Geometric modelling has been a crucial component of the design process ever since the introduction of the first Computer-Aided Design (CAD) systems. Additive Manufacturing (AM) pushes design freedom to previously unachievable limits. AM allows the manufacturing of lattice structures which are otherwise close to impossible to be manufactured conventionally. Yet, the geometric modelling of heterogeneous lattice structures is still greatly limited. Thus, the AM industry is now in a situation where the manufacturing capabilities exceed the geometric modelling capabilities. While there have been advancements in the modelling of heterogeneous lattice structures, the review of relevant literature revealed critical limitations of the existing approaches. These limitations include their inability to model non-linear variation of geometric parameters, as well as the limited amount of controllable geometric parameters. This work presents a novel geometric modelling methodology based on function representation as an attempt to bridge this gap. The proposed approach avoids the manual definition of geometric parameters and provides a method to control them with mathematical functions instead. A software prototype implementing the proposed approach is presented, and several use-cases are analysed.

翻译：几何建模自首个计算机辅助设计（CAD）系统问世以来，始终是设计流程中的关键组成部分。增材制造（AM）将设计自由度推向了此前无法企及的高度，能够制造出传统方法几乎无法实现的点阵结构。然而，异质点阵结构的几何建模仍存在极大局限性，导致当前增材制造行业中制造能力已超越几何建模能力。尽管异质点阵结构的建模研究取得进展，但对相关文献的综述揭示了现有方法的重大缺陷：其一是无法实现几何参数的非线性变化建模，其二是可控几何参数数量有限。本研究提出一种基于函数表示的新型几何建模方法，旨在弥补这一差距。该方法通过数学函数替代人工定义几何参数，实现了参数化控制。本文展示了实现该方法的软件原型，并分析了多个应用案例。