# Concealed Conduit Routing in Building Slabs
## 4 Discussion and Future Work  
Pipe routing algorithms can be characterized by their working environments, routing algorithms, data structures, and applications. In Table 6, we list some typical pipe-routing \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Pipe**} & \multicolumn{3}{c}{**Test 1**} & \multicolumn{3}{c}{**Test 2**} \\ \cline{2-7}  & **\#(Terminals)** & **Length (m)** & **Cost (sec.)** & **\#(Terminals)** & **Length (m)** & **Cost (sec.)** \\ \hline
1 & 4 & 19.92 & 2.59 & 18 & 75.53 & 13.83 \\ \hline
2 & 3 & 22.30 & 1.30 & 15 & 54.68 & 10.37 \\ \hline
3 & 6 & 25.00 & 3.15 & 8 & 72.42 & 19.69 \\ \hline
4 & 2 & 12.56 & 0.40 & 4 & 25.78 & 2.20 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Lengths and routing costs of the pipes in the 2 tests. Figure 9: Three-view projections of the concealed pipes of experiment 2, (**a**) the side view, (**b**) the top view, and (**c**) the front view. research and our work and characterize these methods by using the above factors such that the differences among them can be highlighted. Based on our investigation into the literature, many researchers use [PERSON]'s method and the A* algorithm to find the pipe paths. In their work, workspaces are usually encoded using weighted graphs. However, their applications may be very different. The ACO algorithm and its variants are the second most popular approaches for laying out pipes. Their underlying data structures may be grids or weighted graphs. ACO methods are utilized to find optimal solutions for routing problems with multiple pipes. To our knowledge, there is no research focusing on the routing process inside building slabs. Ours might be the first one. Furthermore, to increase computational efficiency, the proposed method adopts a hierarchical data structure to encode the workspace and a two-stage piping method to arrange the pipe paths. The embedded routing approach and data structure are also different from those adopted by the other researchers. However, our target application is not unique and is similar to those of [6; 14; 15; 16; 17]. The proposed piping method is utilized for laying our MEB systems, though the conduits are concealed by the walls, floors, and ceilings of buildings. In this research, the pipe paths contain only straight segments and 90-degree elbows. In reality, 45-degree bends should be allowed in pipe paths. We believe the execution time and the quality of the piping process might be improved by relaxing the restriction of the bend angle, especially for pipes relying on gravity to deliver materials. By examining the images of Figures 7 and 8, we found that the pipe paths are closer to the boundaries of the slabs. This is because we utilized Equation (1) to form the feasible space. Therefore, the feasible space of the first pipe is adjacent to the slab boundaries and the openings. Then, the first pipe becomes an obstacle, and the distance field is renewed. Next, the feasible space of the second pipe is created adjacent to the slab boundaries and openings as well as the first pipe. This strategy has a ripple effect. The following pipes will be routed within a safe but not far distance from the slab boundaries, openings, and existing pipes. The safety regulations are met, but large spaces may be preserved in the middle portions of the slabs. This aspect is beneficial for exposed conduits because less space is used and the pipes are closer to supporting racks, which are usually built near the surfaces. We believe that it is also good for concealed pipes since users can obtain more free space for drilling the slabs to install hangers or other facilities. Additive Manufacturing (AM) has been proposed to construct buildings [23]. Creating tunnels in slabs manufactured by AM processes will allow users to route electricity wires and computer network cables afterward. Thus, the proposed algorithm can be employed to create concealed pipes in the geometric modeling stages of AM processes.