1. * iMAGIS is a joint project of CNRS, INRIA, INPG and UJF. Phenomenological Simulation of Brooks Fabrice Neyret Nathalie Praizelin iMAGIS / GRAVIR - IMAG * http://www-imagis.imag.fr/

2. iMAGIS-GRAVIR / IMAG

4. If CFD had to be used Very thin resolution, large domain Very thin resolution, large domain ( and stability  very small dt ) Very non-linear equations Very non-linear equations (shockwaves, surf. tension)  Hard and long system solving  Hard and long system solving Unknown parameters Unknown parameters (e.g. boundary conditions) Visible features are emerging phenomena  Hard to control Visible features are emerging phenomena  Hard to controlwhile Water motion is not directly visible Water motion is not directly visible Strong a priori knowledge on the result Strong a priori knowledge on the result Users want some control Users want some control [FM96,97,...] (Navier-Stokes)

5. iMAGIS-GRAVIR / IMAG If surface wave simulation had to be used Very thin resolution, large domain Very thin resolution, large domain Very non-linear equations Very non-linear equations (waves trigger waves) Hard and long system solving Hard and long system solvingwhile Strong a priori knowledge on the result Strong a priori knowledge on the result [FR86,P86,GS97]

6. iMAGIS-GRAVIR / IMAG If Fourier synthesis had to be used Very thin resolution, large domain Very thin resolution, large domain Non-linear phenomena Non-linear phenomena Non uniform wave propagation Non uniform wave propagation (variable depth, obstacles)  Statistical models are helpless  Statistical models are helplesswhile Strong a priori knowledge on the result Strong a priori knowledge on the result Users want some control Users want some control [MWM87,TDG00,Areté]

7. iMAGIS-GRAVIR / IMAG Relying on phenomenological simulation Primitives based: Geometric construction of visual features Choice of the primitives of visual interest Choice of the primitives of visual interest User can control the primitives User can control the primitives “Vector primitives”: independent from rendering resolution “Vector primitives”: independent from rendering resolution Fast, high resolution, large domain Fast, high resolution, large domain

8. iMAGIS-GRAVIR / IMAG

9. Phenomena that are out of scope

10. iMAGIS-GRAVIR / IMAG

12. cgcwcgcw gravity waves: capillary waves: c g = 3 c w 2 c g = 1 c w 2 shallow water: c g = c w (cst) h = 8 cm h = 4 cm h = 2 cm h = 1 cm h = 0.5 cm h = 0.25 cm h = 8 cm h = 4 cm h = 2 cm h = 1 cm h = 0.5 cm   k cwcw gravity waves capillary waves shallow water Wave theory

13. iMAGIS-GRAVIR / IMAG Wave theory cgcwcgcw gravity waves: capillary waves: c g = 3 c w 2 c g = 1 c w 2 shallow water: c g = c w (cst) h = 8 cm h = 4 cm h = 2 cm h = 1 cm h = 0.5 cm h = 0.25 cm capillary waves: c g > c w gravity waves: c g < c w shallow water: c g = c w

14. iMAGIS-GRAVIR / IMAG v c v c v c Typology of stationary waves non dispersive case: c g = c w = c  shockwave v c capillary waves triggered by a shockwave cgcgcgcg capillary waves cwcwcwcw cgcgcgcg gravity waves (dispersives) cwcwcwcw cgcgcgcg

15. iMAGIS-GRAVIR / IMAG Froude waves - shockwaves calculation v c v c v c  Fr = V c sin(  ) = 1 Fr Fr       (Froude number) (slope)

16. iMAGIS-GRAVIR / IMAG Froude waves - shockwaves calculation v c  Fr = V c sin(  ) = 1 Fr Fr supercritical (Fr > 1) subcritical (Fr < 1) fast (Fr > 2)

17. iMAGIS-GRAVIR / IMAG The chosen primitives

18. iMAGIS-GRAVIR / IMAG Our approach 1. Get a stationary velocity field (low res is ok) 2. Build the primitives skeletons 3. Add field perturbations [WH91] 4. ( Build a surface and render )

19. iMAGIS-GRAVIR / IMAG 1. Get a stationary velocity field

20. iMAGIS-GRAVIR / IMAG 1. Get a stationary velocity field

21. iMAGIS-GRAVIR / IMAG 1. Get a stationary velocity field

22. iMAGIS-GRAVIR / IMAG 1. Get a stationary velocity field

23. iMAGIS-GRAVIR / IMAG supercritical (Fr > 1) subcritical (Fr < 1)

24. iMAGIS-GRAVIR / IMAG 2. Build the primitives skeletons 1.2 2.4 0.3 1.5 1.8 0.8 1.6 0.4 1.31.2 1.80.9 1.1 0

25. iMAGIS-GRAVIR / IMAG 2. Build the primitives skeletons

26. iMAGIS-GRAVIR / IMAG

27. 3. Add field perturbations [WH91] Small support fields (vortex,source) attached on particles (passive floaters)

28. iMAGIS-GRAVIR / IMAG A perturbation needs time to propagate: We cannot simply apply the static construction ! A node moves if: V changes locally the previous node has moved perturb V >> perturb V >> 3. Add field perturbations

29. iMAGIS-GRAVIR / IMAG 3. Add field perturbations

30. iMAGIS-GRAVIR / IMAG Conclusion - limitations - future work 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 ?) Hydraulic jumps, foam,...

31. * iMAGIS is a joint project of CNRS, INRIA, INPG and UJF. Phenomenological Simulation of Brooks Fabrice Neyret Nathalie Praizelin iMAGIS / GRAVIR - IMAG * http://www-imagis.imag.fr/

32. iMAGIS-GRAVIR / IMAG Le détail des mouvements est complexe :

33. iMAGIS-GRAVIR / IMAG Exploite-t-on toute la connaissance disponible ? Il y a de grandes régularités dans les scènes naturelles !