Gradient-based representation for open-plan residential layout generation with architectural evaluation

Open-plan layouts challenge conventional representation and evaluation methods due to their ambiguous boundaries and overlapping functional zones. Existing generative approaches commonly rely on discrete functional labels, which limit the representation of spatial continuity and transitional relationships. This study proposes a gradient-based representation that encodes architectural space as continuous spatial fields, enabling the modeling of functional transitions in open-plan residential layouts. A generative framework is employed to produce layout alternatives across datasets and geometric conditions, including orthogonal and non-orthogonal configurations. The generated layouts are converted into vector-based representations to enable architectural analysis. Evaluation is conducted through a multi-layered framework that combines open-plan architectural metrics, spatial performance metrics, and statistical similarity metrics. The comparative evaluation indicates lower wall fragmentation and higher integration values in layouts generated with the proposed representation. The generated layouts also exhibit spatial hierarchies characterized by differentiated relationships between common and private spaces. Differences observed across orthogonal and non-orthogonal morphologies further reveal the influence of geometric conditions on accessibility and spatial organization. The study contributes a representation-driven framework that integrates generation and evaluation, offering a structured method for interpreting spatial relationships in generative design. The findings highlight the role of spatial representation in automated layout generation.