1. Detail-Preserving Fluid Control N. Th ű rey R. Keiser M. Pauly U. R ű de SCA 2006

2. 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

3. Introduction ◇ Realism of fluids is important [CMT04] ◇ The fluid controlling for animation is also important [SY05b] ◇ Fine-scale detail such as small eddies or drops

4. 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

5. 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

6. Related 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

7. Related 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

8. Related 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

9. Related Work ◇ smoke[SY05a] and liquids[SY05b] matched the level set surface of the fluid with static or moving target shape

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

11. 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, m j : the mass of particle j ◇ r j : its postion, ρ j : density of particle j ◇ A j : the field quantity at r j ◇ W(r,h) : smoothing kernel with radius h

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

13. 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

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

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

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

17. 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

18. 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 - p i : position of control particle - v i : velocity of control particle - h i : influence radius (2.5times the average distance)

19. 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

20. 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

21. 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

22. Total Force ◇ Total control force f c (e) = f a (e) + f v (e) ◇ The new total force per volume f(e) = f c (e) + f f (e) ◇ f f (e) : the fluid force from the physical fluid simulation

23. 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

24. Detail-Preserving Control

26. ◇ Smoothed velocity field ◇ This smoothed version of the fluid velocity replaces V(e) in Equation 7

27. Detail-Preserving Control ◇ is low pass filtered velocity ◇ is high pass filtered velocity ◇ v p is the interpolated velocity of the control particles at a fluid element e

28. 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

29. Results 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

30. Results 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

31. Results 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

32. 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

33. 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 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

34. References