## 4 Experimental Results  
Two types of experiments were conducted to find the performance of the proposed EDP and modified OAECD algorithm. An additional simulation has been performed to verify the feasibility of the modified OAECD algorithm for a map with curvilinear obstacles. The first experiment is conducted to compare the approximation error and the number of vertices of the approximated polygon made by EDP and DP. In each experiment, twenty maps were chosen in the pre-created one hundred fifty random maps, each of which is assumed to be 20 \(\times\) 20 m\({}^{2}\) in size and randomly have the position of the obstacle, position of the vertices of each obstacle, and area of the obstacle by using the random function in the math library of the MS Visual C++ compiler. The number of obstacles and vertices of each obstacle were fixed at fifteen. Bezier curve was used for the curvilinear obstacle representation by interconnecting the vertices of each obstacle and creating naturally curved obstacles. Each map was created by an image in bitmap format. The second experiment was conducted to compare the performance of the OAECD algorithm and the VCD algorithm. Similar to the first experiment, the size of the map was assumed as 20 \(\times\) 20 m\({}^{2}\), and the position of the obstacle, positions of the vertices of each obstacle, number of vertices of each obstacle, and number of obstacles in the map were random variables. Table 1 shows the experimental results by averaging the results of each experiment. Here, IA is the percentage area of the inner space of the approximated polygons outside the obstacle regions in comparison with the area of the original obstacle region. OA is the percentage area of the outer space of the approximated polygons inside the obstacle regions in comparison with the area of the original obstacle region. SA is the sum of IA and OA. AVG is the average values for various \(\epsilon\). From Table 1, the average approximation error of the result of the EDP algorithm is approximately 5 times larger than that of DP algorithm to cover the entire area of the original obstacle regions. Table 2 shows the experimental results by averaging the results of ten experiments with 15 random obstacles and 15 random vertices for each obstacle. From Table 2, on average, the result of the EDP algorithm has 2.88 times more vertices than the result of the DP algorithm when \(\theta_{rot}\) for EDP is 30\({}^{\circ}\). Figure 7 shows a graphical representation of Tables 1 and 2. The approximation performance of EDP is worse than DP in the aspects of IA, SA, and average number of verti \begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{\(\epsilon\) (m)} & \multicolumn{3}{c}{**EDP (\%)**} & \multicolumn{3}{c}{**DP (\%)**} \\ \cline{2-7}  & **IA** & **OA** & **SA** & **IA** & **OA** & **SA** \\ \hline
0.05 & 19.05 & 0.00 & 19.05 & 2.45 & 0.70 & 3.15 \\
0.08 & 28.46 & 0.00 & 28.46 & 4.89 & 1.17 & 6.06 \\
0.11 & 37.95 & 0.00 & 37.95 & 7.19 & 1.54 & 8.73 \\
0.14 & 47.63 & 0.00 & 47.63 & 9.26 & 1.83 & 11.08 \\
0.17 & 57.34 & 0.00 & 57.34 & 11.50 & 2.08 & 13.58 \\
0.20 & 67.17 & 0.00 & 67.17 & 13.38 & 2.48 & 15.86 \\
0.23 & 77.11 & 0.00 & 77.11 & 15.52 & 2.76 & 18.28 \\
0.26 & 87.01 & 0.00 & 87.01 & 17.23 & 3.20 & 20.43 \\
0.29 & 96.91 & 0.00 & 96.91 & 19.55 & 3.56 & 23.10 \\
0.32 & 106.7 & 0.00 & 106.7 & 22.00 & 3.86 & 25.85 \\
0.35 & 116.7 & 0.00 & 116.7 & 23.90 & 4.40 & 28.30 \\
0.38 & 127.3 & 0.00 & 127.3 & 26.91 & 4.83 & 31.74 \\
0.41 & 137.9 & 0.00 & 137.9 & 27.99 & 5.27 & 33.26 \\
0.44 & 148.0 & 0.00 & 148.0 & 30.57 & 5.62 & 36.19 \\
0.47 & 158.8 & 0.00 & 158.8 & 32.13 & 5.86 & 37.99 \\
0.50 & 169.5 & 0.00 & 169.5 & 33.11 & 6.60 & 39.72 \\ \hline AVG & 92.72 & 0.00 & 92.72 & 15.53 & 2.99 & 18.52 \\ \hline \end{tabular}
\end{table}