Deterministic τ-based clustering and mould optimization for reusable formwork in curved glulam construction

Abstract This paper presents a deterministic computational workflow for the rationalization of curved glue-laminated beam assemblies through tolerance-based clustering and mold optimization. The method computes equilibrium catenary geometries, evaluates directed Hausdorff deviation, groups beams under a user-defined tolerance threshold, and optimizes shared mold families to reduce formwork requirements. It outputs the number of input curves, the cluster count, the maximum deviation per family, and a tolerance-cluster relationship that supports early-stage design-to-fabrication decision-making. Applied to a curved glulam roof case study, the workflow shows how tolerance governs mold reduction, with three- and eight-cluster scenarios demonstrating the trade-off between geometric fidelity and fabrication complexity, while keeping deviations below one %. A full-scale prototype fabricated from a single optimized jig further demonstrates practical feasibility and controlled as-built accuracy in a low-resource fabrication setting.