Best-Fit Analysis for the Geometry Characterization of Domes

The present work describes a methodology aimed at identifying the theoretical shape of a dome, as conceived by the architect. To this purpose, a novel analysis procedure has been specifically developed to verify the correspondence between the real shape, obtained by a survey, and the geometric one, derived by architectural treatises, when possible. Actually, the common practice of analysing just one profile of a dome is not sufficient to characterize its entire surface since domes often display asymmetries and deformations; this implies that the selected profile may not always be representative of the entire surface. On the contrary, with the best-fit 3D surface analysis here proposed, it is possible to check the overall dome geometry. In fact, the iterative best-fit process enables to determine the axis and the inner profile of the geometric dome, within a fixed accuracy. The study consisted in two phases: (i) data collection by high precision survey with 3D laser scanning technology; and (ii) data analysis, according to both a geometric and analytic procedure. The results obtained by the two procedures were compared in terms of accuracy and computing speed. This dual methodology was applied to the dome of Catania’s Cathedral, built after the 1693 earthquake and completed in 1802.