DetailPreserving Fluid Control N Threy R Keiser M

Detail-Preserving Fluid Control N. Thűrey R. Keiser M. Pauly U. Rűde SCA 2006

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

Introduction ◇ Realism of fluids is important [CMT 04] ◇ The fluid controlling for animation is also important [SY 05 b] ◇ Fine-scale detail such as small eddies or drops

Introduction ◇ 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

Introduction ◇ 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

Related Work ◇ Our control paradigm is based on the concept of control particle, similar to [FF 01] ◇ Control particles are independent of the underlying fluid model [FF 01] A 3 D Control Curve

Related Work ◇ [REN 04] present a method for the directable animation of photorealistic liquids using the particle levelset ◇ [TMPS 03] presented an optimization technique to solve for the control parameters

Related Work ◇ [FL 04] proposed the idea of driving smoke toward target smoke density ◇ [HK 04] derive potential fields from the initial distribution of smoke and target shape

Related Work ◇ smoke[SY 05 a] and liquids[SY 05 b] matched the level set surface of the fluid with static or moving target shape

Fluid Simulation Models ◇ We use two fluid simulation models to demonstrate our control method ◇ Smoothed Particle Hydrodynamics (SPH) ◇ The Lattice-Boltzmann Method (LBM)

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, ρj : density of particle j ◇ Aj : the field quantity at rj ◇ W(r, h) : smoothing kernel with radius h

Smoothed Particle Hydrodynamics (SPH) ◇ Numerically solving the Navier-Stokes equations

The Lattice-Boltzmann Method (LBM) ◇ A grid based method ◇ Each grid cell stores a set of distribution functions ◇ The common three-dimensional LBM model D 3 Q 19

The Lattice-Boltzmann Method (LBM) Streaming ◇ Streaming Collision Relaxation

The Lattice-Boltzmann Method (LBM) ei : nineteen grid velocitys(0~18) wi : w 0=1/3, w 1. . 6=1/18, w 7. . 18=1/36 : physical fluid viscosity

Fluid Control ◇ Generating Control Particles ◇ Controlling fluid using attraction force and velocity force ◇ Detail-Preserving Control

Generating Control Particles ◇ Motion given by precomputed function [FM 97, FF 01] ◇ Shape given by a Mesh [JSW 05] ◇ Motion from another fluid simulation - using SPH, LBM - very coarse simulation - The simulation may even run in realtime to animator

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. 5 times the average distance)

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

Attraction Force ◇ Attraction force on a fluid element e ◇ : global contant that defines the strength of the attraction force ◇ if is negative, it will result in a repulsive 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 the velocity 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

Detail-Preserving Control ◇ The velocity force lead to an averaging of the fluid velocities ◇ Undesirable artificial viscosity ◇ We want the natural smallscale fluid motion

Detail-Preserving Control

Detail-Preserving Control

Detail-Preserving Control ◇ Smoothed velocity field ◇ This smoothed version of the fluid velocity replaces V(e) in Equation 7

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

Results 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

Results and Discussion ◇ The simulation using LBM with a grid resolution took 142 s per frame, including 4 s for computing the control force ◇ These control particles are blended with 5 k control particles sampled from the 3 D model of the human figure

Results and Discussion ◇ The control flow with detailpreservation retains small-scale fluid features ◇ The simulation was done using LBM with a 240*120 grid resolution which took 38 s per frame on average ◇ The computation of the control forces took 2 -4% of the total computation time

Results and Discussion ◇ The mesh is only used to generate a sequence of control particles as described in Section 3. 1 ◇ We used 266 k particles for the SPH simulation which took 102 s per frame including the computation of the control forces which took 14 s

Results 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

Conclusions ◇ 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 lowpass 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

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