Improved Air Mesh Refinement for Accurate Strand-Solid and Self-Collision Handling

This paper presents a novel method for efficiently handling strand-solid and self-collisions using air meshes. Traditional collision handling at the primitive level requires extensive computations, such as time-stepping and solving cubic equations, to ensure simulation stability. Moreover, depending on scene complexity, both discrete collision detection (DCD) and continuous collision detection (CCD) often need to be considered. In this study, we propose an improved approach to collision handling based on the previously introduced air mesh technique. The original air mesh approach does not rely on the simulation mesh itself but instead meshes the surrounding air, approximating its deformation as volumetric changes to detect and predict collisions. To ensure numerical convergence during air mesh refinement, a constraint was imposed to maintain equilateral triangles. However, this method often produced noisy results depending on the scene, and boundary issues became more pronounced in line-based simulations such as hair or fur simulation. To address these issues, we introduce a new constraint during the air mesh refinement process, leading to a more stable and noise-reduced collision handling approach. Our method demonstrates stable results not only for hair simulations but also across various scene types.