## 3 Proposed Methods
### The Continuous Object Area Computation
#### 3.2.2 Refine the Enclosed Area with Mobile Sensors
When the number of sensors is more than 300, the enclosed area sizes of GG, SDT, MDT, and MCH are 136.9-160.1%, 144.9-164.5%, 135.1-157.2%, and 104.8%, respectively. GG and SDT bound a larger area than MDT and MCH. MDT is less than SDT (4.4-6.7%) and close to GG (0.1-2.3%). The area size of MCH is very close to the actual size of the continuous object. Its area is less than that of GG and SDT (22.8-32.7% and 29.6-30%, respectively). Figure 5 evaluates the impact of the communication range \(R\) on the size of the enclosed area. This experiment only evaluates SDT, MDT, and MCH, and did not involve GG. This is because GG does not consider the communication range. In this experiment, the moving step size is \(\gamma/3\), and \(\theta\) is \(R/8\). Let \(\alpha\) be the ratio of the area enclosed by an evaluated method over that of the continuous object. An algorithm is said to have high precision if \(\alpha\) is close to 100%. In this figure, xxR means that the communication range is xxm. For example, 60R-SDT indicates we apply the SDT algorithm with a communication range of 60 m.

Figure 4: Compare the Size of the Enclosed Area. This experiment compares the enclosed area of the methods that use mobile sensors and the traditional ones, without mobile sensors. The precision of MDT and MCH is better than that of GG and SDT. Figure 5: The Impact of the Communication Range on the Enclosed Area. (**a**) The ratio \(\alpha\) of the enclosed area sizes. 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 FPA in the enclosed area. (**c**) The ratio \(\alpha\) of TNA in the enclosed area. (**d**) The ratio \(\alpha\) of the accumulated FPA and TNA in the enclosed area. Figure 5a shows that \(\alpha\) raises when the number of deployed sensors increases in all methods. The values of \(\alpha\) of SDT in 300 sensors are 150%, 167%, and 182% for these three evaluated communication ranges. The values become 172%, 188%, and 204% in 900 sensors. Without adopting the positions of the sensors, the enclosed area size of SDT is 1.5 to 2 times the actual area of the continuous object. For the MDT method, the values of \(\alpha\) are about 125%, 135%, and 152% in the case of 300 sensors for the three evaluated communication ranges. The values become 149%, 157%, and 178% in 900 sensors. MDT decreases \(\alpha\) by at least 22.6% of the value in SDT for all cases. MCH shows the best results against SDT and MDT. The values of \(\alpha\) in 900 sensors are about 103%, 104, and 110% for the three evaluated communication ranges. The results of 100 sensors exhibit different trends because the sensors cannot cover the continuous object completely. Thus, Figure 5b,c shows FPA and TNA for further evaluation. In Figure 5b, FPA increases as the number of sensors increases. Increasing the number of sensors will introduce more obNodes to enclose the continuous object. So, the enclosed area increases. The increasing trend of FPA gradually becomes moderate as the density of deployed sensors grows. Similarly, increasing the size of \(R\) will also include more sensors into the set of obNodes. Because each sensor can cover more area, the size of the total enclosed area grows. In this figure, MDT always has less FPA than SDT in all kinds of R. The FPA of MCH outstands both SDT and MDT, so that its enclosed area sizes are very close to the actual size of the continuous object. Figure 5c shows the sizes of TNA. SDT almost has no TNA because it encloses more parts of FPA to reduce the possibility of generating TNA. Both MDT and MCH have non-zero sizes of TNA, and the size of TNA efficiently reduces as \(R\) grows. Referring to Figure 5b, the payment a using large R is increasing the size of FPA. When the number of sensors is higher than 500, the TNA of MDT is zero. The position adjusting reduces the FPA of MDT.