FreeForm：基於粒子蒙皮特徵模態的降階可變形模擬

摘要

我們提出了一種新穎的無網格降階模擬公式，用於可變形超彈性物體。現有的降階彈性動力學模擬研究，透過網格或神經場來表示輸入幾何，但網格的獲取可能因複雜形狀的掃描與三角化挑戰而困難，而神經場則需要逐形狀最佳化。我們提出採用再生核粒子法（RKPM）表示，藉由求解彈性能量海森矩陣的廣義特徵系統，來建構降階蒙皮權重。我們證明，此公式不僅在訓練速度上比神經場的逐形狀最佳化快40倍，且在與有限元素法的收斂結果比較時，能達到更低的模擬誤差。我們在各種不同表示（包括網格與高斯潑濺）的物體上展示模擬結果，並將此方法應用於機器人模擬的下游任務。

English

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.