Measuring variations in streetscape skeletons under zoning regulations of the building coverage ratio: a theoretical approach

The arrangement of buildings along roads is one of the most fundamental patterns of three-dimensional streetscape skeletons, defined as a set of building heights and setbacks in a district. Under zoning regulations, building heights and setbacks are indirectly controlled by the building coverage ratio (BCR) and the floor area ratio (FAR). In particular, variations in the BCR result in variations in building heights and setbacks. Thus, understanding the relationship among variations in the BCR, building heights and setbacks is important to harmonise streetscape skeletons. However, this relationship has yet to be theoretically investigated due to its complexity. To this end, we formulate the relationship between variations in building heights and setbacks as the function of the variance of the BCR. We show that as the variance of the BCR increases, the increase in the variance of building heights is greater than that in the variance of setbacks. This finding can contribute to controlling variations in streetscape skeletons.