## 3 Proposed Methods
### The Continuous Object Area Computation
#### 3.2.2 Refine the Enclosed Area with Mobile Sensors
Compute the moving direction, \(D=\frac{\sum_{i=1}^{+}\overrightarrow{Q\setminus N}}{|\sum_{i=1}^{+} \overrightarrow{Q\setminus N}|}\),
13. //k is the number of one-hop neighbors that are in different set from \(Q\)
14. (\(Q^{\prime}\),\(Q^{\prime}\),\(Q^{\prime}\)) \(\leftarrow\)(\(Q_{X}\),\(Q_{Y}\)) //store the current location as the last one
15. (\(Q_{X}\),\(Q_{Y}\)) \(\leftarrow\) (\(Q_{X}\) + \(\gamma\)\(\times\)\(D\),\(x\), \(Q_{Y}\) + \(\gamma\)\(\times\)\(D\),\(y\))//update the current location
16. If (the event detection of \(Q^{\prime}\) changes) {
17. Restore the original location, (\(Q_{X}\),\(Q_{Y}\))\(\leftarrow\)(\(Q^{\prime}\),\(Q^{\prime}\),\(Q^{\prime}\),\(Y\))
18. \(Q\).Lock = true
19. \(\}\)
20. \(\}\)
21. \(\}\)
22. \(\}\)
23. \(\}\)
24. Compute \(A_{e}\), the enclosed area of the nodes in set \(\Psi_{o}{}^{c^{\prime}}\) after movement
26. For each \(S\in\Psi_{o}{}^{c^{\prime}}\) {
27. Find the each node \(Q^{\prime}\in\Psi_{o}{}^{c}\), and \(Q^{\prime}\) is a one-hop neighbor of S
28. Replace S with \(Q^{\prime}\)
29. Compute the area \(A^{\star}\), the convex hull constructed by the nodes in \(\Psi_{o}{}^{c^{\prime}}\)
30. If (\(A^{\star}<A_{e}\))
31. Update \(\Psi_{o}{}^{c^{\prime}}=\Psi_{o}{}^{c}-[S]+[Q^{\prime}]\)

## 4 Simulation Results

This section gives the simulation results. The environmental setup of the simulation is presented in the first part. The numerical results and relative discussion are presented in the next part. The evaluation includes the impacts caused by the number of sensors, the radio range, and the moving step size. The planarization algorithms using stationary sensors are also included for evaluation. ### Environment Setup

The ROI is an 800 m \(\times\) 800 m area. The total area size of the ICO presented in this paper is 79,601 m\({}^{2}\). It is an irregular shape without diffusing. The sensors are homogeneous and randomly deployed within the ROI. The estimated numbers of sensors are {100, 300, 500, 700, 900} with communication ranges R set to {60 m, 70 m, 80 m}. The evaluated moving step sizes of the sensors are {\(\gamma\)/2, \(\gamma\)/3, \(\gamma\)/4}, where \(\gamma\) is the maximum moving distance addressed in Section 3.2.2. The simulation results are averaged from 100 random scenarios. This paper defines the terminated threshold, denoted as \(\theta\). When the distance between the boundary nodes with different detecting status is less than \(\theta\), the proposed algorithm terminates. This paper evaluates the existing methods, the Gabriel Graph (\(GG\)) and the Delaunay triangulation with stationary sensors (\(SDT\)), and the proposed ones, the Delaunay triangulation with moving sensors (\(MDT\)) and the convex-hull with moving sensors (\(MCH\)). The evaluation metrics include the size of the enclosed area, the False-Positive Area (\(FPA\)), the True-Negative Area (\(TNA\)), the convergence time of the algorithms, the number of moving sensors, and the total number of sensors' movement. A good algorithm will approximate its enclosed area to that of the continuous object. The FPA is the region included within the enclosed area of an algorithm but not covered by the domain of the continuous object. The TNA is the region covered by the continuous object but not contained within the domain figured by an algorithm. The convergence time evaluates the required time for an algorithm to obtain the output results. The number of moving sensors verifies the number of sensors influenced in boundary adjusting, and the number of sensors' movements checks the number of issued moving instructions. ### Numerical Results

Figure 4 shows the comparison of the enclosed area between the existing planarization algorithms (GG and SDT) and the proposed methods (MDT and MCH). In this experiment, the communication range is 70 m, the moving step size is \(\gamma\)/3, and \(\theta\) is \(R\)/8. The total area size of the ICO is 79,601 m\({}^{2}\). In the case of 100 sensors, the deployed sensors are insufficient to cover the whole continuous object.