Abstract:As a typical traditional military defensive settlement, cantonment is of great significance to recognize its spatial form and construction wisdom for its scientific protection and sustainable development. The article takes Bao’an four cantonments in Tongren City as the research object, and analyzes their spatial morphological characteristics by several mathematical methods. Bao’an four cantonments, namely Bao’an, Wutun, Nianduhu and Guomari, are located in the valley area of Longwu River, a tributary of the upper Yellow River. They not only carry rich historical and cultural heritage, but also are typical representatives of ancient cantonment in the Qinghai-Tibet Plateau. In the early stage of the study, the formation history and current situation characteristics of Bao’an four cantonments were briefly summarized. Then, through AutoCAD software, the outer contour lines of buildings and public activity places, the street road network and the border of Tunpu are digitized, and their building bottom, public space bottom and road axis are obtained. The boundary shape index and the fractal dimension of public space are used to determine the geometric shape of the military camp boundary, and to quantify the degree of compactness and structure of the internal space form of the cantonment. Although the boundary of Bao’an four cantonments is fingerlike, its shape tendency is different. The Nianduhu cantonment is banded, while the other three cantonments are clumpy (Tab.2). Generally speaking, the finger-shaped boundary shape means that the security four cantonments have a high spatial compactness, which is due to the need of military defense function and the influence of local natural geographical environment. There are few agricultural lands around cantonment, and the finger-shaped layout can not only reduce the occupation of cultivated land, but also facilitate the development of agricultural production activities. The fractal dimension values of public space in Bao’an four cantonments are all greater than 1.5 (Tab.3), and the cantonments are strongly structured. This shows that although they are located in different areas, the cantonments are all confined by the fortress wall, and they rely on less public space to organize more residential buildings and public buildings, which is compact. At the same time, Cantonment is a kind of densely distributed settlement of construction groups, so it is suitable to use the axis analysis method in space syntax to analyze and calculate the degree of integration, coordination and control of Bao’an four cantonments, and analyze the spatial similarity and difference between them. The axis of the warm color system of the overall integration degree of Bao’an four cantonments (Fig.6) is mainly concentrated in the central area of the cantonments, indicating that the center of most cantonments is the most accessible and dynamic area, which is closely related to the daily life of residents. The warm color axis of local integration (Fig.7) is mainly distributed in the main entrance and exit of cantonments and its connected streets, or the main movable nodes and their connected streets. For example, Bao’an cantonment is mainly distributed in Dusi Yamen, Chenghuang Temple, Guandi Temple, etc. These spaces have the function of defending the enemy and guarding the passage. The coordination degree of Bao’an four cantonments (Fig.8) is less than the highly correlated level of 0.7, that is, the fitting level of local integration and global integration is not high as a whole. This shows that in order to ensure the safety and defense of the military barracks, attention should be paid to the diversity and difference of local spatial forms during construction, so as to avoid the overall spatial forms being easily recognized and understood. The control degree (Fig.9) of Bao’an four cantonments is mostly blue and light blue in cool color, accounting for more than 65% of the total number of axes, indicating that the mutual control degree and influence of each space in the cantonments are low, and the shielding of a single space is good. The reason is that there are no clear primary and secondary roads, many narrow and tortuous streets and lanes, and many lanes are dead ends, and most intersections are T-shaped, forming a more complicated spatial form, which makes the space of the military camp more private and defensive. The results show that the border shapes of the Fortress are finger-shaped with high compactness and strong structure. The central area has high global integration and accessibility, but the coordination degree of local space is low as a whole, and the ability to perceive the whole space from connectivity is low. Although the degree of mutual control of the interior space is low, it is well sheltered. From these, it can be perspective that the superb wisdom of the ancient Chinese in the construction of cantonments is to construct a compact space enclosure, a center with high accessibility and a strong defensive street layout. These conclusions are conducive to the value recognition, reasonable protection and inheritance development of ancient cantonment on the Qinghai-Tibet Plateau.