Detail-Preserving Fluid Control
description
Transcript of Detail-Preserving Fluid Control
![Page 1: Detail-Preserving Fluid Control](https://reader035.fdocuments.us/reader035/viewer/2022062723/56813c0c550346895da57843/html5/thumbnails/1.jpg)
Detail-Preserving Fluid ControlDetail-Preserving Fluid Control
N. ThűreyR. KeiserM. Pauly
U. Rűde
SCA 2006
![Page 2: Detail-Preserving Fluid Control](https://reader035.fdocuments.us/reader035/viewer/2022062723/56813c0c550346895da57843/html5/thumbnails/2.jpg)
Abstract Abstract
◇ A new fluid control technique- Scale-dependent force control- Preserve small-scale fluid detail
◇ Control particles define local force fields- A physical simulation- A sequence of target shapes
◇ A multi-scale decomposition of the velocity field
◇ Small-scale detail is preserved
![Page 3: Detail-Preserving Fluid Control](https://reader035.fdocuments.us/reader035/viewer/2022062723/56813c0c550346895da57843/html5/thumbnails/3.jpg)
IntroductionIntroduction
◇ Realism of fluids is important
[CMT04]
◇ The fluid controlling for animation is also important
[SY05b]
◇ Fine-scale detail such as small eddies or drops
![Page 4: Detail-Preserving Fluid Control](https://reader035.fdocuments.us/reader035/viewer/2022062723/56813c0c550346895da57843/html5/thumbnails/4.jpg)
IntroductionIntroduction
◇ In previous method, control particles directly
influence the fluid velocity field- It can cause noticeable smoothing effects
◇ To avoid this artificial viscosity, - Decompose the velocity field into coarse- and fine
scale component- Only apply control forces to the low-frequency part- High-frequency components are largely unaffected - small-scale detail and turbulence are better
preserved
![Page 5: Detail-Preserving Fluid Control](https://reader035.fdocuments.us/reader035/viewer/2022062723/56813c0c550346895da57843/html5/thumbnails/5.jpg)
IntroductionIntroduction
◇ We achieve this decomposition by smoothing
the velocity field using a low-pass filter
◇ Velocity control forces are computed with respect to
the smoothed velocity field
◇ Scale-separated fluid control - Much better preserved - More dynamic and realistic looking simulations
![Page 6: Detail-Preserving Fluid Control](https://reader035.fdocuments.us/reader035/viewer/2022062723/56813c0c550346895da57843/html5/thumbnails/6.jpg)
Related WorkRelated Work
◇ Our control paradigm is based on the concept of control particle, similar to [FF01]
◇ Control particles are independent of the underlying fluid model
[FF01] A 3D Control Curve
![Page 7: Detail-Preserving Fluid Control](https://reader035.fdocuments.us/reader035/viewer/2022062723/56813c0c550346895da57843/html5/thumbnails/7.jpg)
Related WorkRelated Work
◇ [REN04] present a method for the directable animation of photorealistic liquids using the particle levelset
◇ [TMPS03] presented an optimization technique to solve for the control parameters
![Page 8: Detail-Preserving Fluid Control](https://reader035.fdocuments.us/reader035/viewer/2022062723/56813c0c550346895da57843/html5/thumbnails/8.jpg)
Related WorkRelated Work ◇ [FL04] proposed the idea of driving smoke toward
target smoke density
◇ [HK04] derive potential fields from the initial
distribution of smoke and target shape
![Page 9: Detail-Preserving Fluid Control](https://reader035.fdocuments.us/reader035/viewer/2022062723/56813c0c550346895da57843/html5/thumbnails/9.jpg)
Related WorkRelated Work
◇ smoke[SY05a] and liquids[SY05b] matched the level set surface of the fluid with static or moving target shape
![Page 10: Detail-Preserving Fluid Control](https://reader035.fdocuments.us/reader035/viewer/2022062723/56813c0c550346895da57843/html5/thumbnails/10.jpg)
Fluid Simulation Models
Fluid Simulation Models
◇ We use two fluid simulation models to demonstrateour control method
◇ Smoothed Particle Hydrodynamics (SPH)
◇ The Lattice-Boltzmann Method (LBM)
![Page 11: Detail-Preserving Fluid Control](https://reader035.fdocuments.us/reader035/viewer/2022062723/56813c0c550346895da57843/html5/thumbnails/11.jpg)
Smoothed Particle Hydrodynamics (SPH)
Smoothed Particle Hydrodynamics (SPH)
◇ As(r) : interpolation value at location r by a weighted sum of contributions from all particles
◇ j : iterates over all particles, mj : the mass of particle j
◇ rj : its postion, ρ j : density of particle j
◇ Aj : the field quantity at rj
◇ W(r,h) : smoothing kernel with radius h
![Page 12: Detail-Preserving Fluid Control](https://reader035.fdocuments.us/reader035/viewer/2022062723/56813c0c550346895da57843/html5/thumbnails/12.jpg)
Smoothed Particle Hydrodynamics (SPH)
Smoothed Particle Hydrodynamics (SPH)
◇ Numerically solving the Navier-Stokes equations
![Page 13: Detail-Preserving Fluid Control](https://reader035.fdocuments.us/reader035/viewer/2022062723/56813c0c550346895da57843/html5/thumbnails/13.jpg)
The Lattice-Boltzmann Method (LBM)The Lattice-Boltzmann Method (LBM)
◇ A grid based method
◇ Each grid cell stores a set of distribution functions
◇ The common three-dimensional LBM model D3Q19
![Page 14: Detail-Preserving Fluid Control](https://reader035.fdocuments.us/reader035/viewer/2022062723/56813c0c550346895da57843/html5/thumbnails/14.jpg)
The Lattice-Boltzmann Method (LBM)The Lattice-Boltzmann Method (LBM)
Streaming
◇ Streaming Collision Relaxation
![Page 15: Detail-Preserving Fluid Control](https://reader035.fdocuments.us/reader035/viewer/2022062723/56813c0c550346895da57843/html5/thumbnails/15.jpg)
The Lattice-Boltzmann Method (LBM)The Lattice-Boltzmann Method (LBM)
ei : nineteen grid velocitys(0~18) wi : w0=1/3, w1..6=1/18,w7..18=1/36 : physical fluid viscosity
![Page 16: Detail-Preserving Fluid Control](https://reader035.fdocuments.us/reader035/viewer/2022062723/56813c0c550346895da57843/html5/thumbnails/16.jpg)
Fluid Control Fluid Control
◇ Generating Control Particles
◇ Controlling fluid using attraction force and velocity
force
◇ Detail-Preserving Control
![Page 17: Detail-Preserving Fluid Control](https://reader035.fdocuments.us/reader035/viewer/2022062723/56813c0c550346895da57843/html5/thumbnails/17.jpg)
Generating Control Particles Generating Control Particles
◇ Motion given by precomputed function [FM97, FF01]
◇ Shape given by a Mesh [JSW05]
◇ Motion from another fluid simulation- using SPH, LBM- very coarse simulation- The simulation may even run in realtime to animator
![Page 18: Detail-Preserving Fluid Control](https://reader035.fdocuments.us/reader035/viewer/2022062723/56813c0c550346895da57843/html5/thumbnails/18.jpg)
Control Forces Control Forces
◇ Attraction force : Force that pulls fluid towards
the control particles
◇ Velocity Force : modifying the velocity of the fluid according to the flow determined by the control particles
◇ Control Particle Variables- pi : position of control particle- vi : velocity of control particle- hi : influence radius (2.5times the average
distance)
![Page 19: Detail-Preserving Fluid Control](https://reader035.fdocuments.us/reader035/viewer/2022062723/56813c0c550346895da57843/html5/thumbnails/19.jpg)
Attraction Force Attraction Force
◇ This force is scaled down when the influence region
of the control particle is already covered with fluid
◇ Scale factor for attraction force
![Page 20: Detail-Preserving Fluid Control](https://reader035.fdocuments.us/reader035/viewer/2022062723/56813c0c550346895da57843/html5/thumbnails/20.jpg)
Attraction Force Attraction Force
◇ Attraction force on a fluid element e
◇ : global contant that defines the strength of theattraction force
◇ if is negative, it will result in a repulsive force
![Page 21: Detail-Preserving Fluid Control](https://reader035.fdocuments.us/reader035/viewer/2022062723/56813c0c550346895da57843/html5/thumbnails/21.jpg)
Velocity Force Velocity Force
◇ Velocity Force on a fluid element e
◇ v(e) : the velocity of the fluid element e
◇ : a constant that defines the influence of thevelocity force
![Page 22: Detail-Preserving Fluid Control](https://reader035.fdocuments.us/reader035/viewer/2022062723/56813c0c550346895da57843/html5/thumbnails/22.jpg)
Total Force Total Force
◇ Total control force fc(e) = fa(e) + fv(e)
◇ The new total force per volume f(e) = fc(e) + ff(e)
◇ ff(e) : the fluid force from the physical fluid simulation
![Page 23: Detail-Preserving Fluid Control](https://reader035.fdocuments.us/reader035/viewer/2022062723/56813c0c550346895da57843/html5/thumbnails/23.jpg)
Detail-Preserving Control
Detail-Preserving Control
◇ The velocity force lead to an averaging of the fluid velocities
◇ Undesirable artificial viscosity
◇ We want the natural small-scale fluid motion
![Page 24: Detail-Preserving Fluid Control](https://reader035.fdocuments.us/reader035/viewer/2022062723/56813c0c550346895da57843/html5/thumbnails/24.jpg)
Detail-Preserving Control Detail-Preserving Control
![Page 25: Detail-Preserving Fluid Control](https://reader035.fdocuments.us/reader035/viewer/2022062723/56813c0c550346895da57843/html5/thumbnails/25.jpg)
Detail-Preserving Control
Detail-Preserving Control
![Page 26: Detail-Preserving Fluid Control](https://reader035.fdocuments.us/reader035/viewer/2022062723/56813c0c550346895da57843/html5/thumbnails/26.jpg)
Detail-Preserving Control
Detail-Preserving Control
◇ Smoothed velocity field
◇ This smoothed version of the fluid velocity replacesV(e) in Equation 7
![Page 27: Detail-Preserving Fluid Control](https://reader035.fdocuments.us/reader035/viewer/2022062723/56813c0c550346895da57843/html5/thumbnails/27.jpg)
Detail-Preserving Control
Detail-Preserving Control
◇ is low pass filtered velocity ◇ is high pass filtered velocity ◇ vp is the interpolated velocity of the control particles at
a fluid element e
![Page 28: Detail-Preserving Fluid Control](https://reader035.fdocuments.us/reader035/viewer/2022062723/56813c0c550346895da57843/html5/thumbnails/28.jpg)
Results and DiscussionResults and Discussion
◇ We have implemented our control algorithm for both an SPH and an LBM fluid solver
◇ Within the SPH solver, the existing acceleration structures can be used to query fluid particles in the neighborhood of a control particle
◇ For the LBM solver, control particles are rasterized to the grid
![Page 29: Detail-Preserving Fluid Control](https://reader035.fdocuments.us/reader035/viewer/2022062723/56813c0c550346895da57843/html5/thumbnails/29.jpg)
Results and DiscussionResults and Discussion
◇ The simulation using LBM with a grid resolution took 142s per frame, including 4s for computing the control force
◇ These control particles are blended with 5k control particles sampled from the 3D model of the human figure
3300
![Page 30: Detail-Preserving Fluid Control](https://reader035.fdocuments.us/reader035/viewer/2022062723/56813c0c550346895da57843/html5/thumbnails/30.jpg)
Results and DiscussionResults and Discussion
◇ The control flow with detail-preservation retains small-scale fluid features
◇ The simulation was done using LBM with a 240*120*120 grid resolution which took 38s per frame on average
◇ The computation of the control forces took 2-4% of the total computation time
![Page 31: Detail-Preserving Fluid Control](https://reader035.fdocuments.us/reader035/viewer/2022062723/56813c0c550346895da57843/html5/thumbnails/31.jpg)
Results and DiscussionResults and Discussion
◇ The mesh is only used to generate a sequence of control particles as described in Section 3.1
◇ We used 266k particles for the SPH simulation which took 102s per frame including the computation of the control forces which took 14s
![Page 32: Detail-Preserving Fluid Control](https://reader035.fdocuments.us/reader035/viewer/2022062723/56813c0c550346895da57843/html5/thumbnails/32.jpg)
Results and DiscussionResults and Discussion
◇ Our detail-preserving approach clearly reduces the artificial viscosity by the control forces
◇ The user can interactively adjust the parameters until the desired coarse-scale behavior of the fluid is obtained
◇ Our framework could also be used to control the deformation of elastic bodies
![Page 33: Detail-Preserving Fluid Control](https://reader035.fdocuments.us/reader035/viewer/2022062723/56813c0c550346895da57843/html5/thumbnails/33.jpg)
ConclusionsConclusions
◇ A detail-preserving approach for controlling fluids based on control particles
◇ We solve the problem of artificial viscosity introduced by the control forces by applying these forces on the low-pass filtered velocity field
◇ Only the coarse scale flow of the fluid is modified while the natural small-scale detail is preserved, resulting in more natural looking controlled simulations
![Page 34: Detail-Preserving Fluid Control](https://reader035.fdocuments.us/reader035/viewer/2022062723/56813c0c550346895da57843/html5/thumbnails/34.jpg)
ReferencesReferences