We introduce a compact, intuitive procedural graph representation for cellular metamaterials, which are small-scale, tileable structures that can be architected to exhibit many useful material properties. Because the structures’ “architectures” vary widely—with elements such as beams, thin shells, and solid bulks—it is difficult to explore them using existing representations. Generic approaches like voxel grids are versatile, but it is cumbersome to represent and edit individual structures; architecture-specific approaches address these issues, but are incompatible with one another. By contrast, our procedural graph succinctly represents the construction process for any structure using a simple skeleton annotated with spatially varying thickness. To express the highly constrained triply periodic minimal surfaces (TPMS) in this manner, we present the first fully automated version of the conjugate surface construction method, which allows novices to create complex TPMS from intuitive input. We demonstrate our representation’s expressiveness, accuracy, and compactness by constructing a wide range of established structures and hundreds of novel structures with diverse architectures and material properties. We also conduct a user study to verify our representation’s ease-of-use and ability to expand engineers’ capacity for exploration.

我们为细胞超材料引入了一种紧凑、直观的程序图表示，这些超材料是小规模的可平铺结构，可以通过构建来展示许多有用的材料特性。由于这些结构的“架构”差异很大（包括梁、薄壳和实心块等元素），因此很难使用现有的表示形式来探索它们。体素网格等通用方法用途广泛，但表示和编辑单个结构很麻烦；特定于体系结构的方法可以解决这些问题，但彼此不兼容。相比之下，我们的程序图简洁地表示了使用带有空间变化厚度注释的简单骨架的任何结构的构造过程。表达高度约束的三周期最小曲面 (TPMS)通过这种方式，我们提出了第一个全自动版本的共轭表面构建方法，它允许新手通过直观的输入创建复杂的 TPMS。我们通过构建各种已建立的结构和数百个具有不同架构和材料特性的新颖结构来展示我们的表示的表现力、准确性和紧凑性。我们还进行了一项用户研究，以验证我们的表示的易用性以及扩展工程师探索能力的能力。