Research: Voronoi tiling for foam structure

[pjt222]

Summary

Investigate using Voronoi tessellation for generating realistic foam cell structures.

Background

Voronoi diagrams naturally arise in foam and bubble physics:

• Each cell in a dry foam approximates a Voronoi cell around the bubble center
• Plateau's rules emerge from minimizing surface area in Voronoi-like structures
• Weighted Voronoi (Laguerre) diagrams account for different bubble sizes

Research Questions

1. Can Voronoi tessellation generate realistic foam geometry more efficiently than N-body simulation?
2. How to combine Voronoi structure with thin-film interference rendering?
3. What algorithms exist for 3D Voronoi/Laguerre diagram computation on GPU?

Potential Approaches

• Power diagrams (Laguerre tessellation) for polydisperse foams
• Centroidal Voronoi tessellation for equilibrium foam structure
• Fortune's algorithm adaptation for 3D
• Jump flooding for GPU-accelerated Voronoi

References

• Weaire & Hutzler "The Physics of Foams" (Oxford, 1999)
• Brakke "The Surface Evolver" (Experimental Mathematics, 1992)
• Voronoi-based foam models in computational geometry literature

Related Issues

• Implement multi-bubble foam system #12 Multi-bubble foam system (current N-body approach)
• Research: Surface optimization framework for foam networks #16 Surface optimization framework

Labels

research, enhancement