## 3 Proposed Methods
### The Continuous Object Area Computation
#### 3.2.2 Refine the Enclosed Area with Mobile Sensors
However, part of the experimental scenarios may overcorrect the enclosed area to generate TNA. When the number of sensors increases, this phenomenon disappears. MCH has more explicitly overcorrection results than the other methods. MCH greedily approximates the actual area of the continuous object to reduce the FPA shown in Figure 5b. This is the main reason why MCH generates more TNA than the other methods. The sizes of the TNA of MDT and MCH are explicitly shown in 100 sensors. This is because the sensors are too few to cover the actual area of the continuous object. Figure 5d shows the accumulated sizes of FPA and TNA. By referring to SDT, MDT can slightly reduce this accumulated size with by adjusting the position of the sensors. The results of MCH are the best indicator that it can fit the actual size of the continuous object more accurately. Figure 6 evaluates the impact of the moving step size on the enclosed area. In this experiment, the communication range \(R\) is 70 m, and \(\theta\) is \(R/8\). Without adjusting the positions of the sensors, SDT has the worst area size shown in Figure 6a. The area size of MDT is close to that of SDT when the moving step size is \(\gamma/2\). Shortening the moving step size to \(\gamma/3\) can refine more than 30% of the area size. However, the improvement of the moving step size \(\gamma/4\) is not as explicit as that of \(\gamma/3\). The reduced area size is less than 5%. MCH has the best results among all the methods when the moving step size is \(\gamma/2\). Similarly, the improved area size using moving step size \(\gamma/3\) is better than that of \(\gamma/2\) from 31% to 36% when the sensors are more than 300. Compared with the result of \(\gamma/3\), using \(\gamma/4\) improves less than 1.5% of the area size. Figure 6b,c indicates the size of FPA and TNA while applying different moving step sizes. All methods' FPA and TNA decrease while the moving step size decreases. For the size of FPA, the results of \(\gamma/3\) and \(\gamma/4\) are very close. This is also consistent with the results in Figure 6a. The final size of the enclosed area, TNA, and FPA are similar while applying moving step sizes \(\gamma/3\) and \(\gamma/4\). The results in 100 sensors do not have the same trend as the others. This is because the sensors cannot fully enclose the continuous object after they adjust their positions. This experiment shows that using a smaller moving step can increase the precision to enclose the actual area of the continuous object. It can be further verified from the accumulated sizes of FPA and TNA shown in Figure 6d. Figure 7 evaluates the impact of terminating threshold \(\theta\) on the number of moving rounds, and Figure 8 shows the corresponding precision of the proposed MCH algorithm. In this experiment, the communication range \(R\) is 70 m, the moving step sizes are \(\{\gamma/3,\)\(\gamma/4\}\), and the number of sensors is 900. The round defined in this experiment is that all obNodes and ibNodes need to adjust their positions. It is similar to the times that the algorithm requests to change the topology of the deployed sensors. When the terminating threshold is large, the mobile sensors can quickly step into the stop status shown in Figure 7. However, the enclosed area will have worse precision, as shown in Figure 8. When the terminating threshold is small, shortening the moving step size can improve the precision, but the number of rounds will increase exponentially. The operation rounds by using \(\theta=R/16\) is more than twice by using \(\theta=R/8\). However, the improved area is 4%. A small terminating threshold makes the sensors frequently adjust their positions within a local region with a minor moving distance, so that the number of rounds grows explicitly. From the results exhibited by these two figures, setting the \(\theta\) at \(R/8\) seems more suitable for compromising the computation convergence and the area precision. Figure 6: The Impact of Moving Step Sizes on the Enclosed Area (**a**) The ratio \(\alpha\) of the enclosed area sizes.