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Innovative Smoke Simulation Using Vortex Filament Primitives for Fluid Animation Techniques

Dive into the world of fluid animation with the Simulation of Smoke based on Vortex Filament Primitives. Explore Lagrangian vs Eulerian approaches, delve into the efficiency of Eulerian velocity grids, and understand the dynamics of vortices induced by geometric interpretations. With an overview of the Biot-Savart Law and detailed discussions on velocity computation, noise generation, and smoke particle rendering, this video presents a comprehensive guide to creating realistic and dynamic smoke simulations. Discover advanced techniques such as closed-form integrals, dynamic-keyframed curves, and the manipulation of filaments to achieve high-resolution animations. Get insights into keyframing fluid animations, algorithmic improvements, and the potential for fluid-editing primitives. Join us on an educational journey towards mastering smoke simulation techniques and unlocking the full potential of fluid animation.

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Innovative Smoke Simulation Using Vortex Filament Primitives for Fluid Animation Techniques

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  1. Prepare video!!!

  2. Alexis Angelidis Graphics & Vision Research Lab Otago - New Zealand Fabrice Neyret GRAVIR / IMAG - INRIA Grenoble - France Simulation of Smokebased on Vortex Filament Primitives

  3. Alexis Angelidis Graphics & Vision Research Lab Otago - New Zealand Fabrice Neyret GRAVIR / IMAG - INRIA Grenoble - France Tangled-Spaghettis

  4. Background Fluid animation approaches: Lagrangian vs Eulerian

  5. Background Fluid animation approaches: Lagrangian vs Eulerian Popular: Eulerian velocity grid [Fedkiw et al.01] [Pighin et al.04] [McNamara et al.04] [Fattal et al.04]

  6. Background Fluid animation approaches: Lagrangian vs Eulerian Popular: Eulerian velocity grid [Fedkiw et al.01] [Pighin et al.04] [McNamara et al.04] [Fattal et al.04] A. Velocity grid B. Update rules

  7. One Alternative – Vortex Methodsvelocityvs. vorticity Curl vorticity w velocity v

  8. One Alternative – Vortex Methodsvelocityvs. vorticity Curl vorticity w velocity v v w

  9. One Alternative – Vortex Methodsvelocityvs. vorticity Curl vorticity w velocity v BIOT-SAVART

  10. w One Alternative – Vortex Methods Fine simulations • Filaments • Features BIOT-SAVART Fluid described with curves What’s induced by these curves?

  11. Geometric Interpretation BIOT-SAVART

  12. Geometric Interpretation BIOT-SAVART Vortex

  13. Geometric Interpretation BIOT-SAVART Vortex Rotation magnitude

  14. Lagrangian Vortex Methods • Entire fluid = curves of vortices ! C0 C3 Dynamics • Curves induce movement • Curves are animated with this movement C2 C1 Consequence • Cheap storage • Dynamic-keyframed curve

  15. Video#2-5

  16. Geometric Interpretation BIOT-SAVART Contributions • Efficiency • stable vortex + noise • closed-form integral • O(N2), accelerated with LOD • time integration • Define smoke particles

  17. Sum of vortices along curves A more convenient amplitude Biot-Savart Cauchy There are closed-forms for the Cauchy kernel integral along a circle and a segment [MS.98] Discrete segments

  18. Large time steps: high order scheme • Biot-Savart tells more than velocity • Traditional forward Euler , BStrajectory = sum of velocities of rotation  • Our schemetrajectory = sum of Rotation 

  19. Levels of detail • We define a bound to the error between a segment and split segments p p q Too detailed Alright Too coarse • We precompute a binary tree for each filament

  20. Noise Smoke Filaments Divergence-free Noise • 3 types of noise vortices : • Tangent vortex • Normal vortex • Binormal vortex Good distribution of directions

  21. Smoke • Particles • accumulate deformation • split when accumulated deformation too big • Rendering • 2D ellipses • Self-shadowing

  22. Video

  23. Smoke solver overview • Filaments induce movement (everywhere) • Filaments are animated with the movement • Smoke-particles are animated with LOD- filaments and divergence-free noise

  24. Conclusion • Separated dynamics & rendering • Efficient & hi-resolution • Not bounded in space • Compact: easy to load and save • Dynamics or keyframes Improvements • Smoke particle merging • Curve split/collapse or resampling • Currently, limited boundary conditions

  25. THANK YOU Questions ? THANK YOU Questions ?

  26. A new integration scheme • With our closed form, induced velocity is given by a 4x4 matrix • Traditional forward Euler  • Our scheme a translation is a translation a rotation is a rotation a twistis a twist 

  27. Simple rotation algebra • Rotation of center c around axis  of anglegiven by the magnitude of 

  28. Motivation A fluid is not an actor Existing fluid-directing techniques areslow OR tedious Aim • A technique for keyframing fluid animation • Not bounded in a cube • Predictable fluid-editing primitives • Fast/Robust

  29. One Alternative – Vortex Methodsvelocityvs. vorticity Curl vorticity w velocity v Biot-Savart To get the motion: computevelocity from vorticity

  30. What does the Biot-Savart Law mean? BIOT-SAVART vortices Vortex vortex Rotation magnitude

  31. change The domain of the BS integral In 3D, vortices concentrate along tubes (with a distribution profile around axis) 1.Integral over a slice of vortices : 2.Integral over a curveof a slice : C 3. Integral on many curves C1

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