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.
Experimentation of a Web Database for Augmented Reality Apps: The Case Study of Ruled Geometries
This paper presents the development and testing of a web-based database designed to support augmented reality applications for the visualization and study of complex geometries. The research focuses on ruled surfaces as a case study, proposing a digital platform that aggregates, classifies, and distributes 3D models enriched with geometric and descriptive information.
The methodology involves the creation of an open and scalable website that enables model visualization, download, and upload, as well as real-time integration with AR applications through APIs and structured data formats such as JSON. A taxonomy of ruled geometries is defined based on combinations of directrices, and a curated dataset of parametric 3D models is implemented to support both educational and experimental uses. The system allows multiple modes of interaction, including direct model download, dynamic linking to AR environments, and collaborative content generation. Results demonstrate that web-based geometric archives can enhance the accessibility, understanding, and dissemination of complex spatial forms, while supporting immersive learning and future integration with emerging environments such as the metaverse.