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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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Alexis Angelidis Graphics & Vision Research Lab Otago - New Zealand Fabrice Neyret GRAVIR / IMAG - INRIA Grenoble - France Simulation of Smokebased on Vortex Filament Primitives
Alexis Angelidis Graphics & Vision Research Lab Otago - New Zealand Fabrice Neyret GRAVIR / IMAG - INRIA Grenoble - France Tangled-Spaghettis
Background Fluid animation approaches: Lagrangian vs Eulerian
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]
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
One Alternative – Vortex Methodsvelocityvs. vorticity Curl vorticity w velocity v
One Alternative – Vortex Methodsvelocityvs. vorticity Curl vorticity w velocity v v w
One Alternative – Vortex Methodsvelocityvs. vorticity Curl vorticity w velocity v BIOT-SAVART
w One Alternative – Vortex Methods Fine simulations • Filaments • Features BIOT-SAVART Fluid described with curves What’s induced by these curves?
Geometric Interpretation BIOT-SAVART
Geometric Interpretation BIOT-SAVART Vortex
Geometric Interpretation BIOT-SAVART Vortex Rotation magnitude
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
Geometric Interpretation BIOT-SAVART Contributions • Efficiency • stable vortex + noise • closed-form integral • O(N2), accelerated with LOD • time integration • Define smoke particles
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
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
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
Noise Smoke Filaments Divergence-free Noise • 3 types of noise vortices : • Tangent vortex • Normal vortex • Binormal vortex Good distribution of directions
Smoke • Particles • accumulate deformation • split when accumulated deformation too big • Rendering • 2D ellipses • Self-shadowing
Smoke solver overview • Filaments induce movement (everywhere) • Filaments are animated with the movement • Smoke-particles are animated with LOD- filaments and divergence-free noise
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
THANK YOU Questions ? THANK YOU Questions ?
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
Simple rotation algebra • Rotation of center c around axis of anglegiven by the magnitude of
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
One Alternative – Vortex Methodsvelocityvs. vorticity Curl vorticity w velocity v Biot-Savart To get the motion: computevelocity from vorticity
What does the Biot-Savart Law mean? BIOT-SAVART vortices Vortex vortex Rotation magnitude
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