3D STRUCTURE ANALYSIS: ARCHITECTURE AS AN EXPRESSION OF THE TIES BETWEEN GEOMETRY AND PHILOSOPHY
Keywords: Euclidean Geometry, Projective Geometry, Non Euclidean Geometries, Mathematics and Philosophy, Mathematics and Architecture, Philosophy of Architecture
Abstract. In recent decades many Geomatics-based methods have been created to reconstruct and visualize objects, and these include digital photogrammetry, Lidar, remote sensing and hybrid techniques. The methods used to process such data are the result of research straddling the fields of Geomatics and Computer Vision, and employ techniques arising from approaches of analytical, geometric and statistical nature. One of the most fascinating fields of application concerns Architecture, which, moreover, has always depended on Mathematics generally and, more specifically, on Geometry.
Throughout history the link between Geometry and Architecture has been strong and while architects have used mathematics to construct their buildings, geometry has always been the essential tool allowing them to choose spatial shapes which are aesthetically appropriate.
Historically, mathematics and philosophy have been interrelated; many philosophers of the past were also mathematicians.
The link between Philosophy and Architecture is twofold: on the one hand, philosophers have discussed what architecture is, on the other, philosophy has contributed to the development of architecture. We will deal with the ties between Architecture, Geometry and Philosophy over the centuries. Although there are artistic suggestions that go beyond time and space, and there are genial precursors, we can identify, in principle, some epochs: the ancient era, the modern era, and finally the contemporary epoch, from the crisis of positivistic sciences to globalisation.