Geometric Analysis of Palazzo Sormani’s Vault through Drawings, Historical Manuals, and 3D Modelling

The oldest part of Milan’s public library, Palazzo Sormani, was built in the 16th century, which was followed by the intricate history of transformations and ownership switches. The research investigates the vaults designed by the architect Francesco Maria Ricchino in 1650 during the major changes of the initial building. The study examines the sail vault over the first-floor staircase landing, combining historical documentation with laser scanning to analyse its geometry and construction techniques. Historical and technical drawings, point clouds, and 3D modelling enabled a comprehensive investigation that revealed significant deviations between the ideal vault form (as described in historical manuals) and the actual structure. The discrepancy between the two can be read in the flattened vault cap and lowered parallel arches, increased on the side of the aperture toward the staircase. By comparing original drawings with manuals by Palladio, Tibaldi, and Guarini, and using digital modelling to visualise geometric anomalies, the study provides insights into Ricchino’s adaptations to existing building constraints. The methodology offers a framework for investigating similar vaulted structures, highlighting potential factors behind geometric irregularities, including construction methods, settling over time, and effects from the 1945 bombing that damaged the palace. This approach enhances understanding of the architectural characteristics of vaults and further supports their preservation.