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Prepare video!!!. Alexis Angelidis Graphics & Vision Research Lab Otago - New Zealand. Fabrice Neyret GRAVIR / IMAG - INRIA Grenoble - France. Simulation of Smoke based on Vortex Filament Primitives. Alexis Angelidis Graphics & Vision Research Lab Otago - New Zealand. Fabrice Neyret

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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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