Spatial compactness metrics and Constrained Voxel Automata development for analyzing 3D densification and applying to point clouds: A synthetic review

Abstract

Abstract A construction operation is known as a complex system whose complicated components can be understood by applying spatial metrics to massive point-based data. Two and three-dimensional compactness metrics are critically reviewed based on the scale of urban modeling, application in urban studies and architecture, and the capability to model spatial and temporal urban changes. This review indicates that there is a lack of a uniform definition of compactness in urban, building and construction studies and a lack of 3D metrics to model spatial and temporal patterns of vertical building developments. To fill these gaps, a new definition of compactness for vertical building developments was developed based on elements of the compactness concept in the literature of urban form in highly dense urban areas by developments of high rise buildings. In addition, spatial data mining methods are suggested for deriving a spatial distribution pattern of building height; a new metric of A* was developed based on 3D Discrete Compactness for comparison of various 3D configurations of the buildings; and Constrained Voxel Automata and volumetric metrics were developed theoretically and proposed for future studies in characterizing spatial and temporal patterns of vertical building developments. It is found that there is a lack of appropriate methodologies to derive the patterns of vertical building development using 3D data such as airborne lidar to meet future needs.