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This research presents the Truchet Tile Grammar, a generative system for crafting geometric tiles and patterns. Drawing its inspiration from the Truchet Tile, originally introduced by Sebastien Truchet in his seminal work Mémoire sur les Combinaisons(1704) and later expanded upon by C.S. Smith in ‘The Tiling Patterns of Sebastien Truchet and the Topology of Structural Hierarchy’ (1987), this grammar establishes shape rules that translate Truchet's conceptual framework into a rule-based specification. The Truchet Tile Grammar comprises three distinct rule sets: 1) Two-Dimensional Tile Rules, 2) Two-Dimensional Pattern Rules, and 3) Extruded Tile Rules. When applied iteratively, this grammar generates extruded two-dimensional tiles. These rule sets can also be independently utilized based on specific design requirements, enhancing the adaptability and utility of this design system.

This research employs shape grammars to generate variations of the Truchet tile to characterize a two-dimensional and three-dimensional generative tiling system.

This systematic review examines the integration of vision systems into robotic fabrication workflows in architecture, emphasizing current methods, computational strategies, and both the potential and limitations of these technologies. The emergence of the Vision-augmented Robotic Fabrication (V-aRF) paradigm represents a significant shift, promising greater precision, adaptability, and creativity in architectural materialization. This is the first paper in the field of architectural robotics to comprehensively review the literature on vision-augmented robotic fabrication. The paper discusses the primary motivations for integrating vision systems in robotic workflows, which include adapting to dynamic robotic workcell conditions and improving the interaction between robotic systems, human agents, and the immediate operational environment. It also underscores critical challenges such as the reliance on controlled operational environments, the computational demands of processing large volumes of data in real time, the difficulties in generalizing systems across diverse materials and techniques, and obstacles in knowledge dissemination and replicability of research findings. By addressing these challenges and harnessing advanced computational methods, this paper presents an implementation-centric methodological framework for V-aRF workflows, which holds the potential for more adaptable fabrication practices. Moreover, it outlines potential future research directions to enhance system autonomy, computational efficiency, and the capability for human–machine co-creation.

Although robotic arms provide precision and control in the fabrication process, they are limited in sensing the environment and responding to it accordingly. This limitation poses significant challenges as robotic tooling operations can only be carried out on surfaces that are knowndigitally. To address this limitation, we propose a vision-based sensing framework to digitally reconstruct and register the work environment prior to robotic tooling operations, with the goal of enabling tooling operations to be carried out on indefinite surfaces. The paper presents the validation of the hardware and software components of the proposed framework for accuracy, reliability, and efficiency in robotic fabrication. Through this validation study, we explore the effects of surface geometry, camera pose configurations, and reconstruction resolution on digital reconstruction and registration accuracy and fabrication feasibility. Moreover, we demonstrate that this framework can be adapted to different fabrication scenarios, including additive and subtractive tooling operations. In a broader perspective, we postulate that the study presented in this paper lays an open-source foundation and a low-cost alternative for future research that can be operationally and computationally scaled and adapted for various areas of applications that deal with complex design-fabrication scenarios.

With an outwardly professed interest in mathematics, Ilhan Koman has produced his nonfigurative, abstract sculptures mostly as various series of forms. The difference and similarity between the works in any series is achieved through repetitions and variations of certain relations between parts. This corresponds to creating a relational system and it requires having control over the underlying principles of that system much as basic design students are encouraged to do. In order to substantiate the implications of work such as Koman’s in learning about design thinking, we first delineate the mathematical concepts in Koman’s “embryonic” approach through visual schemas. These visual schemas are then supplied to first-year design students as guides and design constraints as well as tools to formalize their design thinking. We observe that introducing Koman’s schemas to students helps them grasp how they establish relations between parts in their own design processes.