Volumetric landscape: The mix characteristics and co-agglomeration of 3D space use in compact cities

• Reveal mixed-use characteristics across multiple scales: floor, building and local. • Develop a three-stage approach to identify 3D neighbouring inertia among space uses. • Map local colocation patterns of space uses to capture 3D geographical heterogeneity. • Guide urban function allocation and floor space usage for a volumetric paradigm shift. High-density and compact urban development have become popular globally, leading to volumetric changes in the built environment. However, knowledge of space use interaction in cities remains horizontally dominated. Therefore, beyond traditional land use study, this research aims to study how urban space use mixed within the 3D built environment. We explore the pattern of space uses in the 3D context from the scales of floors, buildings to local area, to better understand how volumetric urbanism shape cities. The City of Sydney in Australia is selected to capture the characteristics of 15 uses with a three-stage approach. The mixed-use degree, based on the Shannon Diversity Index, is crucial in determining the composition of uses within floors and buildings. The hidden pull and push dynamics among space uses illustrate the co-exist and spatial interaction of uses at floor and building scales. The co-agglomeration pattern of space uses from colocation analysis via ArcGIS Pro indicates neighbouring relationships, providing a foundation for the spatial interrelationship of uses for future 3D urban use modelling; while local colocation results indicate the geographical differences, enabling the identification of functional deficiencies in cities. For instance, green and open space was colocated with residential use but shows a local isolation pattern around the CBD, while office use was isolated from residential use but shows a local colocation pattern on the CBD edge. This research contributes to monitoring urban dynamics, supports sustainable governance practices, and advances volumetric perspectives, highlighting the essential transition from land use mix to floor use mix.