POINT CLOUD SEGMENTATION AND FILTERING TO VERIFY THE GEOMETRIC GENESIS OF SIMPLE AND COMPOSED VAULTS

Abstract. This research work proposes a methodology to statistically determine the geometric configuration of a masonry cross vault. Within Cultural Heritage it is possible to find architectural elements with absent or scarce historical sources about design approach or construction techniques. The cross vault case study belongs to a partially destroyed vaulted system distributed along the aisles of ancient Assunta’s Cathedral which is part of the Aragonese Castle on Ischia island, near Naples (Italy). Using photogrammetrical data acquisition, standard geometric analysis, numerical processes, computing and statistics this paper shows a method to objectively determine the geometric shape which best fits one of the existing Cathedral vault according to critical interpretation about stylistic and cultural contents linked to specific geographical and temporal contexts. This paper provides explanations, methods and objective calculation algorithms to find the best-fitting shape for a generic given point cloud and it is aimed at demonstrating the complementarity between descriptive geometry and algorithmic mathematical approaches. The final product of this multidisciplinary workflow is a 3D model deriving from the comparison between an ideal automatic model built thanks to the translation of traditional geometric rules in visual scripting language and an automatic model deriving from the mathematical analysis of survey data, curves and surface, of the architectural element. This experimentation generates 3D models to perform in-depth multidisciplinary tests and AR and VR applications to promote the communication of destroyed or inaccessible cultural heritage.