**1. Introduction**

The ancient temple heritage space is one subcategory of integrated spaces with profound religious architecture, culture, and landscape, which is vital for cultural redevelopment, especially in East Asian countries. With the change and development over thousands of years, the spatial layouts and functionalities of temples in East Asia have been gradually transformed, while many temples have been destroyed or even disappeared due to certain causes, e.g., wartime destruction, lack of maintenance costs, and inappropriate techniques in conservation practices. Spatial planning, planting design, and natural aesthetic values are all the main factors that can affect the conservation and revitalization of ancient temples [1]. Cognitive mechanisms and the characteristics of isomorphic synaesthesia in ancient Chinese temples are also primarily analyzed by some researchers [2]. In recent years, there have been some studies focusing on quantitative estimation for the conservation and management of ancient temples and visitors' sensory perceptions of heritage. Six dimensions in ancient building spaces, i.e., "adoration", " nostalgia', 'liveliness', 'exquisiteness', 'hedonic value', and 'placeness' on visitors' aesthetic experiences are estimated by quantitative methods [3]. A netnographic approach for conducting narrative analysis on heritage

**Citation:** Zhou, K.; Wu, W.; Dai, X.; Li, T. Quantitative Estimation of the Internal Spatio–Temporal Characteristics of Ancient Temple Heritage Space with Space Syntax Models: A Case Study of Daming Temple. *Buildings* **2023**, *13*, 1345. https://doi.org/10.3390/ buildings13051345

Academic Editors: Lucia Della Spina, Maria Rosa Valluzzi, Antonia Russo, Paola Pellegrini and Angela Viglianisi

Received: 27 March 2023 Revised: 16 May 2023 Accepted: 19 May 2023 Published: 21 May 2023

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

tourism marketing is also put forward [4]. An information model of Chinese traditional garden heritage spaces is constructed to improve the accuracy of spatial information and management efficiency, which provides a more convenient solution for the conservation, redesign, and management of temple heritages [5].

Space syntax is a spatial topology algorithm developed by Bill Hillier to estimate and explain the correspondence between spatial form and function quantitatively [6]. The space syntax theory has been widely applied in interdisciplinary space-related fields, which is also applicable to the quantitative spatial estimation for heritage spaces [7]. Space syntax theory suggests that the core of spatial characteristics is the 'association' between spaces [8]. In the spatial configuration system, each geological factor is constrained by the other, and there is a complex internal topological relationship between each element [9]. 'Angular segment analysis' (ASA) and 'visibility graph analysis' (VGA) are two typical space syntax models that have been widely applied in most research, by which complex characteristics of the space are simplified and processed as a grid-based topological system consisting by interconnected constraints [10].

Both ASA and VGA models are effective in representing the spatial configuration changes and the influences by human beings on the space, visualized in a visual graphical language [11]. In the recent decade, spatial syntax has been applied to the study of multiple types of buildings and landscapes, especially been utilized as a convincing tool to assess the spatial organization of cultural heritage sites [12]. Spatial Differences among several typical ancient heritage palaces are compared by multiple space syntax models to guide restoration planning projects for those heritage redevelopment projects, especially for redesigning visitors' routes through the temple heritage [13]. The ASA and VGA models are also applied to estimate the spatial configuration in the case study of temple heritage, e.g., the Canaanite temples, which indicates that the temple heritage spaces are unique in their characteristics, not only in the role they play in the surrounding landscape and region but also in their distinction from the surrounding ancient temple heritage spaces [14].

Space syntax models have also been introduced into some reliable studies related to ancient temples in East Asia. Using spatial syntax modeling, the spatial structure of the Chinese building heritage has been revealed [15]. For instance, the Lion Grove Garden Temple heritage spaces in Suzhou City are estimated based on space syntax theory and found that spatial visual features affect the spatio–temporal distribution of visitors [16]. A space syntax-based analysis method has been developed to assist in improving tourists' spatial cognition in Chinese historic districts for urban designers and landscape architects [17].

However, there are still a few cases of space syntax in space, while the spatio–temporal structural evolution of ancient temples has not been learned thoroughly. Therefore, quantitative estimation by space syntax models is of high potential in the estimation of internal spatio–temporal characteristics of ancient temples, which can offer necessary guidance for the conservation, redesign, reactivation, and redevelopment of similar spaces.

#### **2. Materials and Methods**

#### *2.1. Study Site*

Daming Temple (119.41◦ E, 32.42◦ N) is one of the eight famous monasteries in Yangzhou City, China, which was built during 457–464 A.D. Monk Jianzhen (688–763 A.D., also known as 'Ganjin' in Japanese), the host of the Daming Temple, had once traveled eastward to Japan and built the Tosh ¯ odai-ji Temple, which significantly accelerated the ¯ communication of Mahayana Buddhism culture between China and Japan. Daming Temple has been expanded several times. In the Sui Dynasty, Emperor Yang Jian built the Qiling Pagoda in Daming Temple. During the Northern Song Dynasty, some literati contributed to the design and construction of the temple, e.g., the literatus Ouyang Xiu (1007–1072 A.D.) designed the residence Pingshan Hall in the temple; Su Shi (1037–1101 A.D.), the wellknown writer, calligrapher, and painter, designed and constructed the residence Guling Hall next to Pingshan Hall. During the reign of Qianlong (1736–1796 A.D.) in the Qing Dynasty, Wang Yinggeng (1680–1742 A.D.), a well-known merchant, built the West Garden in

the temple, which was praised by Emperor Qianlong for its scenery. Referring to historical records and ancient literature [18], there was no noticeable change in the spatial layout of the Daming Temple from the end of the Qing Dynasty to 1962. From 1962 to 1973, Jianzhen Memorial Hall by the temple was designed and constructed, which dramatically affected the spatial layouts of the temple garden. After the 1990s, Daming Temple expanded the East District and the West Garden while changes in its spatial layout occurred. Since the 1990s, the financial revenue of the temple has been increasing rapidly for the redevelopment of tourism; thus, the temple's income has been able to cover the large-scale maintenance since the 2010s.

Daming Temple (Figure 1) is a typical representative of a re-activated Buddhism temple in China, which has undergone long-term alterations and expansions. There is an urgent need to study the building space of the Damien Monastery in order to advocate for the conservation and redevelopment of the temple's heritage. Historical maps of 3 periods of Daming Temple were selected respectively, considering the changes in new-built areas, i.e., the construction of Jianzhen Memorial Hall and the expansion of the East District since the 2000s.

**Figure 1.** Two-dimensional map of spaces in the Daming Temple during different periods.

#### *2.2. Methods of Quantitative Estimation*

In the space syntax theory, the spatial structure analysis should focus on the 'spatial configuration', i.e., a set of complex relationships between spaces, all of which are interrelated in a global spatial structure. Spatial configuration can be visualized quantitatively by typical models, i.e., angular segment analysis (ASA), visibility graph analysis (VGA), and agent-based analysis (ABA). These models can reveal the comparability of measures of spatial configuration between different periods of space. The ASA model uses 'angular distance' rather than 'metric distance'. The 'angular distance' can represent the visitors' psychological and cognitive distance, such as the psychological distance expectation when

they pass the steps. The visibility graph analysis (VGA) model in the space syntax system has also been widely adopted in small-and medium-scale spatial studies. As the temple heritage space has been redesigned several times, the structure of the space has changed accordingly. It is, therefore, necessary to visualize the spatial changes quantitatively. In typical Asian temple spaces, the levels of visibility and accessibility are often out of alignment, which can only be represented in the VGA model rather than the ASA model. Therefore, the study involves some parameters and indices in 2 space syntax models mentioned above, which are introduced as follows.

Some indices are commonly used in the ASA and VGA model, including 'Mean depth' (MD), normalized angle integration (NAIN), normalized angle choice (NACH) [19], and connectivity. In the space syntax system, 'depth' is the selected from the system or the amount of space passed through a given starting point. The MD value of a system is the average of all possible steps from a given starting point [20]. Angular segment integration (int.) shows how well each segment is integrated with all other segments, i.e., the total number of directional changes [21]. Angular choice shows the degree of integration of each segment of the path in terms of the lowest total number of angular deviations compared to all other segments. The angular choice analysis shows the potential for through movement in the spatial system [22].

Visual graph analysis (VGA) is a method for evaluating the inter-visibility of spaces. It builds upon the logic of an isovist analysis; it is different in that a visual graph analysis is derived from all the roots of each isovist field from each cell on a given raster. The VGA is applied at eye level (what people can see) and at knee level (where people can move) [23].

In both the ASA and VGA models, the value of connectivity is determined by the number of knots connected to the knot [24], calculated by Formula (1).

$$MD\_i = \frac{\sum\_{j=1}^{n} d\_{ij}}{n-1}, i \neq j \tag{1}$$

where *n*—amount of knot in the system; *dij*—the shortest topological distance between any two points.

The MD value in the VGA model can also be further converted to obtain an 'integration' index. The MD metric is often utilized to express the spatial configuration quantitatively. The 'Connectivity' (con.) index is a static local measure and explains the number of connections that each segment has to its direct neighboring ones. The 'Mean connectivity' (mean con.) index is defined as the average of the connection values of all nodes in the global space [25].

In the ASA model, NACH and NAIN are also adopted in accordance with methods put forward by Hiller et al. [26]. The values of NAIN and NACH can be calculated by Formulas (2) and (3).

$$NAIN\_i = n^{1.2} / \sum\_{j=1}^{n-1} d(i-j) \, ; i \neq j \tag{2}$$

$$NACH\_i = \frac{\log(\sigma\_{s,t}(i) / \sigma\_{s,t} + 1)}{\log\left(\sum\_{j=1}^n d(i,j) + 3\right)}, i \neq j \tag{3}$$

where *n* is the total knot amount; *d* is the shortest distance between point *i* and point *j*.

The 'Intelligibility' index is an indicator of the correlation between the local and the whole in a spatial system. Relevant empirical studies [26] have shown that the intelligibility of space is higher, and visitors will not easily get lost in space, and vice versa. The 'Intelligibility' index can be calculated by the Formula (4).

$$R^2 = \frac{\left[\sum \left(\mathbb{C}\_i - \overline{\mathbb{C}}\right) \left(I\_i - \overline{I}\right)\right]^2}{\sum \left(\mathbb{C}\_i - \overline{\mathbb{C}}\right)^2 \sum \left(I\_i - \overline{I}\right)^2}, \text{ i } \neq j \tag{4}$$

where *C* is the mean of all cell space connectivity values; *I* is the mean of all cell space global integrations.

'Configurational centrality' in spatial syntax is a concept used to describe the degree to which a particular location in a built environment is centrally located in relation to other locations within that environment. It is based on the idea that the spatial layout may affect the way visitors move through spaces [27,28].
