Abstract: As a visiting card of a city, the skyline reflects the overall image and development of the city. However, most evaluations of skylines are subjective, and it still lacks an objective quantitative judgment criterion. This study plans to propose a new judgment criterion for skyline.
　　The following steps acquired the specific classification ranges of the urban skyline: (1) The quantitative factors related to the height of the skyline were extracted, including contour tortuosity, building undulation and the skyline rhythm index. Then, the research objects were chosen 15 physical pictures of skylines of the first-tier cities in China from a horizontal view angle. The skyline profile was simplified and zoomed into the actual size in AutoCAD. The skyline length was fixed at 2,000 m. Numerical values of contour tortuosity, building undulation and the skyline rhythm index were calculated. (2) A questionnaire survey with 220 respondents was carried out. Pearson's correlation analysis and linear analysis of collected data were completed using SPSS software. Pearson's correlation analysis determined the correlation degrees of the above three quantitative factors with pleasure. The linear analysis was to determine fluctuation trends of the above three quantitative factors. (3) A classification dendrogram was developed by the intra-class classification and Pearson's classification. The specific classification ranges were formed by combining with pleasure. 
　　The results of correlation analysis showed that the correlation coefficients (R-values) value of 0.584 for contour tortuosity, 0.432 for building undulation and 0.302 for the skyline rhythm index. Contour tortuosity showed the highest correlation with pleasure, followed by building undulation and the skyline rhythm index successively. The linear analysis showed that pleasure fluctuates with the increase of contour tortuosity, building undulation and skyline rhythm index. Moreover, the skyline evaluation of respondents did not increase accordingly. Therefore, different ranges of indexes correspond to different ranges of pleasure. Next, a systematic cluster analysis of contour tortuosity, building undulation and skyline rhythm index was carried out. Four types of urban skylines and their corresponding characteristics and ranges were acquired. The first type has primary and secondary buildings and generally at least two undulations, with rich contours and explicit density. The second type has 1-2 flat undulations, and building density is very high. The third type has one undulation, and the building density is high. The fourth type has one obvious undulation, and building density is high. These four types of skylines were further classified into three sub-classes according to pleasure scores on the Ketterman scale. Class A is mainly Class-I urban skylines with better pleasure and strong urban economic activity. Class B contains Class-I, Class-II and Class-III skylines with moderate pleasure. Class C is mainly Class-IV urban skylines with poor pleasure.
 　　Some conclusions could be drawn: (1) Since the contour tortuosity shows the highest correlation with pleasure, it is the primary influencing factor of the appearance of the whole skyline profile. (2) When either the contour tortuosity or building undulation or skyline rhythm index rises, the pleasure fluctuates up and down. Thus, the designer should consider the design of the whole skyline profile to control the three factors within the high range of pleasure to ensure aesthetics and subjective pleasure at the same time. The higher contour tortuosity, building undulation and the skyline rhythm index may not bring higher pleasure. Instead, pleasure fluctuates with the increase of contour tortuosity, building undulation and the skyline rhythm index. Therefore, designers should control all three factors within a range of relatively high pleasure during the design of the whole skyline profile, assuring both a beautiful appearance and subjective pleasure. (3) Existing urban skylines can be divided into four types according to the existence of primary and secondary buildings, the number of undulations, richness of the contours and building density. (4) The skyline range that brings people the most pleasure is determined in this study. The optimal ranges of contour tortuosity, building undulation and skyline rhythm index are 1.15-1.97, 0.84-1.29 and 0.38-0.75, respectively. These ranges can provide designers with some references during the urban design. Designers are recommended to increase or decrease numerical values of contour tortuosity, building undulation and skyline rhythm index appropriately to assure aesthetics of the skyline.

Key words: urban skyline, quantitative evaluation, contour tortuosity, building undulation, skyline rhythm index, visual perception quantification

摘要： 天际线作为一个城市的名片，反映了城市的整体形象与发展。对城市天际线的评价，多为主观评价，缺少客观、量化的评判标准。拟提出一种新的天际线的评判标准。首先提取与城市天际线高度有关的量化因子：轮廓曲折度、建筑起伏度与天际线节奏指数，选取15个典型城市天际线照片进行简化分析，通过问卷的形式对220人进行调研；然后利用spss软件，探讨城市天际线的美观感受与美观量化因子之间的关系，得到具体的分类范围；最后形成天际线评价体系，为城市设计者提供参考。

关键词: 城市天际线, 定量评价, 轮廓曲折度, 建筑起伏度, 天际线节奏指数, 量化视觉感受