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Vortex Fluid Structure For Smoke Control

Vortex Fluid Structure For Smoke Control

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Vortex Fluid Structure For Smoke Control

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  1. SCA 2006 Vortex Fluid StructureFor Smoke Control Alexis Angelidis (1) Fabrice Neyret (2) Karan Singh (1) Derek Nowrouzezahrai (1) (1): DGP, U of Toronto (2): Evasion-GRAVIR / IMAG-INRIA

  2. Motivation • Fluid Animation: smoke, clouds, fire, explosion, splashes, sea… • Simulation vs Animation [ Areté Entertainment, inc. 96] [ LOTR ]

  3. Motivation • Fluid Animation: smoke, clouds, fire, explosion, splashes, sea… • Simulation vs Animation • Approaches to control: • Phenomenological, limited • Fake forces • Control by keyframing ‘shapes’ [ Areté Entertainment, inc. 96] [ LotR ]

  4. Motivation [Treuille et al.03],[McNamara et al.04],[Fattal et al.04] Most related work • Density field given at keyframes • Solver between frames What we want • No hand-drawn smoke • Natural control key2 key1 [McNamara et al.04]

  5. Background [AN05] Velocity Vorticity moving quantity representation popular Eulerian our method Lagrangian ‘‘Chart of methods for numerical fluid simulation’’

  6. vorticity Background Velocity Vorticity moving quantity representation popular Eulerian our method Lagrangian 3D field velocity v Rotation in rad s-1 translation in m s-1

  7. vorticity Background Velocity Vorticity moving quantity representation popular Eulerian our method Lagrangian velocity v Curl

  8. vorticity Background Velocity Vorticity moving quantity representation popular Eulerian our method Lagrangian velocity v BIOT-SAVART

  9. Background Velocity Vorticity moving quantity representation popular Eulerian our method Lagrangian Dynamics : Eulerian The flow modifies quantities held at static positions Lagrangian The flow carries floaters that hold the quantities

  10. Background Velocity Vorticity moving quantity representation popular Eulerian our method Lagrangian Eulerian Lagrangian in grid at particle

  11. Background Velocity Vorticity moving quantity representation popular Eulerian our method Lagrangian NAVIER-STOKES ( incompressible )

  12. Background Velocity Vorticity moving quantity representation popular Eulerian our method Lagrangian

  13. Background Velocity Vorticity moving quantity representation popular Eulerian our method Lagrangian VORTICITY EQUATION ( inviscid )

  14. Background Velocity Vorticity moving quantity representation popular Eulerian our method Lagrangian No diffusion Implicit incompressibility compact Unbounded … Easy boundary conditions Easy extra differential eqn …

  15. VORTICITY EQUATION Background Velocity Vorticity moving quantity representation popular Eulerian our method Lagrangian Vorticity: Vortex particle advected, vector stretched vorticity moves as material lines

  16. w Background Velocity Vorticity moving quantity representation popular Eulerian our method Lagrangian Vorticity: Our primitive = curves = tangent

  17. Background Velocity Vorticity moving quantity representation popular Eulerian our method Lagrangian Density: Dedicated particles - passive floaters - for rendering - only where smoke is Density: a quantity at nodes

  18. Lagrangian primitives • Curves carry the vorticity • Each local vortex induces a weighted rotation

  19. Lagrangian primitives • Curves carry the vorticity • Each local vortex induces a weighted rotation

  20. Method of simulation • Vortex particles (for motion) organized as curves. = tangent • Smoke particles (for visualisation) • Curves carry vortices • Vortices induce a velocity field • velocity field deforms curves & smoke At every step: • Advect the curves • Stretch • Advect the smoke

  21. Method of simulation • Vortex particles (for motion) organized as curves. = tangent • Smoke particles (for visualisation) • Curves carry vortices • Vortices induce a velocity field • velocity field deforms curves & smoke At every step: • Advect the curves • Stretch • Advect the smoke

  22. Method of simulation • Vortex particles (for motion) organized as curves. = tangent • Smoke particles (for visualisation) • Curves carry vortices • Vortices induce a velocity field • velocity field deforms curves & smoke At every step: • Advect the curves • Stretch • Advect the smoke

  23. Contributions • A new representation of vortex curves Compact, stable, controlable motion primitives • Controls of the motion primitives • Fast ‘‘noise’’ for fake turbulence details

  24. Contributions • A new representation of vortex curves Compact, stable, controlable motion primitives • Controls of the motion primitives • Fast ‘‘noise’’ for fake turbulence details

  25. Deformation of curves previous approach [AN05] If not refined: undersampling Polygon If refined: too complex Strategy to control complexity

  26. New representation • Solution: harmonic analysis of coordinates x = in y z a pair of coefficients for each harmonic • Reference frame: best ellipsoid Complexity control • Curves described by : • Frame o ex ey ez • Frequencies <cx cy cz>1..N Synthesis Advection Analysis

  27. New representation • Solution: harmonic analysis of coordinates x = in y z a pair of coefficients for each harmonic ez ey • Reference frame: best ellipsoid o ex Complexity control • Curves described by : • Frame o ex ey ez • Frequencies <cx cy cz>1..N Synthesis Advection Analysis

  28. New representation • Solution: harmonic analysis of coordinates x = in y z a pair of coefficients for each harmonic ez ey • Reference frame: best ellipsoid o ex Complexity control • Curves described by : • Frame o ex ey ez • Frequencies <cx cy cz>1..N Synthesis Advection Analysis

  29. New representation • Solution: harmonic analysis of coordinates x = in y z a pair of coefficients for each harmonic ez ey • Reference frame: best ellipsoid o ex Complexity control • Curves described by : • Frame o ex ey ez • Frequencies <cx cy cz>1..N Synthesis Advection Analysis

  30. ez ey … o ex Meaning of description • ez points towards moving direction • Frequencies cx cy cz give texture to the flow • Thickness

  31. Video: representation

  32. Contributions • A new representation of vortex curves Compact, stable, controlable motion primitives • Controls of the motion primitives • Fast ‘‘noise’’ for fake turbulence details

  33. + without with ez ey <cx cy cz>1..N … o ex Control • direction: align ez with tangent • Targets: • Twisting smoke: spin vortices around ez • Edit, delete … • Modulate cx cy cz to texturethe flow

  34. + without with ez ey <cx cy cz>1..N … o ex Control • direction: align ez with tangent • Targets: • Twisting smoke: spin vortices around ez • Edit, delete … • Modulate cx cy cz to texturethe flow

  35. + without with ez ey <cx cy cz>1..N … o ex Control • direction: align ez with tangent • Targets: • Twisting smoke: spin vortices around ez • Edit, delete … • Modulate cx cy cz to texturethe flow

  36. How to control • One cannot just translate the curves: the smoke does not follow • Solution: paddle(servoing ) ez ey o ex

  37. Video: control

  38. Contributions • A new representation of vortex curves Compact, stable, controlable motion primitives • Controls of the motion primitives • Fast ‘‘noise’’ for fake turbulence details

  39. [AN05]: noise = extra vortex particles advected in the flow, no stretch Costly (needs a lot) Source, sampling Tiled vortex noise: noise layer = separate simulation, in toroidal space Tiled in space Additional evolving velocity field Noise: fake turbulence details

  40. [AN05]: noise = extra vortex particles advected in the flow, no stretch Costly (needs a lot) Source, sampling Tiled vortex noise: noise layer = separate simulation, in toroidal space Tiled in space Additional evolving velocity field Noise: fake turbulence details

  41. [AN05]: noise = extra vortex particles advected in the flow, no stretch Costly (needs a lot) Source, sampling Tiled vortex noise: noise layer = separate simulation, in toroidal space Tiled in space Additional evolving velocity field Noise: fake turbulence details

  42. Video: noise

  43. Contributions • A new representation of vortex curves Compact, stable, controlable motion primitives • Controls of the motion primitives • Fast ‘‘noise’’ for fake turbulence details • Velocity cache, rendering

  44. Octree cache • Velocity computed at octree leaves + inbetween interpolation • Velocity computed at every smoke particle &every vorticity curve sample

  45. Octree cache • Velocity computed at octree leaves + inbetween interpolation • Velocity computed at every smoke particle &every vorticity curve sample

  46. Rendering • Thick smoke: plain particles • Thin smoke: adaptive particles[AN05] • accumulate stretching

  47. l n e Rendering • Thin smoke behaves like a surface [ William Brennan ]

  48. Results - video fpsForest fire Genie&lamp Walkthrough Fly Modeler quality5 12 5 18 Final rendering quality0.54 0.2 1. 0.37

  49. Conclusion Vorticity filaments: • Compact, high-res, fast • Good handles to manipulate a fluid • Can be manipulated interactively or post- Future work: • Split/merge • High-quality collisions • 2-phase, buoyancy, … Coupling with grids

  50. Thanks!