Cubic Hermite Lattice Structures
Lattice structures are of growing importance in additive manufacturing, where complex internal geometries are increasingly required for lightweight, high surface-to-volume ratios, multifunctionality, and other superior mechanical properties. Conventional lattice modeling methods typically represent struts with simple primitives, such as cylinders or cones, limiting geometric diversity and the design space. Although recent efforts have increased strut-shape complexity to address this issue, they often do so at the expense of computational efficiency and modeling robustness. As a result, achieving both rich geometric expressiveness and efficient computation remains a challenging problem. In this paper, we present an implicit modeling method that expands the design and optimization space of lattice structures while preserving the modeling robustness and efficiency of implicit representations. In our method, each strut is defined as a convolution surface over a skeletal graph, and its profile shape is controlled by a cubic Hermite curve. By exploiting the polynomial structure of both the convolution kernel and the cubic Hermite curve-controlled profile, we derive analytical expressions for efficient field evaluation, avoiding costly and unstable numerical computation. Four case studies have been conducted to validate the proposed method in terms of profile shape diversity, graded lattice modeling, as well as slicing robustness and efficiency.