This study proposes a computational framework for analyzing museum visitor movement as a geometric and perceptual phenomenon, integrating trajectory analysis with space syntax and isovist-based spatial metrics. The framework combines global and local circuity, angular deviation entropy, and configurational and isovist-derived measures of integration, choice, mean visual depth, and area. Results indicate that spatial configuration strongly structures trajectory geometry: visually integrated environments correspond to more direct movement, while fragmented visual fields produce increased circuity and exploratory behavior. A benchmark case using constructed reference trajectories tests the sensitivity of the framework across contrasting spatial and exhibition configurations. The framework extends space syntax toward a dynamic, trajectory-based model of spatial experience.
This study investigates the staircase enclosed within the pagoda core of Chongguang Pagoda in Hebei Province, China, and proposes a method for the geometric analysis and parametric reconstruction of irregular historical architectural spaces. Based on terrestrial laser scanning, horizontal slicing, footpoint parameters, distance-to-length ratios, and recursive parallel construction, the study reveals a geometric logic characterized by rotational stacking, inward corbelling, local angular adjustments, and tangent-arc transitions. The results show that the staircase cannot be adequately explained by conventional center-based spiral models, but is more appropriately interpreted as a rotationally stacked stair system with vault-like characteristics. The proposed method provides a reproducible mathematical description of complex internal spaces in Chinese pagodas and offers new evidence for architectural-historical interpretation and heritage conservation.
This article examines the development and dissemination of a type of stone vault proposed by the Frenchman Gaspard Monge at the end of the eighteenth century, which, until now, had never been built. Monge never provided a detailed design for this type of vault. However, during the nineteenth century, various authors-Monge's disciples-produced specific designs based on his ideas. This study demonstrates that the general concept behind these vaults, namely the geometric notion of lines of curvature, can be applied to other quadric surfaces, making it possible to imagine alternative types of vaults based on the same principles. The historical interest sparked by the geometric questions underlying these proposals, reflected in academic models, is also highlighted. Finally, the paper critically analyzes the characteristics and construction challenges anticipated by 19th-century authors, in light of the recent practical execution of these vaults.
This study investigates the potential of the Hilbert curve as a geometric ordering mechanism for residential layout generation. A rule-based Python workflow was implemented on an 8 × 8 grid, using partial Hilbert segments as circulation spines. From 1000 candidate circulation spines, 94 computationally complete layouts satisfied predefined programme allocation and topological constraints. The layouts were transformed into circulation graphs and evaluated using space syntax metrics, including connectivity, mean depth, integration, and choice. Configurational variation was analysed through Principal Component Analysis (PCA) and K-means clustering within a morphospace framework. The results show that Hilbert-based ordering generates multiple distinguishable configurational patterns rather than a single deterministic layout type. These findings suggest that explicit geometric ordering can produce measurable configurational diversity for rule-based residential layout generation.
This study presents a computable methodology for examining architectural precedents through machine-derived visual similarity. Using the Serpentine Pavilion archive (2000–2025), the SigLIP vision encoder maps 210 images from 24 pavilion/year groups into a multidimensional latent space. Cosine similarity and graph-theoretical modeling generate two complementary networks: an image-level graph and a pavilion-centroid graph based on averaged, L2-normalized embeddings. The centroid graph provides the primary basis for pavilion-level interpretation by controlling for multiple photographs. Network metrics identify central, bridge, and peripheral cases. Comparison across the two analytical levels shows that network-role assignments are sensitive to image aggregation and the unit of analysis, while bridge roles exhibit greater cross-level consistency. The workflow is reproducible and inspectable without treating AI embeddings as neutral or bias-free representations of architectural morphology.
