<p>Existing mesh-based and voxel-based modeling methods encounter difficulties when dealing with lattice structures with apparent multi-scale characteristics. In this study, we introduce a novel representation framework for lattice structures, achieving an efficient function representation (F-Rep) of various lattice structures. Specifically, the representation comprises three components: a single-scale representation supported by single-scale queries, a middle-scale representation linked to the macro–micro scale, and a multi-scale query mechanism. A unified function representation defines the geometry and topology of microstructure objects. At the same time, a half-face encoded data structure establishes the geometric operations between adjacent microstructure objects. The multi-scale query mechanism, represented by point membership classification, describes the relations between different scale objects. This paper details the efficient algorithms and data structures used in each component. The proposed representation method provides compact, precise, and arbitrarily parameterized coherent microstructures. We illustrate the proposed method with several examples to demonstrate its effectiveness and efficiency for various applications. The spatially varying structure of the gradient lattice is generated through different function fields. Additionally, the proposed method supports various filling strategies, including uniform, conformal, and random lattices, to satisfy diverse design requirements. Moreover, the direct manufacturing approach is implemented based on the multi-scale query mechanism, eliminating the need for auxiliary representations such as polygon meshes or voxels.</p>