Non-Planar Slicing for High-Genus Surfaces with Non-Coplanar Interfaces (2026-01)¶

3D printing enables efficient fabrication of Materially Optimized Reinforced Concrete Elements (MORCE), but conventional planar slicing methods struggle with their complex geometries, leading to layer misalignment and structural instability. Existing non-planar slicing techniques typically produce solid toolpaths with infill material, making them unsuitable for MORCE, which require surface-based geometries with hollow interiors to accommodate reinforcement, casting, and insulation. A few non-planar slicing models for surface-based complex geometries have appeared recently; however, they rely on heuristic methods that require manual input and involve intervention at multiple stages. This paper presents an analytical model for automated non-planar slicing that generates geometry conforming slices by extracting critical geometric features – such as saddle points at bifurcations and boundary edges. The method uses Morse theory to identify the critical points (i.e. saddle points) and geodesic distance fields to generate a geometry-conforming scalar field that accurately captures critical points and non-coplanar interfaces. A bias term is introduced to correct slice non-uniformity near saddle points, ensuring smooth and consistent slicing. The effectiveness of this approach is validated through comparative analysis on three topology-optimised beams. The proposed method achieves perfect interface boundary conformance across all segments and produces uniform layer transitions, demonstrating robust handling of bifurcations and non-coplanar interfaces.