Geometric Assessment of Curvatures in Ribbed Vaults from TLS Point Clouds

The history of construction has always been characterized by an almost dogmatic search for geometric-proportional rules to govern, and sometimes motivate, design and construction choices. This rule, a messenger of physical truths and, at the same time, imbued with mystical meanings, has dominated “building”; from the “great measure” mentioned in the book of Ezekiel to the Renaissance treatises first, and then the modern ones, the geometric rule and proportion have been necessary and sufficient factors in establishing the strength of buildings. Even when the science of construction, as we understand it today, appeared in the 18th century, it often had to give way to the geometric rule, the so-called “science of building”, a little inherited from the past and a little sought after, a little construction practice and a little link between man and the divine. Gothic architecture is emblematic, capable of combining almost ancestral meanings with a spasmodic search for standardisation which, starting from a single wall thickness, could lead to the design of an entire cathedral. Vaulted systems are not immune to this, and although of unparalleled complexity, they often follow basic codified rules based on a single parameter: the curvature of the ribs. This paper proposes an analysis of some case studies in search of these characteristics and their invariance in order to hypothesize an automated process that, starting from the point clouds of the surveys, produces a synthesis representation of the vault curvatures.