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Among the many innovative church constructions in the Île-de-France during the twelfth century that immediately followed the ground-breaking new building of the abbey church of Saint-Denis, the high vaults in the cathedral of Notre-Dame in Paris mark a turning point – both in sheer dimensions and in their quality of execution as stone constructions. On the other hand, some solutions in design and construction that can be observed in these vaults remain unique within the dynamic development of Gothic vaulting in the great cathedrals built in the following years. On closer view it turns out that the general design of the vault as well as its construction details are hardly understood until now, mainly because they have been overlooked in a unifying perspective on Gothic architecture coined by the idealistic view of the Gothic Revival in the nineteenth century. Further, the particular relation between vault design and stereotomy needs to be clarified, and its significance needs to be understood.
Johann Dientzenhofer’s Banz Abbey Church (1710-1718) and Balthasar Neumann’s church of Vierzehnheiligen (1743-1772), both located in Upper Franconia (Germany), are characterised by their masonry vaults, sequences of oval domes separated by double-curved arches. This Late Baroque architecture has been called “Guarinesque”; however, the conceptual connection between the vaults and Guarino Guarini’s architecture remains to be thoroughly investigated. This paper resumes the discussion about the geometric definitions of these vaults using the modern methods of geometric analysis and reverse geometrical engineering, based on 3D laser scanning. The analysis of these scans reveals a design process based on plane circle segments and ovals, while more complex geometric procedures are not necessary to describe the vaults. Further, the relationship between these designs and the procedures of geometric design described in the treatises of stereotomy since the 16th century can be shown. On this background, the relation to Guarini’s Architettura Civile (1737) is discussed.