3D Urban Structural Morphology at the Block Scale: A Geometric Vector Framework Based on Mean Building Volume, Height Variation Coefficient, and Mean Sky View Factor

Three-dimensional urban morphology has gained renewed analytical relevance as advances in remote sensing, photogrammetry, and geospatial data processing have made it possible to derive 3D data and high-resolution digital surface and elevation models. Block-scale morphological analysis remains predominantly two-dimensional, leaving volumetric scale, vertical heterogeneity, and spatial aperture undetectable, while existing 3D approaches treat building metrics as isolated variables or rely on costly semantic city models. This study proposes a parsimonious geometric vector framework in which each urban block is represented as a vector of three conceptually distinct dimensions: Mean Building Volume (MBV, volumetric scale), Height Variation Coefficient (HVC, vertical heterogeneity), and Mean Sky View Factor (SVF, spatial aperture). The framework was operationalized through reproducible GIS and Python 3.12 workflows using a large-scale topographic dataset and a LiDAR-derived Digital Surface Model, and it was tested through K-means clustering of 816 statistical blocks in the municipality of Amadora, Portugal. The results confirm the near-orthogonality of the three dimensions (correlations |r| < 0.25; Variance Inflation Factors ≤ 1.08) and identify five structurally distinct typologies ordered along a volumetric gradient (MBV), in which HVC is the principal differentiating dimension among Types 1–4, and SVF distinguishes Type 5; the partition remains stable under 500-iteration consensus clustering (Adjusted Rand Index = 0.9445). The contribution of this study lies in the transferability of the analytical pipeline rather than of the typology itself, which is specific to Amadora and would require independent derivation elsewhere. The framework provides urban planners with a parsimonious, geometrically transparent, and operationally feasible tool for classifying urban blocks in 3D, complementing 2D analytical approaches and establishing a morphological basis for future climate-responsive analyses.