Renaissance vaults: geometry, nurbs and computational opportunities for reconstruction

Creating an interpretative geometric rep-resentation of architectural shapes is crucial to learn the essence of any architecture, to pre-serve it and to hand it down through the ages to our descendants. Nowadays the generation of an accurate reality-based 3D model from a sur-vey is the first step to set up a geometric model that, before its semantic enrichment, must be geometrically correct. In this paper, we compare different workflows adopted in modelling a Renaissance vault in Santa Maria delle Grazie complex in Milan start-ing from a laser scanner survey acquired within a wider survey campaign of the complex. The vault of the Ancient Sacristy, a Renaissance mas-terpiece by Donato Bramante, has been chosen according to its integrity, despite the bombings suffered by the Complex in 1943. The workflows have been used to optimize a system of com-prehension of the building and to evaluate by analogy a similar vault of the complex added with some reflection at the end: the vault of the Refectory that hosts “the Last Supper” paint-ing. This latter was destroyed by bombing and rebuilt last century on the drawing of a direct survey previously occurred. We can consider the vaulted system as a clear example to practice understanding of the geometric rules of archi-tecture first and the vaulted surface modelling then, to be compared through the principles of descriptive geometry in a dialectical relationship between theory and practice between geometry and construction. In this paper, multi-purpose interpretative models try to read and describe the state of the art and possible declinations of the semantics linked to an architectural object unique in its value.