Phenomenological Simulation of Brooks Fabrice Neyret Nathalie Praizelin
Phenomenological Simulation of Brooks Fabrice Neyret Nathalie Praizelin i. MAGIS / GRAVIR - IMAG * http: //www-imagis. imag. fr/ * i. MAGIS is a joint������ project of CNRS, INRIA,
i. MAGIS-GRAVIR / IMAG
i. MAGIS-GRAVIR / IMAG
If CFD had to be used l l l (Navier-Stokes) [FM 96, 97, . . . ] Very thin resolution, large domain ( and stability very small dt ) Very non-linear equations (shockwaves, surf. tension) Hard and long system solving Unknown parameters (e. g. boundary conditions) Visible features are emerging phenomena Hard to control while l l l Water motion is not directly visible Strong a priori knowledge on the result Users want some control i. MAGIS-GRAVIR / IMAG
If surface wave simulation had to be used [FR 86, P 86, GS 97] l l l Very thin resolution, large domain Very non-linear equations (waves trigger waves) Hard and long system solving while l Strong a priori knowledge on the result i. MAGIS-GRAVIR / IMAG
If Fourier synthesis had to be used [MWM 87, TDG 00, Areté] l Very thin resolution, large domain Non-linear phenomena Non uniform wave propagation l Statistical models are helpless l l (variable depth, obstacles) while l l Strong a priori knowledge on the result Users want some control i. MAGIS-GRAVIR / IMAG
Relying on phenomenological simulation Primitives based: Geometric construction of visual features l Choice of the primitives of visual interest l User can control the primitives l l “Vector primitives”: independent from rendering resolution Fast, high resolution, large domain i. MAGIS-GRAVIR / IMAG
i. MAGIS-GRAVIR / IMAG
Phenomena that are out of scope i. MAGIS-GRAVIR / IMAG
i. MAGIS-GRAVIR / IMAG
i. MAGIS-GRAVIR / IMAG
Wave theory cw h = 8 cm h = 4 cm h = 2 cm shallow water cg cw capillary waves: cg = 3 cw 2 h = 0. 25 cm h = 0. 5 cm shallow water: cg = cw (cst) h = 1 cm h = 2 cm h = 4 cm h = 8 cm h = 1 cm h = 0. 5 cm gravity waves: � cg = 1 cw 2 capillary waves gravity waves l = 2 p k i. MAGIS-GRAVIR / IMAG l
Wave theory capillary waves: cg > cw cg cw capillary waves: cg = 3 cw 2 h = 0. 25 cm shallow water: cg = cw (cst) shallow water: cg = cw h = 0. 5 cm gravity waves: cg < cw h = 1 cm h = 2 cm h = 4 cm h = 8 cm gravity waves: � cg = 1 cw 2 i. MAGIS-GRAVIR / IMAG l
Typology of stationary waves non dispersive case: cg = cw = c shockwave cc c vvv gravity waves (dispersives) cg cw capillary waves triggered by a shockwave c cg v capillary waves g cw c i. MAGIS-GRAVIR / IMAG
Froude waves - shockwaves calculation c v Fr = V (Froude number) c sin(a) = 1 (slope) a Fr a a a c a v a i. MAGIS-GRAVIR / IMAG
Froude waves - shockwaves calculation c v Fr = V c sin(a) = 1 Fr a supercritical (Fr > 1) fast (Fr > 2) subcritical (Fr < 1) i. MAGIS-GRAVIR / IMAG
The chosen primitives i. MAGIS-GRAVIR / IMAG
Our approach 1. Get a stationary velocity field (low res is ok) 2. Build the primitives skeletons 3. Add field perturbations [WH 91] 4. ( Build a surface and render ) i. MAGIS-GRAVIR / IMAG
1. Get a stationary velocity field i. MAGIS-GRAVIR / IMAG
1. Get a stationary velocity field i. MAGIS-GRAVIR / IMAG
1. Get a stationary velocity field i. MAGIS-GRAVIR / IMAG
1. Get a stationary velocity field i. MAGIS-GRAVIR / IMAG
supercritical (Fr > 1) subcritical (Fr < 1) i. MAGIS-GRAVIR / IMAG
2. Build the primitives skeletons 1. 6 1. 1 1. 8 0. 9 2. 4 0. 8 1. 2 0. 4 0 0. 3 1. 5 1. 2 1. 3 1. 8 i. MAGIS-GRAVIR / IMAG
2. Build the primitives skeletons i. MAGIS-GRAVIR / IMAG
i. MAGIS-GRAVIR / IMAG
3. Add field perturbations [WH 91] Small support fields (vortex, source) attached on particles (passive floaters) i. MAGIS-GRAVIR / IMAG
3. Add field perturbations A perturbation needs time to propagate: We cannot simply apply the static construction ! A node moves if: l l perturb V changes locally V >> the previous node has moved i. MAGIS-GRAVIR / IMAG
3. Add field perturbations i. MAGIS-GRAVIR / IMAG
Conclusion - limitations - future work l l l A real-time simulation of (some) animated visual features of brooks ! Vectorial construction (no grid sampling) Perturbations can be random, procedural (von Karman), or user generated. Fade and stop the primitives. Adaptive capillary ripples. Define a rendering method ! (producing a surface ? ) l Hydraulic jumps, foam, . . . i. MAGIS-GRAVIR / IMAG
Phenomenological Simulation of Brooks Fabrice Neyret Nathalie Praizelin i. MAGIS / GRAVIR - IMAG * http: //www-imagis. imag. fr/ * i. MAGIS is a joint������ project of CNRS, INRIA,
Le détail des mouvements est complexe : i. MAGIS-GRAVIR / IMAG
Exploite-t-on toute la connaissance disponible ? Il y a de grandes régularités dans les scènes naturelles ! i. MAGIS-GRAVIR / IMAG
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