The dome of the Basilica de la Virgen de los Desamparados of Valencia is an emblematic example of Valencian baroque architecture and painting. Its shape, oval or elliptical, has been the subject of controversy in various studies. The study of oval domes throughout history is a very interesting field of research because, among other things, the determination of the exact shape is important in order to conclude how it was built. We approach the problem from a new mathematical point of view, calculating the distances between the points that make up the real data cloud and the hypothetical form considered, oval or ellipse. The use of modern graphic surveying techniques, carried out with a 3D laser scanner, and computation with the powerful symbolic and numerical mathematical solver, Mathematica, has allowed us to accurately determine the shape of the dome and determine that its sections are not well-described by ellipses. A better fit is obtained assuming that sections are ovals. The programming and generalization of the mathematical method employed in this work will allow it to be applied to determine the exact geometry of other oval or ellipsoidal vaults.

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椭圆形圆顶。瓦伦西亚圣母教堂的案例

瓦伦西亚圣母教堂的圆顶是巴伦西亚巴洛克式建筑和绘画的标志性例子。它的形状，椭圆形或椭圆形，在各种研究中一直是争论的主题。历史上对椭圆形穹顶的研究是一个非常有趣的研究领域，因为除其他外，确定确切形状对于确定它是如何建造的很重要。我们从新的数学角度来解决这个问题，计算构成真实数据云的点与所考虑的假设形式（椭圆形或椭圆形）之间的距离。使用现代图形测量技术，通过 3D 激光扫描仪进行，并使用强大的符号和数值数学求解器 Mathematica 进行计算，使我们能够准确地确定圆顶的形状，并确定它的截面没有用椭圆很好地描述。假设截面是椭圆形，可以获得更好的拟合。这项工作中采用的数学方法的编程和概括将使其能够应用于确定其他椭圆形或椭圆形拱顶的精确几何形状。