The synthesis of porous, lattice, or microstructure geometries has captured the attention of many researchers in recent years. Implicit forms, such as triply periodic minimal surfaces (TPMS) has captured a significant attention, recently, as tiles in lattices, partially because implicit forms have the potential for synthesizing with ease more complex topologies of tiles, compared to parametric forms. In this work, we show how variable offsets of implicit forms could be used in lattice design as well as lattice analysis, while graded wall and edge thicknesses could be fully controlled in the lattice and even vary within a single tile. As a result, (geometrically) heterogeneous lattices could be created and adapted to follow analysis results while maintaining continuity between adjacent tiles. We demonstrate this ability on several 3D models, including TPMS.

翻译：近年来，多孔结构、晶格结构或微结构几何的合成研究吸引了众多学者的关注。隐式形式（如三周期极小曲面TPMS）作为晶格单元近来受到显著关注，部分原因在于相较于参数化形式，隐式形式能够更便捷地合成更复杂的单元拓扑构型。本研究表明，隐式形式的可变偏移量可同时应用于晶格设计与晶格分析，且晶格中的壁厚与边缘厚度梯度可实现完全控制，甚至可在单个单元内连续变化。由此可创建（几何）异构晶格，使其在保持相邻单元间连续性的同时，能够依据分析结果进行自适应调整。我们通过包括TPMS在内的多个三维模型验证了该方法的可行性。