# Concealed Conduit Routing in Building Slabs
## 3 Results
### Test Case 2  
In the next experiment, we build an apartment building and use it as the target building. Its appearance is shown in Figure 8a. The geometric information of this building is presented in Table 3. It has two units, and each unit is a two-story apartment. In a unit, the upper and lower stories are connected via a staircase. We created 11 windows in total on the front, back, and side walls in each unit. There is a window and a door between the two units on the second floor. Thus, these two units are connected. Each unit has a door in its front or side wall. In summary, the building has 20 slabs and 28 openings. Its size is 16 m \(\times\) 16 m \(\times\) 8 m. The shapes of the slabs and openings are presented in the second and third columns of Table 3. \begin{table}
\begin{tabular}{c c c} \hline
**Components/Dimensions** & **Slabs** & **Opening** \\ \hline \hline \multirow{4}{*}{\begin{tabular}{c} Apartment of 2 units, \\ 2 stories in 1 unit, \\ Width = 16 m, \\ Length = 16 m, \\ Height = 8 m, \\ 4 rooms. \\ \end{tabular} } & \
\begin{tabular}{c} 3 (L 8 m \(\times\) 3 m) doors: \\ 2 doors in 1 st floor, \\ 14 (8 m \(\times\) 4 m) walls, \\ 4 (8 m \(\times\) 8 m) floors, \\ 2 (8 m \(\times\) 8 m) ceilings. \\ \end{tabular} } \\  &
\begin{tabular}{c} 11 windows in the 1 st floor, \\ 2 windows in the 2 nd floor. \\ 2 (4 m \(\times\) 2 m) staircase openings, \\ 1 opening in each unit. \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Geometric information of the building in the second test. Four concealed pipes are to be built. Their parameters are listed in Table 4. They are used to transport electricity, natural gas, water, and air. The first pipe possesses 18 terminals. The second pipe has 15 terminals. The third and fourth pipes have eight terminals and four terminals, respectively. The safety gaps and colors of the pipes are 20, 10, 5, and 2 cm, respectively. Compared with the building model of test case 1, this building has more slabs and openings, and the target pipes possess more terminals too. Hence, the geometrical complexity of the working environment is greatly increased. Figure 8b-e show the progression of the pipe routing process. The first pipe is shown in Figure 8b. Its path is confined within the ceilings and walls of the first and second stories. Its path contains some bends caused by the openings. However, most of its segments are straight. The second pipe is constructed subsequently, and its path is displayed in Figure 8c. A great portion of its path goes through the floors. This is because most of its terminals reside on the first floors and the slabs in the upper story are already occupied by the first pipe. The path of the third pipe (in orange color) is portrayed in Figure 8d. Its path wanders through the spaces left by the first pipe in the upper story. It penetrates the back walls and ceilings to connect the terminals. The fourth pipe is the last to be routed. The remaining workspace is mostly in the front walls. Thus, its path is arranged in the front walls. Its path is shaded in red color and shown in Figure 8e. Figure 8f presents a VR image of the building after the piping process. It reveals the related positions of the pipes inside the building. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Pipe** & **\#(Terminals)** & **Diameter** & **Usage** & **Safe Gap** & **Color** \\ \hline
1 & 18 & 3 cm & Electricity & 20 cm & Green \\ \hline
2 & 15 & 6 cm & Natural gas & 10 cm & Orange \\ \hline
3 & 8 & 8 cm & Water & 5 cm & Blue \\ \hline
4 & 4 & 3 cm & Air & 2 cm & Red \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Pipe parameters in test case 2. Figure 8: Routing concealed pipes in an apartment building, (**a**) the building, (**b–e**) routing pipe 1–4, (**f**) the resultant pipe systems. Our system can produce three-view images to highlight the gaps between the pipes and the spaces between the pipes and the openings. In Figure 9a-c, the orthographical projections of the building and the pipes are shown.