Advected textures Fabrice Neyret EVASION GRAVIR IMAG INRIA

Advected textures Fabrice Neyret EVASION - GRAVIR / IMAG - INRIA Grenoble, France

Purpose: amplifying fluid simulation

Why not simply increase resolution ? l Cost: N log(N) / time step l Storage l Problems with CFD for CG [Lamorlette&Foster 02] l with N=1000^3 Unknown small scale phenomena vs artist desires + phenomenological knowledge

Advecting textures l = Advecting u, v [Max&Becker 96, Stam 99] l Regeneration è blending 3 dephased textures (illusion of motion) è latency = life duration

Problems with texture advection 1 l Choosing the latency 2 l Blending textures 3 l Sub-animation

Problems with texture advection 1 l Choosing the latency 2 l Blending textures è ghosting effects 3 l Sub-animation

Problems with texture advection 1 l Choosing the latency 2 l Blending textures 3 l Sub-animation

1. Advecting textures l A latency value is ok for a range of velocities (V) è bad motion illusion if V < è texture stretching if V >

1. Advecting textures l Adapting latency locally è Layers of given latency + masks è Local criterion – cumulated deform = particle integral of |e| – Target deform d*

1. Advecting textures l Adapting latency locally è Layers of given latency + masks Layer 1: lat 1 Layer 2: lat 2 (>lat 1) Layer 3: lat 3 (>lat 2) è Local criterion – cumulated deform = particle integral of |e| – Target deform d*

1. Advecting textures l Adapting latency locally è Layers of given latency + masks 1 2 3 è Local criterion – cumulated deform = particle integral of |e| – Target deform d*

2. Blending textures l Image textures l Procedural textures

2. Blending textures: image textures l What to do ? (morphing ? )

2. Blending textures: procedural textures Our solution:

3. Sub-animation l Flownoise [Perlin&Neyret 01]

3. Sub-animation l Flownoise for sub-scales è rotations vorticity spectrum è Kolmogorov cascade

3. Sub-animation l Flownoise for sub-scales è rotations vorticity spectrum < è Kolmogorov cascade >

3. Sub-animation l Flownoise for sub-scales è rotations vorticity spectrum < > è Kolmogorov cascade E CFD sub-grid microscale k 0 ke k = 2 p/l

3. Sub-animation l Vorticity energy transfer through scales è distribution law for < è only needs to scale it l > ( power law ( estimate < ) >) Our case: è heterogeneous fluid ( locality -> no Fourier ) è not at equilibrium ( transfer delay -> time ) è user control è relaxation

3. Sub-animation l Vorticity energy transfer through scales è distribution law for < è only needs to scale it l > ( power law ( estimate < ) >) Our case: è heterogeneous fluid ( locality -> no Fourier ) è not at equilibrium ( transfer delay -> time ) è user control è relaxation (user-defined parameters bk and gk )

Results

Conclusion l Mixing lo-res CFD and hi-res animated texture: è A model efficient & controllable Future work: – 3 D applications: detailed clouds & avalanches – Better flownoise control – Manage empty space – Hardware procedural shader