PhysFiT: Physical-aware 3D Shape Understanding for Finishing Incomplete Assembly

Understanding the part composition and structure of 3D shapes is crucial for a wide range of 3D applications, including 3D part assembly and 3D assembly completion. Compared to 3D part assembly, 3D assembly completion is more complicated which involves repairing broken or incomplete furniture that miss several parts with a toolkit. The primary challenge persists in how to reveal the potential part relations to infer the absent parts from multiple indistinguishable candidates with similar geometries, and complete for well-connected, structurally stable and aesthetically pleasing assemblies. This task necessitates not only specialized knowledge of part composition but, more importantly, an awareness of physical constraints, i.e. , connectivity, stability, and symmetry. Neglecting these constraints often results in assemblies that, although visually plausible, are impractical. To address this challenge, we propose PhysFiT, a physical-aware 3D shape understanding framework. This framework is built upon attention-based part relation modeling and incorporates connection modeling, simulation-free stability optimization and symmetric transformation consistency. We evaluate its efficacy on 3D part assembly and 3D assembly completion, a novel assembly task presented in this work. Extensive experiments demonstrate the effectiveness of PhysFiT in constructing geometrically sound and physically compliant assemblies.