## 4 Simulation Results and Discussion
### Comparisons with the Existing Algorithms Based on Obstacles' Densities  
The number of obstacles and their placement in the AOI significantly impact the performance of any CPP algorithm. To validate the proposed algorithm feasibility for coverage missions in 3D urban environments, we compared the proposed algorithm path lengths, computing time and path overlapping results with existing methods using five maps with varying obstacles' densities. For the evaluation, we compared the proposed algorithm results using three obstacles' density values (low, medium and high) on regular shaped AOI. All obstacles were placed randomly in the AOI in all cases. The low density obstacles' AOI has less number of obstacles and most parts of the area are traversable. In such areas, the most parts can be covered with fewer and longer sensor footprints' sweeps. In contrast, the high density obstacles AOI has less traversable parts and the path overlapping can increase due to complex obstacle geometry. The medium density obstacles areas have uniform distribution of obstacles and almost half of the spaces can be covered with the sweeps. The complete description about the AOI sizes used in experiments, and average running time and path length results' comparisons of the proposed CPP algorithm are shown in Table 1. The computing time, path length, and path overlapping results are the average of five runs in Tables 1-3.  
From the results, it can be observed that both computing time and path length increase with an increase in size of the AOI and obstacles' densities. Meanwhile, the proposed algorithm shows 11.2% and 19.7% reduction in computing time compared to the closely related algorithms. From the path length point of view, the proposed algorithm shows 9.1% and 4% reduction as compared to BCDH-CPP and CA-CPP method, respectively. When the environment complexity is low and AOI size is small  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Area of Interest Size**} & \multicolumn{2}{c}{**BCDH-CPP Algorithm**} & \multicolumn{2}{c}{**CA-CPP Algorithm**} & \multicolumn{2}{c}{**Proposed-CPP Algorithm**} \\ \cline{2-7}  & **Avg. Time (s)** & **Avg. Length (m)** & **Avg. Time (s)** & **Avg. Length (m)** & **Avg. Time (s)** & **Avg. Length (m)** \\ \hline
500 \(\times\) 600 \(\times\) 300 & 13.53 & 8910.34 & 17.94 & 7901.12 & 10.54 & 8201.56 \\
1000 \(\times\) 1200 \(\times\) 300 & 18.40 & 35,997.11 & 22.89 & 34,807.  
(i.e., the first two cases), the CA-CPP algorithm yields shortest length path compared to proposed algorithm. Meanwhile, as the AOI size and obstacle densities grow, the performance of the proposed algorithm improves on both metrics (i.e., path lengths and computing time). Apart from the path lengths and computing time comparisons, we compared the proposed algorithm path overlapping results with the two closely related algorithms in each map (listed in Table 1). The proposed algorithm path overlapping results in average and its comparison with the existing methods are shown in Table 2.  
The proposed algorithm on average gives 9.98 % improvements compared to the existing algorithms on five different maps of varying AOI size and obstacles densities. Furthermore, in all cases, the proposed algorithm gives the coverage ratio \(C_{ratio}\) of 1.0 that represents the perfect coverage (i.e., 100%). The proposed approach can be applied in indoor and outdoor environments for a variety of applications specifically for the aerial inspection in urban environments. In the proposed algorithm, the footprints' sweeps fitting and final paths are calculated offline. Meanwhile, the proposed algorithm can be applied in two phases: offline and online. The sweeps can be fitted in an offline phase and path searching can be done in an online phase.