# A Global Continuous Multi-Scale Terrain Contour Simplification Method Based on the Level Set
## 3 Experiments and Results
### Results and Analysis
#### 3.2.1 Results and Visual Analysis  
This section compares the deformation process of the multi-scale simplified contours produced by the aforementioned three methods under the same source and target scale conditions. In this way, we guarantee that the simplified result generated by these methods is a transformation between the same two scales. The source contour scale was taken as the initial scale (i.e., 1:50,000), whereas the target contour scale was taken as the target scale (i.e., 1:200,000). The target contour of the CCSM was simplified by the DP algorithm and was the same as that of the DP algorithm. To easily detect changes in the shape of the simplified contours, the three simplification methods all produced 100 simplified contours (including the initial and target contours). Table 1 presents the parameter settings for generating these contours. For CCSM, the number of horizontal planes was set to 100. The DP algorithm was iterated 100 times, and the reduction of the reservation point decreased at a rate of 0.01. The WM algorithm was iterated 100 times, and the bend reduction rate was 0.01.  
Figure 9 shows the experimental results obtained by the DP algorithm, WM algorithm, and CCSM. No. 1 denotes the initial contour and No. 100 denotes the target contour. The intermediate simplified contours between the initial and target contours are represented by serial numbers (Nos. 2 to 99). We only show here the key shape of a few intermediate simplified results obtained by the three methods during the entire simplification process. Figure 9a shows the simplified results obtained by the DP algorithm. According to Table 1, when the DP algorithm was used for simplification, the num  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Number of horizontal planes (CCSM method) & 100 \\ Reduction rate of points (DP algorithm) & 1\% \\ Reduction rate of bends (WM algorithm) & 1\% \\ \hline \hline \end{tabular}
\end{table}
Table 1: Experimental parameter settings of three simplification methods for generating 100 simplified contours.  
Figure 8: Contour line dataset with a scale of 1:50,000 in the northeastern part of Huimin, Chongqing, China.  
decreased; ideally, the shape of the contour line should be changed accordingly. However, the shapes of the contours were almost unchanged until No. 81. Afterward, as indicated by the blue dotted rectangle, the shapes of the simplified contours changed starting from No. 85. Meanwhile, the shapes of the simplified contour line behind (Nos. 86 to 100) changed in a jump way. Figure 9b shows the simplified results obtained by the WM algorithm. According to Table 1, the bend number continuously decreased when the WM algorithm was used for simplification. The shapes continuously changed from Nos. 1 to 24. However, from Nos. 24 to 44, the shapes barely changed. From Nos. 44 to 45, the shape of the contour abruptly changed, and some key features were lost. Figure 9a,b indicate that the simplified contours generated by the DP and WM algorithms are discontinuous. Meanwhile, Figure 9c shows the simplified results obtained by the CCSM method. The ordinal number in this figure corresponds to the \(i\) value of \(Z_{i}\), that is, the height of the intersecting horizontal planes (described in Section 2.3.1). Unlike the findings of the DP and WM algorithms, Figure 9c shows that the simplified contours generated by CCSM are progressive and include a level of detail that varies continuously. Moreover, the local characteristics were well preserved during the transformation through a few scale ranges (Nos. 1 to 70). Above all, the shapes of the simplified contours generated by CCSM continuously changed between the initial and target contours. CCSM can also yield better continuous multi-scale simplified contours compared with the DP and WM algorithms.