Three-dimensional visibility graph analysis and its application

Graph-based visibility analysis, developed from space syntax and social network theory, embraces mutual visibility between locations in a spatial system. It helps designers and researchers to decode spatial cognition and behavior, but methodological constraints limit its application to two-dimensional floor plans. In this study, we propose a new visibility graph analysis that can be used in three-dimensional built environments, such as multilevel atrium buildings or urban environments with canopies or overpass bridges. Furthermore, we draw a distinction between a generic visibility graph and a targeted visibility graph. In the former, an occupiable location is considered as both the origin and target of visibility lines. In the latter, we further take into account the visible space or specific targets in a system. Visible locations are spaces people can see but cannot necessarily physically occupy. With this differentiation, the visibility graph system is more amenable to new applications in three-dimensional architectural and urban design while retaining a mapping back to the original two-dimensional visibility graph method through the generic visibility graph. Four examples illustrate the application of the proposed visibility graph analysis in complex three-dimensional building and urban environments.