# Research on the Calculation and Analysis of Ski-Track Areas Based on Laser Point Clouds
## 4 Experiment and Discussion
### Results and Analysis  
Afterward, a visual comparison is conducted at the data level. The ski runs were divided into five test areas of 10 m \(\times\) 5 m, as shown in Figure 9. Table 1 provides the  
Figure 5: Triangulation generation and boundary extraction of dense point cloud based on Graham algorithm: (**a**) represents triangular mesh generation; (**b**) represents boundary extraction. Figure 8: Triangulation generation and boundary extraction of sparse point cloud based on proposed algorithm: (**a**) represents triangular mesh generation; (**b**) represents boundary extraction. Figure 6: Triangulation generation and boundary extraction of dense point cloud based on proposed algorithm: (**a**) represents triangular mesh generation; (**b**) represents boundary extraction. Figure 7: Triangulation generation and boundary extraction of sparse point cloud based on Graham algorithm: (**a**) represents triangular mesh generation; (**b**) represents boundary extraction. statistical results of the calculation and counting of the area of the measurement area using total stations and differential positioning equipment, the Graham algorithm, the concave hull algorithm, and the algorithm presented in this paper. Figure 9 depicts a schematic diagram of the sampling area and the 3D point cloud image of the sampling area, with Figure 9a showing the schematic diagram and Figure 9b showing the real 3D point cloud image. Based on the coordinate information in Figure 9a, we can determine the actual range of the point cloud in Figure 9b. Additionally, this paper examines the accuracy and validity of the proposed method in comparison to other approaches. The standard measurement area of 10 m by 5 m is selected based on the total station and differential positioning equipment and other factors are ignored for subsequent calculations. In addition, the criteria for selecting samples from other test areas are the same. The results of Table 1 indicate that, using the existing method [25], ski-run point clouds can effectively be extracted from the five sample areas so that subsequent area calculations and statistics can be performed using the Graham measurement method, the concave hull measurement method, and the proposed method. By analyzing Table 1, together with performing simple calculations, it is evident that, although the calculation results for the three methods are larger than the standard value (as part of the point cloud extraction process, snow network information may be included, which will be improved in a targeted manner in the future), the error offsets are different. For each of the five groups of measurement areas, the Graham algorithm error offsets were +19.56%, +24.42, +15.54, +27.86% and 33.26%, respectively, and the average error was +24.13%. Based on the concave hull algorithm, the error offsets for the five groups of measurement areas were +20.08%, +36.86%, +17.52%, +34.64%, and +37.30%, respectively, with an average error of +29.28%. As a result of use of the proposed algorithm, the error offsets for the five groups of measurement areas were +10.64%, +12.52%, +4.06%, +15.50%, and +23.78%, respectively, with the average error being +13.30%. Furthermore, our algorithm achieved an average performance improvement of 10.83% with respect to the Graham algorithm and 15.98% with respect to the concave hull algorithm based on the experimental results. As shown by \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Test Area** & \begin{tabular}{c} **Graham** \\ **Algorithm/m2** \\ \end{tabular} & \begin{tabular}{c} **Concave Hull** \\ **Algorithm/m2** \\ \end{tabular} & \
\begin{tabular}{c} **Proposed** \\ **Algorithm/m2** \\ \end{tabular} &
\begin{tabular}{c} **Standard** \\ **Value/m2** \\ \end{tabular} \\ \hline
1 & 59.78 & 60.04 & 55.32 & 50.00 \\
2 & 62.21 & 68.43 & 56.26 & 50.00 \\
3 & 57.77 & 58.76 & 52.03 & 50.00 \\
4 & 63.93 & 67.32 & 57.75 & 50.00 \\
5 & 76.63 & 68.65 & 61.89 & 50.00 \\ \hline \hline \end{tabular}
\end{table}