Geometrical Analysis of Oval Domes through Architectural and Mathematical Methods. The Case of the Dome of the Camarín of the Virgin of El Puig (Valencia, Spain)

Abstract

ABSTRACT The study of oval geometry domes encompasses a broad and interesting field of research that can be approached from multiple points of view. This paper shows the multidisciplinary approach developed for the analysis of the geometry of this type of domes from the architectural and mathematical points of view. This research paper focuses on the geometric study of the dome of the Camarín of the Virgin, of the Monastery of El Puig de Santa Maria (Valencia, Spain), an emblematic building of Valencian history and architecture. It begins with a survey by means of a multi-image photogrammetry and other surveying methods obtaining a point cloud that has served as a base for the geometric analysis. The approach to this analysis is through graphic and mathematical gradients, which allows to determine the graphic layouts and equations that best define the shape of the dome as well as drawing up a geometric construction hypothesis, which is consistent with the data. The conclusion obtained is that the dome is generated by an elliptical plan and five-centered oval arches in the vertical sections and the methodological process developed can applied to other cases.