## Case Study  
As a case study, the acquisition of shape information and registration were performed on three interior/exterior spaces and two types of equipment using the proposed method. An example of these spaces is shown in Figure 7. This example space is a photograph of an indoor plant that is actually in \begin{table}
\begin{tabular}{c c c} \hline \hline
**Experiment** & **Calculated** & **Algorithm Results** \\ \hline
1 & 29 & 29 \\
2 & 21 & 20 \\
3 & 18 & 18 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Calculate for the verification of the algorithm. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Node Size** & **x** & **y** & **z** \\ \hline
1 & 0 & 6 & 2 \\
1 & 0 & 8 & 2 \\
1 & 2 & 10 & 2 \\... &... &... &... \\
1 & 14 & 8 & 2 \\
1 & 14 & 10 & 2 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Experimental results using a virtual appliance. operation. Specifically, the indoor plant used for the case study was the underground plant room of the Multi Research Lab #2 located at the Natural Sciences Campus of Sung Kyun Kwan University, Suwon, Korea. The equipment considered for the study was two existing boilers with the size of 1 (m) \(\times\) 1 (m) \(\times\) 2 (m) (including all connected pipes) housed in the plant room. In configuring the equipment for the study, the protruded surfaces of the boiler due to the external irregularities (i.e., control valves, gauges, etc.,) were included as part of the equipment while external connections, such as connecting pipes were segregated from the boiler in random length and not considered as part of the boiler. The goal of the experiment was to rearrange boilers' location within the same plant room so as to install another equipment. Table 7 below summarizes the space and equipment information of the case study. The case study experiment was conducted based on a three-step process: (1) build 3D shape information, (2) perform 3D data simplification, (3) apply space matching algorithm and analyze space to place the equipment. Figure 8 shows these steps and the algorithm process involved in the case study. \begin{table}
\begin{tabular}{c c} \hline \hline
**Item** & **Summary** \\ \hline Space Location & Underground Plant Room, Multi Research Lab \#2, Natural Sciences Campus, \\  & Sung Kyun Kwan University \\ Type of Equipment & Electronic Water Heater Boiler (2 ea.) \\
3D Grid & 1 (m) \(\times\) 1 (m) \(\times\) 2 (m) & 1 (m) \(\times\) 1 (m) \(\times\) 4 (m) \\ Case Study Goal & Rearrange boilers’ location within the plant room to make space for another \\  & equipment \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Summary of the experiment space and equipment. Figure 7: An example space for shape information acquisition and registration. Specifically, 3D shape information was constructed in the first step by first acquiring the 3D shape information using laser scanner, registering scanned data, and then by removing noises. In the second step, 3D data simplification was accomplished through unit size setting, 3D grid data conversion (data simplification) for node application and setting the reference node. Finally, space arrangement was performed in the third step by applying space matching algorithm and analyzing space. The 3D grid method described above was applied to convert the data for calculating the space and equipment point clouds. This process is shown in Figure 9.  
Figure 10 shows the software processing sequence. Input data can be divided into four configurations: the setting part to configure the grid box size to perform the space analysis; the input part to add point cloud data of the space to be analyzed; the tool part to set the starting coordinate point for installation; and lastly the start part to perform the final algorithm and calculation. The user first sets the grid box size according to the accuracy to be obtained and inputs the shape information data collected through the laser scanning operation. Thereafter, the data for setting a required space are further added to start the calculation.