## 5 Discussion
### Boundary Size and Processing Time for Building Component  
Because the boundary size of 10 m is too small to represent an unbounded half space, as shown in Table 4, then, it is not used in assessing the processing time of building components, instead, a larger boundary size, 100,000 m, has been added. For the same reason mentioned above, the processing time of 10 repetitions under the same condition is calculated. Five building components are used for  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Entity ID** & **10 m** & **100 m** & **1000 m** & **10000 m** \\ \hline House-1 & 67512 & 1.16 KB & 1.16 KB & 1.16 KB & 1.16 KB \\  & 75323 & 1.16 KB & 1.16 KB & 1.16 KB & 1.16 KB \\ \hline Institute & 230613 & 1.16 KB & 1.16 KB & 1.16 KB & 1.16 KB \\  & 230623 & 1.16 KB & 1.16 KB & 1.16 KB & 1.16 KB \\ \hline House-2 & 36317 & 1.16 KB & 1.16 KB & 1.16 KB & 1.16 KB \\  & 36367 & 1.16 KB & 1.16 KB & 1.16 KB & 1.16 KB \\ \hline \hline \end{tabular}
\end{table}
Table 7: Boundary sizes and file size of corresponding B-Reps for half spaces.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **Entity ID** & **10 m** & **100 m** & **1000 m** & **10000 m** & **Max diff** \\ \hline House-1 & 67512 & 7.97 s & 8.04 s & 8.12 s & 8.14 s & 0.36 s \\  & 75323 & 7.89 s & 7.68 s & 7.66 s & 7.55 s & 0.33 s \\ \hline Institute & 230613 & 7.66 s & 7.56 s & 7.57 s & 7.68 s & 0.12 s \\  & 230623 & 7.68 s & 7.84 s & 7.74 s & 7.66 s & 0.18 s \\ \hline House-2 & 36317 & 8.85 s & 8.80 s & 8.17 s & 7.93 s & 0.91 s \\  & 36367 & 8.54 s & 8.06 s & 7.96 s & 8.18 s & 0.58 s \\ \hline \hline \end{tabular}
\end{table}
Table 8: B-Rep producing time (20,000 repetitions) for unbounded half spaces.  
this purpose. The total processing time for each building component under each boundary size is presented in Table 9.  
For building components from House-1 and Institute, there is a clear increasing trend in the processing time as the boundary size grows. The relationship between processing time and boundary size for these entities can be described using a linear equation, and high correlation coefficients have been noticed, around 0.98, as shown in Figure 12a. However, the increment in processing time is not very significant between neighboring boundary sizes. For example, consider the entity with ID 67536 from House-1 model, the total processing time increases to 3.76 s at the largest tested boundary size from 3.56 s at the smallest tested boundary size, with an increase of only 0.2 s, or 5.6%.  
For the entities from House-2, however, the trend is not that obvious. Although trend lines can be drawn, they cannot accurately describe the data. As shown in Figure 12b, the correlation coefficients for entity ID 36346 and ID 36396 are only 0.729 and 0.208, respectively. However, they roughly show the positive correlation between processing time and boundary size. Considering that clipping is mainly used to represent walls and the usage is quite low, it is reasonable to believe that the processing time for the whole BIM model is not greatly affected by the increase of boundary size.  
Please note that more boundary sizes need to be tested if a more accurate quantitative relationship between boundary size and processing time is to be determined, but this is not carried out in this study, as the quantitative relationship is not that decisive for this study.