## 3 Results and Discussion
### Feasibility Analysis  
At first, in order to demonstrate the accuracy of the proposed method, 677 points with a sampling interval of 10 m--that is, from DK562 + 600 to DK569 + 200 on the design section--were selected for the experiment. Track parameters and main stake coordinates were calculated by ERROS. The result is shown in Table 1. It is not difficult to find that different curve units have different plane optimal results. Unit 1 and unit 2 curves have a small radius and a short curve, which is smaller than the arc-diameter ratio of the unit 3 and unit 4 curve elements, resulting in a slightly poorly fitting optimization result. However, in general, the deviation of the parameters of the four curve units after reconstruction optimization is controlled within 5 mm, which indicates that the reconstruction method has a high precision for the parameters' calculation of the curve. The comparison of the calculations and designs of the main stake coordinates and mileage is shown in Table 2. It is found that the reconstruction optimization value and the design value are basically in accordance with one another. It is only at the intersection of the first transition curve and the circular curve (HY point) on the unit 1 curve that the result is not same as the design value, and the horizontal and vertical coordinate deviation are about 5 m. After carefully comparing the design sample points data, it is found that the HY point of the design is at point no. 36, and the HY point obtained by ERROS is the 35 th point, which may also be caused by the small arc-diameter ratio. However, thinking differently, it is shown that even at a small arc-diameter ratio, the calculated value of the proposed differs from the design value in one sampling point. Considering the high density and small spacing of the point cloud data, the coordinate deviation will be reduced to a large extent when using point cloud data as the input. In addition, after obtaining the curve parameters and the coordinates of the main stake points, the mileage of each element point of the track plane curve is calculated by combining the railway starting mileage. It can be found from Table 2 that the railway mileage after reconstruction optimization is not very different from the design value, and is also controlled within 1 m, even in the HY point on the unit 1 curve. It shows that the proposed method can not only accurately reconstruct the curve parameters, but also accurately calculate the main stake coordinates and mileage. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Curve Parameters** & & **1** & **2** & **3** & **4** \\ \hline \multirow{3}{*}{circular curve radius} & _design_ & 5000 & 2500 & 800 & 800 \\  & _calculation_ & 5000.004 & 2499.997 & 800.002 & 7999.998 \\  & _deviation_ & 0.004 & 0.003 & 0.002 & 0.002 \\ \hline \multirow{3}{*}{the first transition curve length} & _design_ & 120 & 120 & 150 & 150 \\  & _calculation_ & 120.005 & 119.998 & 149.999 & 150 \\  & _deviation_ & 0.005 & 0.002 & 0.001 & 0 \\ \hline \multirow{3}{*}{the second transition curve length} & _design_ & 120 & 120 & 150 & 150 \\  & _calculation_ & 119.996 & 120.002 & 150 & 150.003 \\  & _deviation_ & 0.004 & 0.002 & 0 & 0.003 \\ \hline \multirow{3}{*}{full curve length} & _design_ & 481.874 & 809.212 & 647.045 & 919.006 \\  & _calculation_ & 481.867 & 809.222 & 647.056 & 919.002 \\  & _deviation_ & 0.13 & 0.07 & 0.03 & 0.05 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The calculation results of curve parameters compared with the design data (m). \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**No.