Non-planar slicing for high-genus surfaces with non-coplanar interfaces

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.