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Urban sprawl has led to various economic, social, and environmental problems. Therefore, it is very significant to improve the efficiency of resource usage and promote the development of compact urban form. It is a common topic that measuring urban compactness is done with certain ways and methods as well. Presently, most urban compactness measurement methods are based on two-dimensional (2D) formats, but methods based on three-dimensional (3D) formats that can precisely describe the actual urban spatial conditions are still lacking. To measure the compactness of the 3D urban spatial form accurately, a 3D Compactness Index (VCI) was established based on the Law of Gravitation and the quantitative measurement model. In this model, larger 3D Compactness Index values indicate a more 3D-compact city. However, different urban scales may influence the discrepancy scale of different cities. Thus, the 3D Compactness Index model was normalized as the Normalized 3D Compactness Index (NVCI) to eliminate such discrepancies. In the Normalized 3D Compactness Index model, a sphere with the same volume of real urban buildings in the city was assumed as the most compact 3D urban form, and which was also calculated by 3D Compactness Index processing. The compactness value of the normalized 3D urban form is obtained by comparing the 3D Compactness Index with the most compact 3D urban form. In this study, 1149 typical communities in Xiamen, China, were selected as the experimental fields to verify the index. Some of communities have a quite different Normalized 3D Compactness Index, although they have a similar Normalized 2D Compactness Index (NCI), respectively. Moreover, comparing with the 2D Compactness Index (CI) and Normalized 2D Compactness Index (NCI), the 3D Compactness Index and Normalized 3D Compactness Index can describe and explain reality more precisely. The constructed 3D urban compactness model is expected to contribute to scientific study on urban compactness.

A Promotional Construction Approach for an Urban Three-Dimensional Compactness Model—Law-of-Gravitation-Based