Surface Offsetting: A Survey from Geometric Construction to Neural Implicit Representations

Surface offsetting is a fundamental geometric operation in computer-aided design, manufacturing, robotics, and computational physics. Despite its conceptual simplicity, generating offset surfaces robustly and efficiently for complex and irregular geometries remains a persistent challenge, hindered by self-intersections, topological inconsistencies, and feature degradation. This paper reviews recent advances in the field of surface offsetting, offering a structured overview of the evolution of techniques from classical constructive methods to contemporary neural implicit representations. Our survey addresses a gap in the literature, as prior foundational reviews over the past two decades in this field focused primarily on parametric methods. We introduce a taxonomy that organizes existing algorithms into five principal classes: Constructive, Spatial Discretization, Optimization-based, Field-based, and Learning-based approaches. An analysis of 46 representative algorithms reveals trade-offs in algorithm design: achieving both geometric accuracy and topological correctness proves difficult, and representation choices introduce inherent complexity constraints. We identify open problems including offset generation for surfaces with open boundaries, preservation of thin features, and resolution of self-intersections in concave regions. These challenges point toward promising research directions, including extending classical offset theory to non-manifold and open-boundary domains, developing scalable geometric predicates, and designing hybrid neural representations that disentangle distance-field smoothness from geometric sharpness.