Physics-Based Sphere Packing for Lagrangian Mesh Morphing

This paper studies tetrahedral meshes as the body representation for differentiable simulation and computational design. Both change the shape of a body throughout an optimization and need meshes that follow large shape changes while keeping their interior nodes in correspondence. 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 lower element-volume spread 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: https://anonymous.4open.science/r/jamtet/.