BEST FIT ANALYSIS IN THE GEOMETRY CHARACTERIZATION OF DOMES

The analysis of an ancient building is not independent from the investigation of its generating model; moreover, as confirmed by historic documents, architectural shapes are generally based on precise geometric rules. Especially in the construction of daring structure like domes, the design often followed rules derived from the direct observation of famous examples, considered as reference models, as well as from the study of historic treatises, as those written by Fontana, Vittone e Valadier. These treatises proposed an ideal shape for domes, trying to reach the optimum balance between stability and beauty. The present work illustrates the results of a wider research on historic and constructive aspects of several domes built between the XVIII and the XIX century in eastern Sicily, after the devastating 1693 earthquake. The study describes how to identify the original geometric shape of a dome, by comparing the geometric rules and the correspondence between the real and the geometric shape. To this purpose, a novel analysis procedure has been here specifically developed. In fact, the common practice of analyzing just one profile is not sufficient to define the entire dome 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 a best-fit 3d surface analysis, it is possible to check the overall dome geometry. In this way, the iterative best-fit process allows determining the axis and the internal diameter of the geometric dome, within a set accuracy. This method was applied to the case study of the Catania Cathedral and may be extended to determine the geometric rules adopted in other late baroque Sicilian domes. The shape of the examined dome, completed in 1802, well corresponds to the dome model drawn by Giovanni Biagio Amico, the most famous Sicilian treatise writer of the time. The study consisted of two phases: data collection by high precision survey with 3d laser scanning technology, and data analysis. After verifying that the surveyed intrados profile matched Amico’s one, the relative revolution surface was generated and a best fit analysis to the surface obtained by the survey was performed, according to both a geometric and analytic procedure. In the first procedure we used the native functions of several modeling software packages, such as 3DReshaper, which allowed obtaining the displacement between the two surfaces and the best location of the geometric axis. In the second one, through a non-linear regression analysis, using Matlab software, we fitted the survey data to the analytic equation that describes the profile of the theoretic dome and, using the internal diameter as a variable parameter, we defined the position of the geometric axis. The results obtained with the two procedures were compared in terms of accuracy and computing speed. Once the procedures will be tuned, it will be possible to apply them to a larger number of cases.