1. Simulation and Rendering of Liquid Foams Hendrik Kück (UBC, Vancouver) Christian Vogelgsang (FAU Erlangen, Germany) Günther Greiner (FAU Erlangen, Germany) Graphics Interface 2002

2. Motivation Liquid foams can be found in many places in the real world Very difficult / impossible to recreate using standard techniques extremely complex microscopic structures unique optical properties complex dynamic behaviour Liquid foams can be found in many places in the real world Very difficult / impossible to recreate using standard techniques extremely complex microscopic structures unique optical properties complex dynamic behaviour

3. Goals Visually convincing simulation and rendering of liquid foams Not: Physically accurate But: Efficient Interaction with external objects Integration into existing raytracing systems Visually convincing simulation and rendering of liquid foams Not: Physically accurate But: Efficient Interaction with external objects Integration into existing raytracing systems

4. Outline Structure and dynamics of liquid foams Previous work Simulation of foam dynamics Shading Results Future Work Structure and dynamics of liquid foams Previous work Simulation of foam dynamics Shading Results Future Work

5. Structure of liquid foams

6. Plateau borders Liquid Films Plateau border cross section

7. Dynamics of liquid foams Viscoelastic, can behave like Solids (elastic deformation) Fluids (viscous flow) Film rupture Rising bubbles Viscoelastic, can behave like Solids (elastic deformation) Fluids (viscous flow) Film rupture Rising bubbles

8. Physics Durian, 1995 2D foam dynamics Physics Durian, 1995 2D foam dynamics Previous work Computer Graphics Almgren & Sullivan, 1993 Surface Evolver, Interference Colours Icart & Arquès, 1999 ‚2D‘ foam, Interference colours Glassner, 2000 Soap bubbles, Interference colours Durikovic, 2000 Soap bubble dynamics, Mass-spring-damper system

9. General approach Use simple model in simulation step Fixed size spheres No explicit computation of foam micro geometry Forces acting on spheres Output sphere geometry In ray-tracing step Reconstruct liquid films and Plateau borders Use appropriate shading models Use simple model in simulation step Fixed size spheres No explicit computation of foam micro geometry Forces acting on spheres Output sphere geometry In ray-tracing step Reconstruct liquid films and Plateau borders Use appropriate shading models

10. Bubble  Bubble Forces Soap films minimize surface area due to surface tension

11. Bubble  Bubble Forces Soap films minimize surface area due to surface tension

12. Bubble  Bubble Forces Soap films minimize surface area due to surface tension

13. Bubble  Bubble Forces Soap films minimize surface area due to surface tension 120 °

14. Bubble  Bubble Forces Model with 2 spring forces per pair of overlapping spheres Attractive force Repulsive force Model with 2 spring forces per pair of overlapping spheres Attractive force Repulsive force

15. Simulation Forces acting on spheres due to Contact with other spheres/bubbles Viscosity Air resistance Gravity Contact with external objects Assumption: Bubbles have no mass  Forces have to add up to 0 for each bubble Results in 1. order ODE system Forces acting on spheres due to Contact with other spheres/bubbles Viscosity Air resistance Gravity Contact with external objects Assumption: Bubbles have no mass  Forces have to add up to 0 for each bubble Results in 1. order ODE system

16. Simulation Start with randomly generated bubbles Initial simulation to get a stable configuration For each animation frame Randomly add/remove spheres Numerical integration to compute sphere positions for that point in time Generate sphere geometry Flatten spheres at external objects Start with randomly generated bubbles Initial simulation to get a stable configuration For each animation frame Randomly add/remove spheres Numerical integration to compute sphere positions for that point in time Generate sphere geometry Flatten spheres at external objects

17. Rendering Special shader Invoked at every ray/sphere intersection Has to Decide if intersection corresponds to Plateau border or liquid film Perform shading using corresponding shading model Special shader Invoked at every ray/sphere intersection Has to Decide if intersection corresponds to Plateau border or liquid film Perform shading using corresponding shading model

18. Shading model selection Base decision on the order in which the ray enters and leaves spheres Shading only for some intersections Approximate separating films by averaging of adjacent intersections Base decision on the order in which the ray enters and leaves spheres Shading only for some intersections Approximate separating films by averaging of adjacent intersections Bubble 1 Bubble 2

19. 2 different cases Overlap of 3 spheres Empty space between spheres 2 different cases Overlap of 3 spheres Empty space between spheres Plateau Borders

20. Liquid Film Shading Fresnel reflection (Interference Effects) Fresnel reflection (Interference Effects)

21. Plateau Border Shading High curvature Refraction & total reflection randomize light direction Our shading model Simple light diffusion approximation (multiple scattering) Single scattering High curvature Refraction & total reflection randomize light direction Our shading model Simple light diffusion approximation (multiple scattering) Single scattering

22. Results Implemented for Mental Ray ® as combination of geometry shader and material shader Resolution: 800x630 ~700 bubbles ~4 s. simulation40 s. rendering

23. Future work Improve shading models Interference effects Simulation of multiple scattering Level of detail approach Efficient simulation and rendering of arbitrary dense foams at arbitrary scale Improve shading models Interference effects Simulation of multiple scattering Level of detail approach Efficient simulation and rendering of arbitrary dense foams at arbitrary scale

24. Questions Acknowledgements This project was supported by Animation/VFX (SZM Studios, Munich, Germany) Special thanks to Horst Hadler and Michael Kellner Acknowledgements This project was supported by Animation/VFX (SZM Studios, Munich, Germany) Special thanks to Horst Hadler and Michael Kellner