mean water surface
Meso-scale: individual & structured wavesMicro-scale: continuous field of small waves
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We need river velocityCause of many meso-scale phenomena
Advect surface featuresModel water motion in three scales
Macro-scale: mean flow
Meso-scale: individual perturbationsMicro-scale: continuous irregular fluctuations
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We need river velocityCause of many meso-scale phenomena
Advect surface featuresModel water motion in three scales
Macro-scale: mean flow
Meso-scale: individual perturbationsMicro-scale: continuous irregular fluctuations
We wont solve ALL phenomena in this thesis . 41
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Introduction
Previous work
Strategy overview
Contributions1: Macro-scale2: Meso-scale3: Micro-scale
Conclusion42
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Introduction
Previous work
Strategy overview
Contributions1: Macro-scale
2: Meso-scale3: Micro-scale
Conclusion43
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GoalShape of rivers
Mean flow of rivers
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GoalShape of rivers
Mean flow of rivers
GIS or previous work[KMM88]
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Inputriver shape (described as a network)
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Assumption a 2D steady flow
Visually convincing velocityDivergence free IncompressibleBoundary-conformingFlowing from source to sink (given flow rate Q)
Continuous
Requirements of algorithmsFast, scalable and controllable
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Some existing work [BHN07] suggestusing stream function to get divergence-freevector field
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Stream function is defined such that
Incompressibility
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Properties of stream functionConst along boundariesRelates to the volume flow rate
Extend to a river networkGiven flow rates and a river network all boundary values
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Given flow rates, and boundary valuesHow to determine the internal field ?
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AssumptionIrrotational (potential) flow
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Observe a numerical solution of a Laplaceequation
Streamlines (isocurve of stream function) 53
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[GW78]Interpolant of the Inverse-Distance Weightedinterpolation (IDW) [She68] similar to theharmonic functions.
We adapt IDW
local for the performance reasonsprovide parameters for controlling velocity profile
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d distance to boundariesf smooth functions search radius
p parameters
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Our result Numerical solution
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Finite difference
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Interpolation relies heavily on distance queryAcceleration needed
Combine with tile-based terrain [BN07]Generate an acceleration data structure in eachnewly created terrain on-the-fly
Please see the thesis for more details .
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Procedural river flowFast
Scalable Calculate at needed Velocity locally dependent
Controllable Control velocity: flow rates, interpolation parameters Edit shape of river on-the-fly
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Introduction
Previous work
Strategy overviewContributions
1: Macro-scale
2: Meso-scale3: Micro-scale
Conclusion61
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GoalModeling individual & structured wave features onriver surfaces, with our constraints. Real-time Scalability Controllability
Quality
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High-resolution required for simulation andrendering
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Construct the vector features from a givenvelocity field without numerical simulation
Shockwave
Ripples
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ProblemsNeed to be improved robustness & efficiency
No solution for surface reconstruction and rendering
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Improve on existing model [NP01]Result Mean flow shockwave curves (wave crests) Animated by adding perturbation to the mean flow
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Improve on existing model [NP01]Result Mean flow shockwave curves (wave crests) Animated by adding perturbation to the mean flow
Macro-scale
Meso-scale, [WH91]
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Improve on existing model [NP01]Result Mean flow shockwave curves (wave crests) Animated by adding perturbation to the mean flow Very efficient
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Improve on existing model [NP01]
Construct appropriate representation from
wave features for high-quality rendering
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lo-res base water surface + hi-res wave surface
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lo-res base water surface + hi-res wave surface
Macro-scale
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lo-res base water surface + hi-res wave surface
Meso-scale
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Feature-aligned mesh reducesgeometric aliasing ( normal-noise)
Not feature-aligned Feature-aligned74
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Define wave surface as sweeping a waveprofile along the wave curve
User defined Wave profile
Wave curve
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Water surfacemesh
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Sample by a quad meshaligned the wave curve
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Wave curve
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Accurate normals from the wave profile
u
v
B
NT
P(u,v)
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Mesh stitching ?Re-mesh base surface at each frame, tooexpensive
We solve it in the rendering stage
Please refer to the thesis for more details
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Simply draw two wave strips with Z-buffer
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Generate a dedicated mesh at crossing
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Final result
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Approach: feature-based vector simulationSimulation: construct & animate vector featuresRendering: featured-based representation
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Introduction
Previous work
Strategy overviewContributions
1: Macro-scale
2: Meso-scale3: Micro-scale
Conclusion
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Goal Modeling small scale animated surface features
Approachdynamic textures
Two workWave sprites Focus on performanceLagrangian texture advection Focus on quality
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IntroductionPrevious workStrategy overviewContributions
1. Macro-scale2. Meso-scale
3. Micro-scale Wave sprites Lagrangian texture advection
Conclusion87
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Sprite: a small textured element Sprites in texture world [LN03,LHN05]
to get large high-resolution texture , low memory Idea: combine animation + texture sprites
to get very large river with animated details,efficiently.
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How should sprites behave for our purposes ?Sprites -> represent waves reconstructed texture should conserve the spectrum
Well distributed, avoiding holes and overcrowding The more overlapping, the more texture spectrum biasing
The density of sprites should be adaptive
Convey the flow motion
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Dynamic adaptive samplingA set of particles in world space advected by flowKeep Poisson-disk distribution in screen space.
Attach a textured sprite to each particle
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Dynamic adaptive samplingA set of particles in world space advected by flowKeep Poisson-disk distribution in screen space.
Attach a textured sprite to each particleWhy ?
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Uniform densityOverlapping as little as possible
Easy to ensure spatial continuitySuperimposing sprites (with r=d) ensures no-holes
r r = ddiameter of poisson-disk
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Dynamic adaptive samplingA set of particles in world space advected by flowKeep Poisson-disk distribution in screen space
Attach a sprite to each particle
Auto-adapt to distance
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AlgorithmAdvect particles with the flow in world spaceDelete particles out of the view frustumDelete particles violating the minimum distancerequired by the Poisson-disk distribution (inscreen space)
Insert particles to keep Poisson-disk distribution
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AlgorithmAdvect paticles with the flowDelete particles out of the view frustumDelete particles violating the minimum distancerequired by the Poisson-disk distribution (inscreen space)Insert particles to keep Poisson-disk distribution
Boundary-sampling algorithm [DH06]
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Spatial continuitySmooth kernelConstrained sampling issues near boundary
Temporal continuityFading in/out
Please refer the thesis.
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A set of sprites well distributedEach sprite Live in texture space maps to a portion of a reference texture
Reconstruct the global textureSprite has circular kernel in screen space , butellipse in object space So we superimpose them in screen space
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Efficient GPU. Inspired from [LN05]
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Wave-spritesTexture flow surface with scene-independentperformance (in real-time)
Limitation
No sprite deformation consideredSliding of texture between sprites bad especially in place where velocity gradient is high
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IntroductionPrevious workStrategy overviewContributions
1. Macro-scale2. Meso-scale
3. Micro-scale Wave sprites Lagrangian texture advection
Conclusion102
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A technique of dynamic textureConform to the input flowConserve texture properties (e.g. spectrum)
PurposeAugment coarse simulation with small scale
appearance
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Advect texture coordinatesTexture follow flow and deformBut, over stretching destroy texture properties
Regenerate a textureAfter a delay: latency
Blend two de-phased textures Illusion of advection
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How to choose a reasonable latency ? high bad conservation of spectrum low bad conformation to flowGood one: adapt to local flow condition
(deformation)
In [MB95], only one global value
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Idea: adaptive local latency
Local deformation metrics
MIPmap -like approach:Multiple layers of texturesEach layer = Eulerian advection methodAssign different latency to each layer For each pixel, interpolate two nearest layersaccording to local s
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latency of all layers are bounded in arange
e.g. For zero-velocity , the ideal latency should beinfinity close to still area, we cant choose agood latency value
Interpolation : not accurate
Eulerian formalismnot optimal in large sparse domain (clouds, fire)
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Advected by flow
Dynamic Poisson-disk
distributiond
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Init: regular grid
Kernel radius = d
Patch size > 2d
Map to a random portionStore (u, v) at nodes
U
V
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Nodes advected by flow
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Nodes advected by flow
Delete a patchExceed some deformationmetric
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Nodes advected by flow
Delete a patchExceed some deformationmetric
Patch boundary intersectswith kernel
A new patch would be generated nearby automatically
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Temporal & spatialInsert / delete temporalSmooth kernel spatial
Define various temporal and spatial weights on grid nodes
Please see details in the thesis
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Encode all patches into one texture T patchTexcoords (u, v)Weights w(x, t)
Accessing the advected textureFor each pixel
Determine the patches covering current pixel Access reference texture via T patch Blending with weights (only kernel parts!)
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Compare against Eulerian advectionFFT To evaluate the appearant spectrum
Optical flow To evaluate the appearant motion
Input reference texture 3-octave Perlin noise
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Various input flow
Please see my webpage for more video results
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Rotation Shear Free Boundary
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We target textures specified by globalproperties, e.g. spectrum
Useful for natural flow
For non-noise texturesMany of them work wellHigh-structured ones Suffer from ghosting effects Future work: choose best match portion from reference
texture
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A new texture advection methodLagrangian formalism Brings decorrelation of texture mapping and
regeneration eventsLocal patches Ensure continuous texture animation Provide accurate distortion metric
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Introduction
Previous work
Strategy overview
Contributions
Conclusion
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By using our modelsOne can achieve real-time , scalable , andcontrollable river animation with temporally andspatially continuous details on current desktop
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Macro-scaleVelocity: more studies on parametersInfluence of slope of river bed
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Meso-scaleHydraulic jumps, ship waves and wakes ...
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Micro-scale I: wave spritesVarious reference textures: domain wise controlSprites density: adaptive to flow condition
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Micro-scale II: Lagrangian texture advectionExtend to 3D volumeImprove: for high-structured texture
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Put models together
Integrate with existing systems
Google Earth, Proland [BN08], video games
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a Ph.D. Defense by
Qizhi Yu
Under the Advisements of
Dr. Fabrice Neyret
Dr. Eric Bruneton
November 17, 2008