## 3 Proposed Methods
### The Continuous Object Area Computation
#### 3.2.2 Refine the Enclosed Area with Mobile Sensors
The value of \(\alpha\) is the ratio of the area enclosed by an evaluated method over the practice size of the continuous object. An algorithm is said to have high precision if \(\alpha\) is close to 100%. (**b**) The ratio \(\alpha\) of the FPA in the enclosed area. (**c**) The ratio \(\alpha\) of the TNA in the enclosed area. (**d**) The ratio \(\alpha\) of the accumulated FPA and TNA in the enclosed area. Figure 9 compares the moving costs spent by the mobile sensors. In this experiment, the communication range R is 70 m, \(\theta\) is \(R/8\), and the evaluated moving step sizes are \(\{\gamma/3,\,\gamma/4\}\). This experiment compares the proposed MCH and the method that uses a fixed number of mobile sensors traveling along the selected boundary line to improve the precision of the boundary area [15], denoted as MobSnsr. The sensor's moving speed is 5 m/s. It is the parameter used by MobSnsr in [15]. The number of mobile sensors of MobSnsr evaluated in this experiment is [3; 4; 5]. The x of MobSnsr-x represents the number of mobile sensors. In addition, the virtual force-based methods proposed in [21; 22], are also compared, denoted as vForce. Figure 8: The Precision of the Enclosed Area with Different Terminated Thresholds. When the terminating threshold is small, shortening the moving step size can improve the precision, but the number of moving rounds will increase exponentially (referring to Figure 7). Setting the \(\theta\) at \(R/8\) is more suitable for compromising the computation convergence and the area precision. Figure 7: The number of Moving Rounds with Different Terminated Thresholds. Shortening the moving step size will increase the number of terminating rounds. When the terminating threshold grows, the number of moving rounds decreases. This is because the mobile sensors can quickly step into the stop status. Figure 9a shows the number of moving sensors used for refining the boundary. The number of mobile sensors in MobSnsr is steady, but the proposed MCH adapts the moving sensors according to the initial deploying topology. Although MCH moves more sensors

Figure 9: The Number of Moving Sensors and the Convergency Time of Refinement. The experiment evaluates the number of moving sensors and the convergency time of the algorithm for moving to the stable state. (**a**) The number of moving sensors of MCH and the method in [15]. (**b**) The average convergency time for moving sensors to meet the stable status. (**c**) The precision of the enclosed area. to refine the boundary, the number of sensors is generally less than 10% of the deployed sensors. The method vForce using the virtual force model makes all deployed sensors continuously adjust their locations to fit the practice area of the continuous object. Therefore, all deployed sensors are moved. Figure 8(b) shows the average convergence time in which the mobile sensors finish the boundary-area-refining task. The average time of MobSnsr is about three to five times the time spent by MCH. The vForce method makes all the sensors continuously adjust their positions. Because all the sensors adjust their locations simultaneously, its convergence is still better than that of MobSnsr. A special note is its convergence time decrease as the number of sensors increases. This is because high -density deployed sensors will quickly make the sensors diffuse to the uncovered area. Therefore, the convergence time decreases. Figure 8(c) shows the precision of the enclosed area of the experiment in Figure 3:0 MCH can provide higher accuracy than MobSnsr (1-2.5%). The area precision of the MobSnsr method does not explicitly improve while increasing the number of mobile sensors. However, when the moving step size is \(\gamma/4\), the area precision is about 102%. The increasing number of mobile sensors is no more than three. The vForce can achieve higher accuracy than MCH and MobSnsr when the sensors are diffused from the covered area of the continuous object.