Exploring Geometric Transformation Procedures Through Physical Models and Holography

Abstract

The combination of digital and traditional methodologies in visualisation is an integral aspect of architectural and design practice. This integration is particularly evident in the generation of forms and shapes, from initial conception to realisation, facilitating the interplay of diverse fields. These hybrid methods involve volumetric transformations grounded in geometric principles, defining tools for generating and analysing shapes by incorporating 3d modelling and advanced manufacturing techniques.
This paper critically reflects on the relationship between geometry and form development by exploring the geometrical transformations of regular polyhedra. Using operative design as a tool for spatial formation, a catalogue of shapes is generated to examine how their combination can inform potential design processes. The physical and geometric qualities of the objects produced are analysed using 3D-printed models, complemented by traditional holographic representations. In particular, optical holography is employed as a visualisation medium, offering dynamic and immersive perspectives and revealing the complexity of geometric forms, engaging the viewer in a multidimensional experience.
This research highlights the fundamental role of geometry in architecture and design, encouraging the development of a structured framework of geometric principles and operations. This framework is designed to support iterative and dynamic design processes, enhancing the understanding of spatial relationships and serving as a heuristic tool for addressing the challenges of spatial complexity.