FreeForm：基于粒子蒙皮本征模的降阶变形模拟

摘要

我们提出了一种新颖的公式，用于可变形超弹性物体的无网格降阶模拟。现有降阶弹性动力学模拟方法中，输入几何体通常由网格表示，但复杂形状的扫描与三角剖分存在困难，或由需要逐形状优化的神经场表示。我们提出采用再生核粒子方法（RKPM）表示，通过求解弹性能量Hessian矩阵上的广义特征系统，能够构建降阶蒙皮权重。实验表明，与神经场的逐形状优化相比，该公式不仅实现40倍训练加速，而且在与有限元方法收敛结果对比时，模拟误差更低。我们在网格和高斯飞溅等多种表示形式的不同物体上展示了模拟结果，并验证了该方法在机器人模拟下游任务中的应用。

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.