## 2 Materials and Methods
### 3D Virtual Reconstruction of the Power Corridors
#### 2.5.1 Collecting the Description Data of Power Corridors  
We used a third-party 3D modeling software, 3 ds Max (Version 2021), to reconstruct the 3D virtual models of the power corridors. The required size data were obtained using the linear triangulation (LT) method typically employed in photogrammetry and computer vision applications [47]. Then, the parameters needed by Cesium for rendering and 3D visualization, i.e., 3D locations, posture angles, and hanging points of the power towers, were precisely collected. The implementation procedure is discussed below. 1. Determining the 3D location of a tower in Cesium environment: The 3D location of a tower is defined as the geometric center (red dot in Figure 7a) of the bottom profile determined by its four-tower bases. Although the reconstructed 3D tower structure elements are not complete or clear, the positions of the tower bases can be recognized and measured in their corresponding 3D realistic models. We loaded and displayed the 3D realistic model into Cesium globe on the client side and derived the 3D location of a tower by averaging the manually measured 3D positions of its four-tower bases. Cesium allows the client to provide 3D visualization of a real 3D model on the Earth, which is represented by the World Geodetic System 1984 (WGS84) ellipsoid. Therefore, the computed 3D point location of the tower is represented in WGS84 coordinates and referred to as T(\(lon_{\text{T}}\), \(lat_{\text{T}}\), \(alt_{\text{T}}\)) (Figure 7a), which contains two parts: (1) geographic coordinates (\(lon_{\text{T}}\), \(lat_{\text{T}}\)) that refer to the longitude and latitude values, and (2) \(alt_{\text{T}}\) that refers to the geodetic height relative to the ellipsoid surface along the normal direction. 2. 3D virtual modeling of a tower supported by photogrammetric data: This step includes three parts: (1) collecting the required size data of a tower based on the LT method, (2) 3D virtual modeling of a tower, and (3) data conversion and storage. First, the LT method that uses the two equations for perspective projection to solve for the 3D object point was used to derive the data size of a tower. To exploit the LT method, we search the images in which a tower occurred. This can be realized by reprojecting the 3D location of a tower to the image space using a known projective matrix of each image given by the AT processing step earlier, according to Equations (1) and (2). At this step, we used the photos captured with coarse-scale photogrammetry as candidate images, and the number of retrieved target images was denoted as \(p\). Further, to improve positioning accuracy, a well-conditioned model should satisfy the constraint of the intersection angle \(\gamma\), which is the angle between the two adjacent images mapped by the same points. This angle is calculated using Equation (4). The smaller the value of \(\gamma\), the greater the coordinate error of the object point. The range of \(\gamma\) is set to 30\({}^{\circ}\) to 90\({}^{\circ}\) in this paper. Note that the 3D location coordinates of a tower used for photogrammetric reprojection should use the SC system. Therefore, a coordinate transformation process is required from WGS84 to the SC system. In this study, the geographic coordinates of the tower location (\(lon_{\text{T}}\), \(lat_{\text{T}}\)) are converted to the 2D Gauss planar coordinate (\(X_{\text{T}}\), \(Y_{\text{T}}\)) using the cartographic projections and coordinate transformations library (PROJ), which is a generic library for transferring coordinates among various geospatial reference systems [48]. Regarding the 1D leveling height \(H_{\text{T}}\), we used the known fitting model concerning the case region between geoid and ellipsoidal height for height transformation from \(alt_{\text{T}}\) to \(H_{\text{T}}\). The converted 3D point location of this tower is represented as \(\tilde{X}_{\text{T}}=\left[X_{\text{T}},Y_{\text{T}},H_{\text{T}}\right]^{\text{T}}\) to fit the need of Equation (4).