The Palatine Chapel Revealed: Methods and Tools for the Geometric Interpretation of Aachen Cathedral

This study presents an integrated workflow combining digital surveying and 3D modeling for the geometric analysis of architec-tural surfaces, with application to the vaulted system of the Palatine Chapel, the Carolingian nucleus of Aachen Cathedral. Since 2022, a collaborative research initiative has conducted an extensive 3D survey of the entire complex. Based on these data, the investigation addressed the morphology of the vaulted structures, focusing on their geometric genesis. The chapel is organized around a central octagon with three levels, surrounded by two ambulatories that mediate the transition to a sixteen-sided pe-rimeter. The lower ambulatory, covered by groin vaults alternating quadrangular and triangular bays, produces a highly permeable space. The upper ambulatory is more articulated, defined by semicircular arches that structure spatial rhythm in plan and ele-vation, with radial chapels and triangular transitional units. The analysis distinguished the geometric principles of triangular and quadrangular vaults by comparing ideal mathematical models with point cloud data. The proposed workflow proved effective in linking constructive knowledge with morphological analysis, clarifying the relation between design intent and built form. The results provide new evidence on medieval construction processes, reference models, and the technical expertise required to achieve complex vaulted systems.