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.

摘要

椭圆形几何圆顶的研究涵盖了一个广泛而有趣的研究领域，可以从多个角度进行探讨。本文展示了为从建筑和数学角度分析此类圆顶的几何形状而开发的多学科方法。

本研究论文的重点是对圣母卡马林圆顶、El Puig de Santa Maria 修道院（西班牙巴伦西亚）的几何研究，这是巴伦西亚历史和建筑的标志性建筑。它首先通过多图像摄影测量和其他测量方法进行测量，获得作为几何分析基础的点云。

这种分析的方法是通过图形和数学梯度，它允许确定最能定义圆顶形状的图形布局和方程式，并制定与数据一致的几何构造假设。得出的结论是，圆顶是由一个椭圆平面和垂直截面中的五中心椭圆拱产生的，所开发的方法过程可以应用于其他情况。