Vibrational Affine Body Dynamics

Rigid-body and affine body dynamics are default simulation modalities for rigid or near-rigid objects. Their low-rank kinematic models inherently preclude vibrational responses that stiff bodies exhibit during abrupt impacts or contacts. Simulating such behavior with full or reduced finite element method (FEM) requires high spatial resolution and small time steps, which significantly increases computational costs of system solving and collision handling. We propose vibrational affine body dynamics (VABD), a novel simulation framework that captures these missing high-frequency vibrations while preserving excellent efficiency and robustness, even in complex scenarios. VABD introduces a carefully constructed secondary vibration subspace that augments standard affine body dynamics to encode high-frequency deformation on top of the time-varying affine frame, while remaining orthogonal to this evolving affine subspace with respect to the system matrix. This subspace design enables efficient reduced simulation with improved expressiveness. For collision handling, VABD employs medial-axis-based proxies and interleaves medial continuous and discrete collision detection to balance robustness and performance across different motion scales. We train a neural MAT (medial axis transform) mapping from reduced vibrational coordinates to medial primitives, enabling collision responses to be coupled back to the reduced system with well-defined derivatives. To efficiently solve the resulting implicit system, we introduce a Newton-quasi-Newton solver that exploits the fact that collision Hessians remain largely unchanged under small time steps, which effectively suppresses the overhead of repeated Hessian construction while retaining strong second-order convergence. Experiments demonstrate that VABD produces realistic vibrational responses for stiff objects undergoing intensive and extensive collisions. In terms of performance, VABD is orders of magnitude faster than FEM-based or reduced simulation approaches.