## 2 Materials and Methods
### 3D Virtual Reconstruction of the Power Corridors
#### 2.5.1 Collecting the Description Data of Power Corridors
After optimal view selection, the actual size data was derived using the LT method. For example, in Figure 7b, we assumed that only two optimal views were retrieved for the tower depicted in Figure 7a. Then, we manually measured the projected image coordinates of the two endpoints (red crosses) of this tower's side trestle (green lines in Figure 7b) in each optimal image. After that, their corresponding 3D spatial coordinates in the SC system were computed based on the LT method according to Equation (1), using the corresponding homogeneous coordinates of the image and 3D points. This side's trestle length (i.e., spatial distance labeled with 21.218 m) is further calculated. Others demanded the same way to obtain size data. Second, once the required data size of a tower was known, we used the third-party 3D modeling software to complete the virtual 3D reconstruction of the tower in the actual model scale. This study employs the 3 ds Max software, which is commonly used in 3D modeling, and the result was exported in OBJect (OBJ) format, widely used in exchanging 3D software models [49]. Third, the OBJ standard was converted to Graphics Library Transmission Format (gITF). using the obj2 glft tool to load and display the model in the Cesium virtual globe. We chose gITF because it enjoys broad support and free licensing, can be saved as text or binary, and supports the entire scene with assemblies, colors, and materials. It should be noted that the structure type of the towers in the same power corridor may differ, meaning that one power corridor may comprise several tower types. In our study, we discriminated them with a model filename, e.g., i.gITF, where \(i\) is an identifier of the \(i\)th tower type, ensuring that the same type of tower has a unique identifier. The storage and access methods are the same as that of the realistic 3D model as discussed above. \[\gamma=\arccos\frac{\left(t_{i}-\tilde{X}_{\text{T}}\right)\cdot\left(t_{j}- \tilde{X}_{\text{T}}\right)}{\left\|t_{i}-\tilde{X}_{\text{T}}\right\|\cdot \left\|t_{j}-\tilde{X}_{\text{T}}\right\|}\ (i,j=1,\ \ldots,p)\text{ with }i\
eq j \tag{4}\]  
Figure 7: Workflow diagram for reconstructing power corridors. (**a**) Determining the position and orientation parameter in the Cesium virtual globe, (**b**) collecting the size data of a tower based on the LT method, (**c**) the reconstructed 3D virtual model and 3D visualization in the Cesium environment, and (**d**) partial results of one reconstructed power corridor. Determining the orientation parameters of a tower in Cesium virtual globe: We obtained the gITF-based 3D virtual models of the towers. However, when rendered in a Cesium virtual globe, the reconstructed 3D virtual tower model utilizes a relative coordinate system with six-degree-of-freedom (DOF). As we obtained the 3D location of the power T(\(\mathit{lont_{T}}\), \(\mathit{lat_{T}}\), \(\mathit{alt_{T}}\)) in step (1), there are three other orientation parameters defined by three angles (i.e., heading, pitch, and roll) relative to the Cartesian coordinate system that is a three-dimensional, earth-centered reference system used in Cesium virtual globe, in which locations are identified by their \(x\) (East), \(y\) (North), and \(z\) (Zenith) values. When the Cartesian coordinate origin was placed at the location as T(\(\mathit{lont_{T}}\), \(\mathit{lat_{T}}\), \(\mathit{alt_{T}}\)), the corresponding geometric meanings of the above three angles are depicted in Figure 7a. The pitch and roll angles were set to zero in our study. The heading angle, corresponding to the orientation angle defined in the 2D Gauss planar coordinate system commonly used in surveying and mapping fields, was computed using the line-segment vector formed by the two sequentially selected tower bases (blue dots in Figure 7a) in the Cesium environment. This value should be within 0\({}^{\circ}\) to 360\({}^{\circ}\). We have developed a tool contained in \"GIS tools\" (Figure 3) to compute the value of the heading angle.