Building height is one of the most important determinants of streetscapes. According to zoning regulations in countries such as Japan, building heights are indirectly controlled by the floor area ratio (FAR). The maximum FAR and the building coverage ratio (BCR) represent the main tools of zoning regulations, which legally regulate building shapes and volumes based on plot sizes at the district scale. If plot sizes and shapes are uniform due to zoning regulations, uniform building shapes (both their plane shapes and heights) may emerge. However, in Japan, plot sizes and shapes are not only non-uniform but irregular. Furthermore, the plot is a conceptually and analytically ambiguous concept and data regarding plot shapes and building heights are unavailable. Therefore, it is difficult to understand the relationship between variations in building heights and zoning regulations. These issues prompt the following research question: How can we estimate building height distribution under zoning regulations at the district scale? To answer this question, plot shapes are objectively defined as area Voronoi cells whose generators are building polygons and road networks. Then, the following two analyses are carried out in downtown districts of the Tokyo metropolitan region. First, the relationship between plot sizes, BCR and building heights is analysed. It is found that building heights scale sub-linearly to plot sizes. Second, following this relationship, the probability density function of building heights under zoning regulations is theoretically derived as a log-normal distribution, primarily estimated from building density, road network density, average road width, BCR and FAR. This is compared with the empirical distribution of discretised building heights and the difference is investigated. Furthermore, how to harmonise variations in building heights is discussed by considering their opportunities and external costs. These findings are expected to provide urban planners with a theoretical basis for creating harmonious streetscapes.

建筑高度是街景最重要的决定因素之一。根据日本等国家/地区的分区规定，建筑物的高度由建筑面积比（FAR）间接控制。最大FAR和建筑物覆盖率（BCR）代表了分区法规的主要工具，分区法规根据区域规模的地块大小合法地监管建筑物的形状和体积。如果由于分区规定，地块的大小和形状一致，则可能会出现统一的建筑物形状（包括平面形状和高度）。但是，在日本，地块的大小和形状不仅不均匀而且不规则。此外，该地块在概念上和分析上都是模棱两可的概念，有关地块形状和建筑物高度的数据不可用。因此，很难理解建筑物高度的变化与分区规则之间的关系。这些问题引发了以下研究问题：如何根据分区规章在区域范围内估算建筑物的高度分布？为了回答这个问题，将地块形状客观地定义为区域Voronoi单元，其生成器正在构建多边形和道路网络。然后，在东京都会区的市区进行以下两个分析。首先，分析了地块大小，BCR和建筑物高度之间的关系。结果发现，建筑物的高度与绘制的大小成线性比例。其次，按照这种关系，在分区规则下，建筑物高度的概率密度函数理论上推导为对数正态分布，主要根据建筑物密度，路网密度，平均道路宽度，BCR和FAR估算。将其与离散建筑物高度的经验分布进行比较，并研究差异。此外，通过考虑其机会和外部成本，讨论了如何协调建筑物高度的变化。这些发现有望为城市规划者提供创建和谐街道景观的理论基础。