From physical modeling to interactive systems for physics-based graphics simulation

Physics-based simulation produces vivid and realistic effects in computer graphics by modeling coupled physical processes across a wide range of materials and scales. Achieving such realism often requires simulation formulations that can robustly handle discontinuities (e.g., fracture), heterogeneous material responses, and large systems of interacting entities. This dissertation makes three contributions that collectively progress from offline simulation toward integrated, accessible, and interactive physics-based modeling. First, we introduce a Lagrangian particle-based framework for coupled deformation, fracture, and diffusion in thin membrane-like structures, enabling detailed and heterogeneous crack growth for both in-plane and out-of-plane motion. Unlike classical PDE-based approaches that face difficulties at crack singularities, our formulation adopts an integral perspective related to nonlocal mechanics, which naturally supports fracture evolution while coupling diffusion-driven stresses that induce complex crack-path heterogeneity. Second, we present an agent-to-agent contagion--immunity formulation for simulating infectious disease spread within moving crowds. In contrast to population-level compartmental models such as SIR, our method models transmission and immune response at the individual level and supports interactive exploration of interventions including immunity and vaccination while crowd motion is computed offline. Finally, motivated by the limitations of staged workflows that separate computation from visualization and interaction, we propose Weber, an end-to-end web-based simulation framework implemented in Rust and compiled to WebAssembly. Weber integrates computation, visualization, and interaction from the outset and provides a lightweight domain-specific language for defining and modifying simulation models and parameters directly in the browser. To address performance constraints of web environments, Weber incorporates multiple levels of simulation-specific optimizations, enabling interactive execution while preserving numerical robustness. Experiments show that Weber approaches native performance for grid-based simulations while substantially improving accessibility, portability, and ease of experimentation.