# Physics-based Sphere Packing for Lagrangian Mesh Morphing

arXiv: https://arxiv.org/abs/2610.08880 · HTML: https://mlsanity.com/paper/2610.08880/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 36 references that are in the map.
- First posted on arXiv 6 Oct 2026.

## Builds on (most cited first, 9 of 9)

- [Deep Marching Tetrahedra: a Hybrid Representation for High-Resolution 3D Shape Synthesis](https://mlsanity.com/paper/2111.04276/) (2021)
- [DiffTaichi: Differentiable Programming for Physical Simulation](https://mlsanity.com/paper/1910.00935/) (2019)
- [PlasticineLab: A Soft-Body Manipulation Benchmark with Differentiable Physics](https://mlsanity.com/paper/2104.03311/) (2021)
- [Learning Deformable Tetrahedral Meshes for 3D Reconstruction](https://mlsanity.com/paper/2011.01437/) (2020)
- [Evolution Gym: A Large-Scale Benchmark for Evolving Soft Robots](https://mlsanity.com/paper/2201.09863/) (2022)
- [TetSphere Splatting: Representing High-Quality Geometry with Lagrangian Volumetric Meshes](https://mlsanity.com/paper/2405.20283/) (2024)
- [SoftZoo: A Soft Robot Co-design Benchmark For Locomotion In Diverse Environments](https://mlsanity.com/paper/2303.09555/) (2023)
- [Generating Freeform Endoskeletal Robots](https://mlsanity.com/paper/2412.01036/) (2024)
- [Accelerated co-design of robots through morphological pretraining](https://mlsanity.com/paper/2502.10862/) (2025)

## Abstract (arXiv)

This paper studies tetrahedral meshes as the body representation for differentiable simulation and computational design. Fixed-connectivity meshes degrade under large morphs, while remeshing from scratch discards node correspondence. We present JamTet, a physics-based sphere-packing framework for volumetric meshing and morphing. We contribute (i) a GPU-parallel mesher combining octree-hierarchical packing with constrained Delaunay tetrahedralization, producing more uniform element volumes than TetGen and fTetWild; (ii) Lagrangian mesh morphing that preserves interior-node identities by re-equilibrating the same spheres within changing shapes and rebuilding the boundary and connectivity, remaining inversion-free where fixed-connectivity and TetSphere meshes invert; and (iii) a differentiable GPU simulator in JAX, with mass-spring edges and a volumetric Neo-Hookean term, integrated with mesh morphing in a design pipeline. In soft-robot morphology design experiments, interior-node gradients improve swimming fitness by 0.73-1.07 over a matched surface-only variant, while voxelized versions of the same designs yield 32-63% lower fitness. These results establish sphere packing as a practical volumetric mesh representation for gradient-based shape optimization. Code and media: under review.