Dal rilievo alla forma. Metodologie di best-fit 2D e 3D per l'analisi e l’interpretazione dell’architettura costruita

This work explores the use of 2D and 3D best-fit methodologies as tools for the quantitative and interpretative analysis of historical architecture, proposing a methodological approach capable of integrating mathematical, geometrical, and historical-critical expertise. The objective is to adapt and customize geometric fitting algorithms for the analysis of three-dimensional models derived from digital surveys, with the aim of reconstructing the ideal geometric model of built architecture and supporting its interpretation through objective and verifiable parameters. The proposed methodology develops and applies different types of best-fit analyses (linear, circular, rectangular, planar, and spherical), with particular attention to the study of column shafts, for which specific criteria of compatibility and classification are defined. The research is structured around a series of significant case studies, including works by Donato Bramante (the Cloister of Santa Maria della Pace, the Bramante Staircase, and the Tempietto of San Pietro in Montorio) as well as earlier monuments (Temple of Antoninus and Faustina, Hagia Sophia, and the Pantheon). The comparative analysis of these architectures allows for the identification of relationships among construction systems, proportional schemes, and compositional logics, thus providing a coherent framework of the geometric and structural principles underlying historical architecture. The results demonstrate how this methodological approach can serve as a bridge between the exact sciences and the humanities, offering a way to reinterpret the architecture of the past through rigorous computational tools that remain sensitive to critical and interpretative dimensions. The project thus stands as a contribution to the science of integrated surveying, capable of combining numerical precision with historical insight, and guiding research toward a deeper, measurable, and shareable understanding of built architecture.