Point Cloud Segmentation and Filtering To Verify the Geometric Genesis of Simple and Composed Vaults

Abstract

<p><strong>Abstract.</strong> 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.</p>

Algorithmic Modeling for Complex Vaults in Vittone’s Civil Architecture Between Archival Drawings and Realizations

“…The first phase of work involved the analysis and creation of the main vault surface of this room, a cloister on a rectangular base of 7.27 × 6.76 m and a rise equal to 2.10 m. The analysis of the point cloud of the sections of the main vault portions allows us to prefer, both for adherence to the cloud, a geometric construction from ellipse arcs as opposed to polycentric arcs with three centers, with a final result more controllable and manageable during the construction phase of the visual algorithm (Lanzara et al 2019) (Fig. 2).…”

Banded vaults with independent arches: analysis of case studies in Turin baroque atria

“…This results in finding and analysing the characteristic sections of the vaulted structure [19], in this case the component of bands generated by independent arches.…”

Parametric Library for Ribbed Vaults Indexing

“…To extract planar geometries (perimetral, diagonal, crown and tiercerons arches), we have done the point cloud sections using a series of vertical planes perpendicular to the spring plane (Lanzara et al, 2019). Then, point cloud segments were analyzed according to visual scripting logic.…”