Spatial Intelligence Lab
Hi-Fi Physics Team
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.
Traditional FEM-based simulation requires volumetric meshing, which is a challenging problem by itself on arbitrary shapes, and requires comprise between speed and accuracy. Furthermore, it may not even be well-defined for modern, imprecise point-based representations such as 3D Gaussian Splats.
FreeForm offers a novel approach for mesh-free reduced-order simulation of deformable, hyperelastic objects. It uses the Reproducing Kernel Particle Method (RKPM) to discretize the object's geometry and parameterize the deformation subspace. Instead of relying on time-consuming per-shape optimization of neural fields like in Simplicits, FreeForm efficiently derives a set of optimal skinning eigenmodes by solving a generalized eigensystem on the Hessian matrix of the elastic energy using highly efficient linear algebra routines. This allows for the construction of high-quality, reduced-order bases (skinning weights) in a significantly faster training stage. Once the skinning weights are determined, they are used in a reduced-order elastic simulation stage to perform time stepping. For more details, please refer to the paper.
| Dataset | Method | Training time (s) | Fix Side (↓) | Pull Farthest (↓) | Pull Boundary (↓) |
|---|---|---|---|---|---|
| Thingi10K | Simplicit | 121.44 ± 10.15 | 8.97e-03 | 5.58e-02 | 3.37e-02 |
| RKPM | 3.19 ± 2.48 | 6.87e-03 | 3.75e-02 | 3.11e-02 | |
| Simready | Simplicit | 117.45 ± 1.13 | 2.16e-09 | 9.38e-04 | 8.83e-04 |
| RKPM | 3.49 ± 2.39 | 1.01e-09 | 4.75e-04 | 4.16e-04 | |
Our method achieves a significantly speedup in finding optimal skinning eigenmodes compared to Simplicits. Moreover, our skinning weights lead to more accurate simulation results shown on the right side of the table. Please see videos below for more details.
We compare our method with other methods in reference to the golden standard Finite Element Method (FEM) results in the standard beam bending and twisting tests. Our method method consistently outperforms the Simplicits baseline, and also full-order MPM and SPH simulation given enough Degrees of Freedom (DOF).
We compare our method with Simplicits on shapes from the Thingi10K dataset under three types of boundary conditions (visualized by yellow points in the videos). Our method shows more accurate and expressive deformations than Simplicits.
We compare our method with Simplicits on shapes from the Simready dataset. The objects are simulated using physical parameters estimated by VoMP.
We thank Sangeetha Grama Srinivasan for helping us with comparisons to SPH.