发表机构
Columbia University（哥伦比亚大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出JamTet，一种基于物理的球体填充框架，用于四面体网格生成和拉格朗日变形，在软体机器人设计中通过内部节点梯度显著提升适应度。
AI 中文摘要
本文研究四面体网格作为可微仿真和计算设计中的体表示。固定连接性的网格在大变形下会退化，而从头重新网格化会丢失节点对应关系。我们提出了JamTet，一个基于物理的球体填充框架，用于体积网格生成和变形。我们的贡献包括：(i)一个GPU并行网格生成器，结合八叉树层次化填充与约束Delaunay四面体化，产生比TetGen和fTetWild更均匀的单元体积；(ii)拉格朗日网格变形，通过在变化的形状内重新平衡相同的球体并重建边界和连接性来保持内部节点身份，在固定连接性和TetSphere网格反转的情况下保持无反转；(iii)一个基于JAX的可微GPU模拟器，具有质量-弹簧边和体积Neo-Hookean项，与网格变形集成在设计流程中。在软体机器人形态设计实验中，内部节点梯度将游泳适应度提高了0.73-1.07，相比于仅表面变体，而相同设计的体素化版本适应度低32-63%。这些结果确立了球体填充作为基于梯度的形状优化的实用体积网格表示。代码和媒体：审阅中。
英文摘要
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.
