Error de las velocidades

6.1.2.1 Test for the flood area mechanism with regular shape objects

One VWM was released to test the flood area mechanism. In this test, the volume of the cube was measured. The parameters impacted the simulation process, i.e., the diameter of VWM and running time. As expected, no human inspection and intervention were required during this simulation. A simple termination condition, i.e., the running time of simulation, was applied, which was significantly different from conventional modeling methods. More interestingly, an absolute true volume of the cube, 𝑉_{𝑎𝑏𝑠𝑜𝑙𝑢𝑡𝑒}, was generated even before the VWM was released. That was because the only variable in this physical scenario, i.e., the geolocation of the VWM, had no ability to break the completeness of the cube. What it could be affected was the efficiency of the simulation. 𝑉_{𝑓𝑙𝑜𝑜𝑑} was used to represent the instant volume flood area. With the flying of time, the difference between 𝑉𝑓𝑙𝑜𝑜𝑑 and 𝑉𝑎𝑏𝑠𝑜𝑙𝑢𝑡𝑒 diminished into an ultra-small scale. Figure.6-10 shows thesequence of VWM footprints shortly after the simulation started.

Results and discussion for virtual water displacement methods

Figure 6-10. The footprint recording of a VWM; (a) to (h) are arranged ascending by the application

running time; the number is the total generated footprints.

This simulation ended with 1,438,814 footprints generated. However, some of voxels were visited by the VWM many times, and others were not visited at all. There were 1,000,000 voxels in total, and 561,025 of them were visited in the end. The re-visiting rate, 2.56, was calculated by footprints divided by the number of visited voxels. This re-visiting rate indicated the efficiency of simulation and no ability to affect 𝑉𝑎𝑏𝑠𝑜𝑙𝑢𝑡𝑒 also. Due to the VWM was attracted by a random changing gravity field, re-visiting the same voxels would happen naturally and could not be avoided. Therefore, a compensatory strategy was employed. That was the buffering.

By applying buffering to raw footprints, there was no need to wait for a full visit of all voxels in the vessel. According to equation 5-11, an appropriate buffer would extend the flood area of each footprint significantly. Fig.6-11 shows the comparing of the measuring result of the cube using different buffering length. Without buffering, it could not visually distinguish the cube from the raw footprint, as shown in Fig.6-11(a). After applying buffering with 1 unit, as shown in Fig.6-11(b), the cube was extracted clearly from raw footprints. However, there were speckles on the wall area, indicating the un-visited voxels by the VWM even with buffer applied. From another perspective, compared to the inner areas, the wall areas of the vessel had less opportunity to be visited.

Figure 6-11(c) and (d) shows different approaches to further process the result in Fig.6-11(b). By applying an outliner filter, as shown in Fig.6-11(c), the redundant area of the cube was removed. Otherwise, this redundant area could be achieved by extending the buffering length from 1 to 2. However, as shown in Fig 6-11(d), over buffering would occupy the voxels belong to the measuring target and led to an underestimation of the cube volume.

Figure 6-11. The comparing of the measuring result of the cube using different voxel buffering; (a) no

buffering; (b) buffered with 1 unit; (c) buffered with 1 unit and outliners were removed; (d) buffered with 2 units.

In the development of stage one of VWD, it was observed that VWMs responded differently to the three regular shape objects. On the contrary, the flood area mechanism in this stage two showed insensitive to shapes. Table 6-2 shows the measuring results for the cube, sphere, and cylinder objects. Compared to Fig.6-6, the flood area was much more stable than the original VWD mechanism in stage one. The most likely reason was that the simulation of interaction among VWMs was canceled in this stage. Consequently, the source of error was limited.

Results and discussion for virtual water displacement methods

Table 6-2. Results for the VWD process using flood area mechanism on three regular shaped objects.

Objects True volume VWD volume Relative difference Footprints Buffering distance

Cube 125,000 132,845 +6.28% 246,540 1

Sphere 64,043 66,946 +4.53% 436,519 1

Cylinder 193,129 208,673 +8.05% 323,855 1

Mean: +6.29%

6.1.2.2 Artificial stems results

After the feasibility of the flood area mechanism was proved. The point clouds of artificial stems were able to be processed. Figure 6-12 shows the simulations result and the raw footprints of this simulation using the “stem” point cloud. This figure was organized using the form of Eq.5-11, i.e., the equation of the primary mechanism of flood area mechanism. In plain language, this mechanism was purring water into a swimming pool, with trees inside, until full of water.

Figure 6-12. The visual demonstration of Eq.5-11 using the result of a VWD processing on the "stem"

point cloud.

Figure 6-13 and Table 6-3 shows the stem volume measured using flood area mechanism for the "stem" point cloud and the "stem with branches" point cloud. Before the simulation began, the quantity of voxels in the virtual space (vessel) was determined as 2,812,500. In order to improve the measuring accuracy to the maximum degree, the simulations were processed as long as possible. As a result, the raw footprints recorded in both simulations were much greater than the quantity of voxels in the virtual space at a few times more.

Figure 6-13. Measuring the “stem with branches” point cloud using flood area mechanism; (a) the

measuring process using single VWM; (b) the measuring process using multiple VWMs; (c) the measuring result; (d) overlaying of VWD result and the original point cloud.

However, the visit of all voxels in the virtual space using VMWs was tough to be achieved. Instead of a full visit, buffering was also an approach to extend the ability to occupy voxels for VWMs. For example, a footprint could occupy a voxel under normal circumstances. After buffered with 3 units, for the "stem" point cloud, a raw footprint occupied the surrounding 343 voxels. In total, 2,428,355,965 voxels were marked as visited voxels. It was about 863 times greater than the quantity of voxels in the virtual space. A similar calculation for the "stem with branches" point cloud was also analyzed. After buffered with 2 units, each raw footprint occupied 125 voxels. In total, 1,1148,874,125 voxels were marked as visited voxels. It was about 408 times greater than the quantity of voxels in the virtual space. Compared to the results of regular shape objects, there were only 2.86% and 1.84% overestimation in those two point clouds, respectively. The high re-visiting rate was the reason for the improvement of accuracy.

Table 6-3. The result for VWD process on two artificial stems.

Objects Ture Volume VWD Volume Relative Difference Footprints Buffering Distance

Stem 23,709 24,344 +2.68% 7,079,755 3

Branches 27,946 28,459 +1.84% 9,190,993 2

Results and discussion for virtual water displacement methods

6.1.2.3 Discussion: approaching true values by the accumulation of time

The repeated measurement was a usual approach to enhance the accuracy in a conventional measuring process [27]. For example, the manual measurement errors in a DBH measuring process could be diminished using repeated measurements. Compared to the measuring process in reality, no repeated measurement was required in the CVM process. As previously stated (in 5.1.2.6), the absolute true value of the measuring target was generated at the moment, when the virtual space was established. Specifically, for this flood area mechanism, with the accumulated running time, the VWD instant volume 𝑉𝑓𝑙𝑜𝑜𝑑 was approaching to 𝑉𝑎𝑏𝑠𝑜𝑙𝑢𝑡𝑒. Therefore, the repeated measurement was not necessary to be applied. The improvement of accuracy was provided by increasing the simulation time. The raw footprint record of the cube object (Fig.6-11) was analyzed. The increment of the unique voxels detected by VWMs is shown in Fig. 6-14 (left). It was observed that the increment decreased after the fast uprising in the initial stage. The differential increments of unique voxels for every 0.1% of the total generated frames are presented in Fig.6-14 (right). It was obvious that the differential increments of unique voxels always decreased with the accumulated time. This indicated that the VWMs had less possibility to detect new un-visited voxels with the accumulated time. Finally, the VWMs would achieve a full visit for every accessible area, if the running time was long enough.

Figure 6-14. The unique voxels detected by VWMs with the increasing of running time for the cube