# Photogrammetry-Based 3D Textured Point Cloud Models Building and Rock Structure Estimation
## 4 The Accuracy Verification of the 3D Point Cloud Model  
The accuracy of the textured 3D point cloud model includes two aspects: length accuracy and angle accuracy. The exposed surface of the slope fluctuates obviously. It is inconvenient to conduct measurements with a compass and a tape; therefore, the accuracy verification is conducted with a total station. The length accuracy is verified directly by comparing the distance between two points obtained by Meshlab and the total station. The angle accuracy is verified by comparing the orientations of joints obtained by the two methods. The orientations are calculated according to the normal vectors of the joint planes, which can be solved by at least three non-collinear points. Taking Figure 5 as an example, \(P_{1}\), \(P_{2}\), and \(P_{3}\) are the inflection points of a joint, and they are non-collinear. A fitting plane (shown as a blue dash circle in Figure 5) can be obtained by the least square method with the coordinates of the three inflection points, and then the normal vector (\(\mathbf{n}\) (\(x_{n},y_{n},z_{n}\))) of the fitting plane can be calculated. The dip and dip direction (corresponding to \(\beta\) and \(\alpha\), respectively, in Figure 5) of the fitting plane can be inferred based on the normal vector of \(\mathbf{n}\). The dip direction is defined as the angle between north and the horizontal projection of the normal vector, which ranges from 0 to 360. The dip is the dihedral angle between the horizontal plane and the joint, which runs from 0 to 90. Figure 4: Textured 3D point cloud model of the rock slope at the physical scale. Figure 5: Relationship between the normal vector of a joint and its corresponding orientation. As can be seen from the above introduction, the measurement accuracy of the total station is vital for the accuracy verification of the textured 3D point cloud model. An outdoor experiment was carried out to obtain the actual measurement accuracy of the total station and to verify the applicability of the calculation method of joint orientations. The main equipment used in the experiment included a total station, tripod, compass, tape, vernier caliper, and measuring pad. Seven reflective stickers were attached to the measuring pad, denoted as A, B, C, D, E, F, and G. Figure 6 displays the main equipment used in the experiment. The outdoor experiment was conducted as the following steps:  
1. Identify the specific model and brand of the total station to be tested and make sure that it is properly calibrated and in good working condition. 2. Choose a suitable outdoor site for the experiment, taking into account factors such as the terrain, weather conditions, and availability of reference points. 3. Set up the total station at a fixed position and level it carefully. Use a tripod and make sure that the instrument is stable and properly oriented. 4. Place the measuring pad at a known distance from the total station and mark it clearly with a reflective target or prism. 5. Take multiple measurements of the measuring pad using the total station, varying the horizontal and vertical angles and the distance. Record the measurements carefully and accurately, taking into account any sources of error or uncertainty. 6. Repeat the measurements at different times of day or under different weather conditions to assess the effect of environmental factors on the accuracy of the total station. 7. Compare the measured distances and angles with the actual values of the measuring pad obtained from a reference source with a vernier caliper. 8. Calculate the errors and uncertainties in the measurements and analyze the results to determine the actual measurement accuracy of the total station under the given conditions. The measuring pad was placed 10 m away from the total station in the directions of east, west, south, and north. In the direction of west, 4 different distances of 10 m, 30 m, 50 m, and 100 m were selected. A total of seven different combinations of direction and  
Figure 6: Main equipment used in the outdoor experiment.