Modeling Highly-Deformable Liquid

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Modeling Highly-Deformable Liquid
Advisors Cheng-Chung Lin and Jung-Hong Chuang

• Chih-Wei Chiu
• Computer Graphics and Geometry Modeling
  Laboratory
• National Chiao Tung University
• June 25, 2002

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Agenda

• Introduction
• Previous Work
• Method
• Result
• Conclusion

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Modeling Fluids

• Particles
• A particle represent a fixed-mass fluid element
• There may be interaction forces between particles

• Volume
• Partition the scene into many cells
• Every cell carries a density function
  representing the proportion of air and liquid
• Surface can be inferred from density functions

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Computational Aspect

• Particles
• Number grows with cube of resolution
• Computationally expensive

• Volume
• Only one equation for each cell to evolve the
  density function (more on this later)
• Computationally economical

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Geometry Aspect
smooth

• Particles
• No straightforward way to extract a smooth
  surface
• Resolve details independent of grid resolution

• Volume
• Iso-surface can be extracted from the volume data
• Potentially under-resolve details if the grid is
  too coarse

not smooth
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Proposed Method

• Since volume method and particles have nearly
  complemented strength and weakness
• Combination of particles and volume method
• Track initial fluid by volume
• Resolve highly-deformed regions by particles

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Previous Work

• Wave Simulation
• Surface is a parametric function can be animation
  over time
• Fourier synthesis Mastin 87
• Wave-tracing Tso 87
• Particle Systems
• Very heuristic, Cheap computation
• Ship wakes Goss 90
• Thin-film water splash Ashraf 99
• Splash subsystem particles are generated when
  the water surface is under impact OBrien 95
  Mould 97

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Previous Work

• Molecular Dynamics
• Simulate elastic and inelastic objects and
  viscous fluids
• Computational expensive for large volume of fluid
• Lack of coupling between velocity and pressure
• SPH (Smoothed Particle Hydrodynamics)
• Deformable object Desbrun96
• Lava Stora 99
• Advantages
• More economical than molecular dynamics
• Couple pressure and velocity

Thats why we choose it!
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Previous Work

• 3-D Navier-Stokes Equations
• Produce the most realistic motion but are very
  computationally expensive
• Initiated by Foster 96
• Used MAC formulation dated by 1965
• Semi-Lagrangian integration allows large time
  step without harming the accuracy Stan99
• Implicit Surface
• Represent fluid volume by a density function
  Kunimatsu 01
• Hybrid model Foster 01
• Dynamic implicit surface
• Allow particles to locally correct surface value

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Outline
Our Methods !!!
Partition the scene by a grid (only in the first
time-step)
Performed per time-step
Performed during rendering
pn vn
grid
Fluid dynamics solver
Subdivision
vn1
high resolution grid
Fn
Interpolation
Evolve density functions
high resolution Fn1
Fn1
Convert particle volumes to F
Generate particles in the drastic motion region
particles positions
high resolution Fn1 with particle volumes
existing particles
new particles
Extract iso-surface
polygon mesh
Move particles by SPH
Rendered using a ray-tracer
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Modeling Splash

• Problem
• Grid may be too coarse to resolve the detail
  features in a surface cell
• Put particles in all surface cell is too
  computational expensive
• Solution
• Introduce particles in the cell with drastic
  motion

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Drastic Motion Criterion

• Seed particles in the surface cell with drastic
  motion

Fluid traveling distance in a time step
Fluid particle should not travel more than one
cell size in a time step 0lt?lt1

• Lower ? tends to produce more particles

• Limit the maximum number of particles in a cell
• Existing particles provides more accurate
  approximation

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Volume Fractions
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Particle Seeding

• Particles are randomly positioned inside the
  interface (fluid side)

v
Reconstructed interface
u

• Particles velocities are linearly interpolated in
  the cell

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Interface Reconstruction

• Approximate the interface by a plane axbyczd0

(a,b,c)
Cut volume
Vf

• Normal is easy to compute, e.g. by spatial
  gradients

• Find d so that the cut volume given by the
  interface is Vf Scardovelii 00

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Next Slide
Partition the scene by a grid (only in the first
time-step)
Performed during rendering
grid
My own method !!!
Subdivision
high resolution grid
Interpolation
Evolve density functions
high resolution Fn1
Fn1
Convert particle volumes to F
particles positions
high resolution Fn1 with particle volumes
Extract iso-surface
polygon mesh
Move particles by SPH
Rendered using a ray-tracer
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Subdivision Volume Fractions
Small particles are directly rendered as blobs
Convert particles volumes to F
Subdivision interpolation
iso-surface extraction
Smooth surface
Coarse grid
Fine grid
Without converting particles to F
iso-surface extraction
Non-smooth surface
iso-surface extraction
Without subdivision interpolation
Non-smooth surface
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Why Blobs Doesnt Work?
Non-smooth surface
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3x3x3 subdivision
Convert particles to volume fractions
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Result

• Computational grid - 28x24x28
• Simulation time per frame 8 60 sec
• Cycles per frame - 5
• Average number of particles - 500
• Rendering time per frame 1.5 4 min
• Subdivision 3x3x3

• AMD Athlon 1000 MHZ
• 512 MB DRAM

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Control the Number of Particles
?0.2
?0.1
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Comparison 1
O'Brien,J.F. Hodgins,J.K., "Dynamic Simulation
of Splashing Fluids", in Proceedings of Computer
Animation '95, pp.198-205, 1995.
Generate particles when the vertical velocities
of a column exceed a predefined threshold
Mould,D. Yang,Y.H., "Modeling Water for Computer
Graphics", Computers Graphics, vol.21, no.6,
pp.801-814, 1997.
Extend OBrien et al. Allow droplets to split.
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Comparison 2
Foster,N. Fedkiw,R., "Practical Animation of
Liquids", Computer Graphics, pp.23-30, 2001.

• Hybrid model
• Dynamic level set implicit surface.
• Marker particles locally correct surface.

Enright,D. Marschner,S. Fedkiw,R., "Animation
and Rendering of Complex Water Surfaces", in
Procceeding os SIGGRAPH 2002, 2002 (to appear).
Extend Foster 01 Put particles on both sides of
the surface.
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Comparison 3

• Heuristic Approach

Identify drastic motion region and generate
particles.
Autonomous particles moves independently of the
fluid.

• Marker Particles

Place particles near the surface to capture
drastic motion.
Passive particles velocities are interpolated
from the grid node velocities.
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Conclusion

• A hybrid approach integrating particles
  (Lagrangian method) and volume fractions
  (Eulerian method)
• A scheme to identify drastic motion area and seed
  particles
• Smooth surface by converting particles to volume
  fractions