## 4 Results and Discussion  
This section explains the simulation experiments and corresponding results. The performance of the proposed PP method was analyzed using two criteria: time complexity and path length compared to prior studies. To make the proposed PP method a benchmark, we compared the simulation results with randomized motion planning and visibility graph-based algorithms. The simulation tests were performed and compared using Matlab v. 9.8.0.1451342 (R2020a) on a computer running Windows 10 with 8 GB of RAM and a 2.6 GHz CPU. In the tests, we assumed a 25 kg fixed-wing UAV similar to ones used in existing studies. We took into account both global and local constraints in the simulations. The parameters of the local constraints (i.e., on the UAV) were a 1 m wingspan and a maximum turning angle at a radius of \(\pi/6\). The minimum and maximum flying altitudes were \(h_{min}=23\) m, \(h_{max}=155\) m. The global constraints belonged to the geometry of obstacles in \(W\). We consider six complexity parameters that can significantly hinder the quality of a \(P\) and the UAV's safety while selecting a space size. We assumed that the UAV had enough battery power to complete the task in one flight. The safe distance to avoid collisions with obstacles was \(10m\) (\(d_{safe}=10\) m). We assumed that wind was negligible during the flight. The proposed method finds \(P\) using an ESWG that respects both global and local constraints. The weights of space complexity parameters were \(w_{1}=0.2\), \(w_{2}=0.1\), \(w_{3}=0.2\), \(w_{4}=0.2\), \(w_{5}=0.1\), and \(w_{6}=0.2\). We assigned values to these weights by considering the significance and influence of each parameter on the accurate space selection for an optimal/quasi-optimal pathfinding. We tested our method with diverse combinations of the weight values, and analyzed the accuracy of space selection for optimal/quasi-optimal paths. Subsequently, we determined the best combination of these weight indexes' values that make accurate space selection consistently. Furthermore, these weight values were validated via numerical analysis by computing optimal paths from numerous maps using whole \(W\), and analyzing the number of times optimal paths tend to lie in the selected space. The locations for \(s\) and \(t\) were chosen randomly during experiments. We compared our PP method's performance with two existing algorithms: the ApVL algorithm proposed by [PERSON] et al. (2018) and the RRT*-AB algorithm proposed by [PERSON] et al. (2018). Both comparison algorithms are state-of-the-art for PP. We tested them on our maps to compare the performance of our method with them. We show a sketch of the 3D maps employed in the experiments and three exemplary paths from each method in Figure 8.  
Figure 7: Example about the working of an A* algorithm for low-cost pathfinding.  
The path produced by the proposed PP method was more smooth and shorter than the paths from the other methods. To analyze and compare the proposed PP method's results, we designed three distinct scenarios with sufficient obstacles in the 3D environment maps. Each scenario was tested with all three methods, and the results were analyzed. All obstacles had a random width, depth, and height with a rectangular-shaped base. Comprehensive details on maps counts, map sizes, \(s\) and \(t\) locations, numbers of obstacles and their geometric information, etc. are given in each scenario description below.