On the boundary detection for particle-based methods: visibility, learning, interval analysis, metrics, and applications - Sandim, Marcos Henrique Alves (2020)
This thesis is a comprehensive study of the definition, development, and evaluation of boundary detection methods for particle systems. A particle system is a variety of datarepresentation used in many fluid simulation methods, such as Smoothed Particle Hydrodynamics (SPH) and Position-Based Fluids (PBF) use particle systems as their primary representation for the fluid. Other techniques, such as Fluid-Implicit-Particle (FLIP) and Affine Particle-In-Cell (APIC), use particle systems as a supplemental representation. In both cases, the knowledge about the boundaries of the particle system can be useful, as it gives crucial information to improve the precision and quality of the simulation, of the generation of a free-surface, or to resample or redistribute particles in critical regions. Despite all that, this is still a poorly defined problem and with costly and error-prone solutions. In light of this, we introduce a mathematical definition for the problem, and, starting from this definition, we explore four distinct solutions. We based our solutions on visibility tests, machine learning, and a combination of interval arithmetic and computational geometry. We thoroughly tested our solutions using different classes of problems and measured their efficiency. Given the results, we can affirm that each of our solutions has characteristics that make them well suited for several distinct use cases.