This paper explores the application of Artificial Intelligence (AI) in design and geometric analysis processes in the CAD environment, with reference to Descriptive Geometry. Although the use of AI in academia is constantly growing, the implementation of artificial intelligence tools for solving geometric problems remains limited. In this context, this research proposes an experimental approach to automate the creation and manipulation of NURBS geometric entities, focusing on the ellipse as a case study. This document details the process of converting curves generated by the ‘Archimedes Compass’ in a 3D space into NURBS ellipses. The conversion is achieved through programming in Python and facilitated by ChatGPT. The analysis shows how the mathematical exactness typical of NURBS may not always be compatible with the requirements of certain geometric procedures, making integration with dedicated algorithms and AI tools necessary. In a broader perspective, the work shows the potential of textual programming and AI in simplifying and generalising complex processes, enabling new levels of precision and flexibility in virtual modelling. Finally, the results obtained and possible future perspectives in different areas of drawing and geometric representation are discussed.
Digital Reconstruction of the Paradox—Escher’s Relativity
This paper explores the digital reconstruction of Escher’s Relativity through geometric analysis, 3D modeling, and extended reality applications. Starting from a perspective decoding of the lithograph, the authors reconstruct a coherent three-dimensional architectural model that preserves the paradoxical spatial logic of the original image. The model is then implemented in augmented reality environments, allowing users to experience and navigate the impossible space at full scale. The study demonstrates how XR technologies can enhance the understanding of perceptual paradoxes, enabling immersive interaction with complex spatial illusions while highlighting the relationship between geometry, perception, and representation.
Perspective Between Representation and AR: the Apse of the Church of St. Ignatius
This contribution studies the ways in which Augmented Reality (AR) can communicate and disseminate knowledge about our cultural heritage in general and, in particular, Architectural Perspectives (AP). The focus is to increase our knowledge and understanding of perspective technique and how the latter deals with the unique mix between the real architectural environment and an illusory space, in this case the decorations of the presbytery and apse of the Church of St. Ignatius in Rome. The specific objective of the study is the possibility to use the Pozzo’s treatise to “augment” its fruition, accompanied by a virtual visit in order to gather more in-depth information about the perspective construction that creates the effect of spatial expansion thanks to this expedient. This decoration is in fact one of the rare cases of a perspective representation of a pictorial project, in turn also a perspective designed by Pozzo; this design is the “activation” element of an AR experience that immediately illustrates the perspective bravura of its creator.
Wood Inlays and AR: Considerations Regarding Perspective
The contribution reflects on the options provided by recent Augmented Reality (AR) applications to the knowledge and enhancement of a nationally and internationally renowned cultural asset: perspec-tive wood inlays.The methodology envisages two closely–connected stages initially involving perspective decoding and ensuing reconstruction of the illusory model, followed by the creation of a set–up for the AR pursuant to the digitalization of the three–dimensional model.In AR, perspective is the ideal tool to virtually experience the space represented in the decoration; at the same time it provides the most suitable solutions required to optimise the AR project.