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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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simulation of smoke based on vortex filament primitives

Alexis Angelidis

Graphics & Vision Research Lab

Otago - New Zealand

Fabrice Neyret

GRAVIR / IMAG - INRIA

Grenoble - France

Simulation of Smokebased on Vortex Filament Primitives

tangled spaghettis

Alexis Angelidis

Graphics & Vision Research Lab

Otago - New Zealand

Fabrice Neyret

GRAVIR / IMAG - INRIA

Grenoble - France

Tangled-Spaghettis

background
Background

Fluid animation approaches: Lagrangian vs Eulerian

background1
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]

background2
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

slide10

w

One Alternative – Vortex Methods

Fine simulations

  • Filaments
  • Features

BIOT-SAVART

Fluid described with curves

What’s induced by these curves?

slide12

Geometric Interpretation

BIOT-SAVART

Vortex

slide13

Geometric Interpretation

BIOT-SAVART

Vortex

Rotation magnitude

lagrangian vortex methods
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
slide16

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
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
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
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
divergence free noise

Noise

Smoke

Filaments

Divergence-free Noise
  • 3 types of noise vortices :
    • Tangent vortex
    • Normal vortex
    • Binormal vortex

Good distribution of directions

smoke
Smoke
  • Particles
    • accumulate deformation
    • split when accumulated deformation too big
  • Rendering
    • 2D ellipses
    • Self-shadowing
slide23

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
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
slide25

THANK YOU

Questions ?

THANK YOU

Questions ?

a new integration scheme
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
Simple rotation algebra
  • Rotation of center c around axis  of anglegiven by the magnitude of 
motivation
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 methods velocity vs vorticity3
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
What does the Biot-Savart Law mean?

BIOT-SAVART

vortices

Vortex

vortex

Rotation magnitude

the domain of the bs integral

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