Curvature-informed paths for shell 3D printing

The construction of thin, doubly-curved shells poses significant challenges, often necessitating expensive fabrication techniques and extensive formwork. Non-planar 3D printing enables precise fabrication of these geometries with reduced formwork. Curvature plays an important role in the design of non-planar print paths. Nevertheless, designing print paths informed by curvature presents a complex challenge, as there are various curvature properties to consider. Although the significance of curvature has been studied extensively in methods like grid shell construction and surface paneling, its impact on the design of print paths has been overlooked. This paper addresses this gap by examining print paths as curves embedded in doubly-curved surfaces, analyzing their normal curvature, geodesic curvature, and geodesic torsion along and orthogonal to the print direction, and evaluating their effects on printing feasibility and surface quality. The findings are applied to print a large-scale anticlastic surface, with reflections on the impact of different curvature alignments.