## 4 Validation and Results
### Clipping  
Figure 10 presents an example of the clipping process using the wall entity with ID 228278 for the Institute model. The detailed clipping processes have been presented as well as the location of the wall in the final building model. The depth of this clipping is four, however, it is found that the first and second clipping is actually the same, thus, only three clippings are presented.  
Figure 10: Generating a wall entity (ID 228278) for the Institute model.  
Figure 9: Examples of half spaces. (**a**) Half space (230613) with 0% transparency; (**b**) half space (230613) with 30% transparency; (**c**) half space (67512) with 0% transparency; and (**d**) half space (67512) with 30% transparency.  
Figure 11 represents the location of generated clipping geometry in the building models, i.e., House-1, Institute, and House-2 models. The geometry of these IFC models has been generated as expected. From the figure, it can be noticed that clipping is mainly used to represent irregular walls on the highest story of a building. Please note that the openings in the walls have not yet been extracted from the extruded walls.  
Details about building components originally represented by clipping are given below in Table 5, including entity ID, type of element, clipping depth, quantity of bounded half space and unbounded half space, and if the generated B-Rep is closed.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **Entity ID** & **Type** & **Depth** & **Bounded** & **Unbounded** & **Is Closed?** \\ \hline \multirow{4}{*}{House-1} & 60012 & Wall & 2 & 2 & 0 & Yes \\  & 67536 & Wall & 1 & 0 & 1 & Yes \\  & 67828 & Wall & 2 & 2 & 0 & Yes \\  & 75347 & Wall & 1 & 0 & 1 & Yes \\ \hline \multirow{4}{*}{Institute} & 227944 & Wall & 8 & 8 & 0 & Yes \\  & 228278 & Wall & 4 & 4 & 0 & Yes \\  & 228563 & Wall & 2 & 2 & 0 & Yes \\  & 228951 & Wall & 6 & 6 & 0 & Yes \\  & 229235 & Wall & 2 & 2 & 0 & Yes \\  & 2299520 & Wall & 2 & 2 & 0 & Yes \\  & 229966 & Wall & 8 & 8 & 0 & Yes \\  & 230389 & Wall & 7 & 7 & 0 & Yes \\  & 230647 & Wall & 2 & 0 & 2 & Yes \\  & 230935 & Wall & 2 & 2 & 0 & Yes \\ \hline \multirow{4}{*}{House-2} & 36346 & Column & 1 & 0 & 1 & Yes \\  & 36396 & Column & 1 & 0 & 1 & Yes \\  & 102921 & Wall & 1 & 1 & 0 & Yes \\  & 103158 & Wall & 1 & 1 & 0 & Yes \\  & 103276 & Wall & 1 & 1 & 0 & Yes \\  & 103338 & Wall & 1 & 1 & 0 & Yes \\  & 103611 & Wall & 1 & 1 & 0 & Yes \\  & 103724 & Wall & 1 & 1 & 0 & Yes \\  & 102443 & Wall & 2 & 2 & 0 & Yes \\  & 102583 & Wall & 2 & 2 & 0 & Yes \\  & 102860 & Wall & 1 & 1 & 0 & Yes \\  & 138980 & Wall & 3 & 3 & 0 & Yes \\ \hline \hline \end{tabular}
\end{table}
Table 5: Details about building components originally represented by clipping, including entity ID, type of element (Type), clipping depth (Depth), quantity of bounded half space (Bounded), quantity of unbounded half space (Unbounded), and if the generated B-Rep representation is closed (Is closed).  
Figure 11: Location of generated clipping geometry in each building model.  
For House-1, only four wall entities are represented by clipping with a maximum clipping depth of 2. For Institute, ten wall entities are represented by clipping with a maximum clipping depth of 8. For House-2, apart from ten wall entities, two column entities are also represented by clipping with a maximum clipping depth of 3. Both bounded and unbounded half spaces are involved, but the majority are bounded half spaces. As with House-1 and Institute, all the B-Reps are logically closed. For all three models, both bounded and unbounded half spaces are involved, and all the generated B-Rep representations have passed the \"Is Closed\" test, which means they are all logically closed solid model. This means the proposed method can automatically process any types of clipping, even those with a clipping depth larger than 4, and generate valid B-Rep into the shapefile format.