Physics-based Sphere Packing for Lagrangian Mesh Morphing

arXiv cs.GR details JamTet, a physics-based sphere-packing framework for volumetric meshing and morphing aimed at differentiable simulation and computational design. The pitch is straightforward: preserve node correspondence through large deformations instead of throwing away the mesh and starting over.

The system combines octree-hierarchical packing with constrained Delaunay tetrahedralization on the GPU, and the authors say it produces more uniform element volumes than TetGen and fTetWild. More importantly for optimization loops, the same interior spheres are re-equilibrated as the shape changes, then the boundary and connectivity are rebuilt around them.

That Lagrangian approach is meant to stay inversion-free where fixed-connectivity meshes and TetSphere can fail, which matters for soft-body simulation, robotics, and any gradient-based shape search that depends on stable correspondence. The pipeline also includes a differentiable JAX simulator with mass-spring edges plus a volumetric Neo-Hookean term.

In soft-robot morphology tests, interior-node gradients improved swimming fitness by 0.73-1.07 over a surface-only variant, while voxelized versions of the same designs landed 32-63% lower. Code and media are still under review, but the paper makes a strong case that sphere packing could be a practical volumetric representation for optimization-heavy workflows.