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The high-fidelity simulation of thin, flexible structures like textiles and hair is a fundamental problem in computer graphics, crucial for applications from digital garment design to the creation of realistic digital humans. Simulating these materials presents significant computational challenges, including complex nonlinear contact interactions and vast parameter spaces that make traditional numerical methods inefficient or unreliable. Conventional equilibrium solvers often fail to navigate complex energy landscapes. Dynamic simulators often fail to find a true physical equilibrium because they rely on artificial damping to halt motion. This non-physical process can trap the system in a suboptimal local energy minimum or create unrecoverable errors like self-intersections, preventing it from reaching its correct, lowest-energy state.
To address problems where physical accuracy and the ability to trace a full solution path are paramount, such as in textile design exploration, the thesis first presents a robust physics-based framework for static yarn-level simulation using numerical continuation. We formulate yarn relaxation and parameter exploration as homotopy problems, enabling the robust tracing of equilibrium solution paths. To prevent topological errors, our contact-aware algorithm robustly finds a valid solution path. When the predictor step causes a yarn penetration, the algorithm recovers by automatically reducing its step size and tightening its error tolerance, ensuring the final result is free of such errors.
While this physics-based method provides high accuracy for static problems, its computational cost makes it unsuitable for real-time dynamic scenarios like character animation. To address the distinct challenge of efficient and generalizable animation where inference speed is critical, the thesis then explores a contrasting, data-driven paradigm. We present HairFormer, a two-stage neural architecture that learns to simulate dynamic hair in real time for arbitrary hairstyles, body shapes, and motions. A static network first predicts a physically plausible drape, which informs a dynamic network that generates expressive secondary motions. Trained with self-supervised, physics-informed losses, this approach excels at performance and generalization where traditional solvers are too slow.
To demonstrate a practical application, the dissertation explores a forward homogenization pipeline that bridges microscopic yarn physics with macroscopic cloth behavior. This pipeline was implemented using a dynamic solver, which required running numerous simulations across a sampled domain of strain values.
To demonstrate a practical application, the dissertation explores a forward homogenization pipeline that bridges microscopic yarn physics with macroscopic cloth behavior. This pipeline was implemented using a dynamic solver, which required running numerous simulations across a sampled domain of strain values.
The discussion section will then propose how the static numerical continuation solver would be a more powerful tool for this task. By mathematically associating strain with the control variable λ of the homotopy, one could trace the entire continuous stress-strain response in a single run instead of relying on discrete sampling. Furthermore, the discussion demonstrates how even a simple, first-order continuation method is capable of detecting and navigating through limit points and bifurcations along the solution path, illustrated with a two-yarn example. The method’s robustness in handling the highly nonlinear forces that arise from these yarn interactions is significantly enhanced by a back-tracking line search within its corrector step. This ensures the solver converges even when encountering abrupt changes from contact, highlighting the potential of the static solver to efficiently generate the high-quality data required for such multiscale processes.