FreeForm：基于粒子蒙皮模态的降阶可变形仿真
FreeForm: Reduced-Order Deformable Simulation from Particle-Based Skinning Eigenmodes
用 RKPM 粒子表示替代网格或神经场来构造降阶蒙皮权重，使高斯泼溅等非网格几何可直接参与可变形仿真，为视觉重建出的 3D 资产提供免逐形状优化的物理动画接口。
原文依据 We show our simulation results on a wide variety of objects in different representations including meshes and Gaussian splats
摘要译文
由模型翻译 · 术语统一 · 请对照原文核对关键结论我们提出了一种用于可变形超弹性物体的无网格降阶仿真的新形式。现有的降阶弹性动力学仿真工作要么用网格表示输入几何，而由于复杂形状的扫描与三角化存在困难，网格往往难以获得；要么用神经场表示，而神经场需要逐形状优化。我们提出采用再生核粒子方法（RKPM）表示，从而可以通过在弹性能的 Hessian 矩阵上求解广义特征系统来构造降阶蒙皮权重。我们证明，与神经场的逐形状优化相比，该形式不仅带来 40 倍的训练加速，而且在以有限元法的收敛结果为参照进行评估时，还能取得更低的仿真误差。我们展示了在包括网格与高斯泼溅在内的不同表示形式的多种物体上的仿真结果，以及本方法在机器人仿真这一下游任务中的应用。
英文原文摘要 1052 字符
We present a novel formulation for mesh-free, reduced-order simulation of deformable hyperelastic objects. Existing work in reduced-order elastodynamic simulation represents the input geometry by either meshes, which can be difficult to obtain due to challenges in scanning and triangulating complex shapes, or by neural fields that require per-shape optimization. We propose to adopt a Reproducing Kernel Particle Method (RKPM) representation, which enables the construction of reduced-order skinning weights by solving a generalized eigensystem on the Hessian matrix of the elastic energy. We demonstrate that this formulation not only leads to a 40x training speedup compared with the per-shape optimization of neural fields, but also achieves lower simulation error when evaluated against the converged results of finite element method. We show our simulation results on a wide variety of objects in different representations including meshes and Gaussian splats, as well as the application of our method in the downstream task of robot simulation.