# Research on the Calculation and Analysis of Ski-Track Areas Based on Laser Point Clouds
## 5 Conclusions  
In conclusion, in this paper, the RANSAC method was used in order to determine the optimal ski-track plane using the extracted ski-run point clouds [25] (DOI: 10.3390/app12115678). The ski-track point clouds were projected onto the fitting plane to produce a plane point cloud. After constructing the triangular network using the growth algorithm, we proposed an improved algorithm for extracting ski-run boundary points from point clouds to obtain high-precision ski-run edges, connecting them with line segments in order to form polygons. In the final step, the discrete Green's formula was used to calculate the area of the ski track. In order to verify the feasibility and effectiveness of the method, five groups of 10m x 5m test areas on the ski tracks were selected. A comparison of the measurement error offset ratios of the [PERSON] algorithm, the concave hull algorithm, and the algorithm proposed in this paper, produced values of +24.13 percent, +29.28%, and +13.0%, respectively. It can be seen that the method proposed in this paper had the lowest error offset, demonstrating that it represents an improvement and is feasible. Lastly, we used the method proposed in this paper to calculate the ski-run area (based on two sets of point cloud data for the Zhangjiakou Wanlong Ski Resort and two sets of point cloud data for the Beijing Winter Olympic Cross-country Skiing Center), with values obtained of 6294.09 m\({}^{2}\), 3921.18 m\({}^{2}\), 1191.98 m\({}^{2}\) and 316.18 m\({}^{2}\), respectively.  
A further analysis of the above-mentioned error offsets indicated that the error offsets calculated by the three methods were all positive, suggesting that the ski-run point cloud extraction was not absolutely accurate. Further research will be conducted on the ski-track extraction method in order to improve its accuracy and correctness in the future.  
Conceptualization, W.W. and H.Z.; methodology, W.W. and C.Z.; software, W.W.; validation, W.W., C.Z. and H.Z.; formal analysis, W.W.; investigation, W.W.; resources, C.Z.; data curation, W.W.; writing--original draft preparation, W.W.; writing--review and editing, C.Z.; visualization, W.W.; supervision, C.Z. and H.Z.; project administration, C.Z.; funding acquisition, C.Z. All authors have read and agreed to the published version of the manuscript. This research was funded by the National Key R&D Program of China, Special Project of \"Science and Technology Winter Olympics\" (2018 YFF0300802). Not applicable. Not applicable.  
Figure 13: The second group of data-processing results for the Beijing Winter Olympics National Cross-country Skiing Center (Parameters: T = 2.0 cm, A = 0.7, D = 40 cm): (**a**) color point cloud; (**b**) ski-track boundary.  
Data Availability Statement: Not applicable. Conflicts of Interest: The authors declare no conflict of interest. Abbreviations The following abbreviations are used in this manuscript: RANSAC Random Sample Consensus 2D and 3D Dimensions and 3 Dimensions MODIS Moderate Resolution Imaging Spectroradiometer AVIRIS Airborne Visible/Infrared Imaging Spectrometer Modis Moderate-Resolution Imaging Spectroradiometer TIN Triangular Irregular Network UAV Unmanned Aerial Vehicle LiDAR Light Detection and Ranging PCL Point Cloud Library