Research map / 3D vision / NeRF and radiance fields
PIE-NeRF: Physics-based Interactive Elastodynamics with NeRF
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Integrates meshless quadratic generalized moving least squares (Q-GMLS) hyperelastic simulation with instant-NGP NeRF to produce interactive, physics-based novel-view elastodynamic animations.
Problem
Synthesizing nonlinear, time-coherent, physically grounded elastodynamic motion of NeRF scenes is under-explored because physical simulation normally needs explicit meshes or voxel proxies and is expensive.
Approach
Discretize hyperelasticity meshlessly by placing Q-GMLS kernels over Poisson-disk particles adaptively sampled by NeRF density gradient, integrate energy at integrator points, and use quadratic displacement warping to retrieve rest-pose colors for rendering.
Key results
- Runs interactively in real time on an NVIDIA 3090 with a few dozen (e.g., 78) Q-GMLS kernels, with total per-frame time in the tens of milliseconds.
- Results are nearly indistinguishable from FEM ground truth on tetrahedral meshes while using far fewer kernels than FEM vertices.
- PIE-NeRF runs about two orders of magnitude faster than PAC-NeRF in the reported examples; ARAP compression loses nearly 40% of volume while Neo-Hookean preserves it.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use Neo-Hookean energy instead of ARAP energy | PIE-NeRF · Chocolate jelly compression | volume preservation: nearly 40% | Helped |
| use PIE-NeRF instead of PAC-NeRF | NeRF-based elastodynamics · Large-deformation rendering | speed: two orders | Helped |
| use quadratic warping instead of linear warping (ablation) | PIE-NeRF · NeRF rendering under large deformations | visual quality | Helped |
| use quadratic warping instead of linear warping (ablation) | PIE-NeRF · Runtime | time cost | Hurt |
Limitations
- Dense 30n x 30n system from global Q-GMLS kernel influence requires Cholesky solve
- Conversion from implicit NeRF to explicit meshless proxy is not fully avoided
- Quadratic warping is more expensive than linear warping
Experimental setup
Datasets: NeRF synthetic scenes BlenderNeRF synthetic codimensional scenes
Benchmarks: FEM ground-truth comparison on synthetic scenes PAC-NeRF comparison
Metrics: visual similarity to FEM ground truth run time breakdown (ms) volume preservation percentage
Baselines: PAC-NeRF ARAP-based NeRF editing linear warping FEM ground truth
Builds on: NeRF instant-NGP Q-GMLS PAC-NeRF Neo-Hookean
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