# Wall Structure Geometry Verification Using TLS Data and BIM Model
## 3 Case Study
\begin{table}
\begin{tabular}{c c c c c c c c} \hline n & a\({}_{\text{IFC}}\) & a\({}_{\text{PoC}}\) & b\({}_{\text{IFC}}\) & b\({}_{\text{PoC}}\) & c\({}_{\text{IFC}}\) & c\({}_{\text{PoC}}\) & d\({}_{\text{IFC}}\) [m] & d\({}_{\text{PoC}}\) [m] \\ \hline
1 & 1.0000 & 0.9999 & 0.0000 & 0.0023 & 0.0000 & 0.0006 & \(-\)13.400 & \(-\)13.444 \\
2 & \(-\)1.0000 & \(-\)0.9999 & 0.0000 & 0.0022 & 0.0000 & 0.0005 & 16.235 & 16.252 \\
3 & 1.0000 & 0.9999 & 0.0000 & 0.0013 & 0.0000 & 0.0004 & \(-\)16.350 & \(-\)16.378 \\
4 & \(-\)1.0000 & \(-\)0.9999 & 0.0000 & 0.0005 & 0.0000 & 0.0014 & 19.250 & 19.240 \\
5 & 0.0000 & 0.0021 & \(-\)1.0000 & \(-\)0.9999 & 0.0000 & 0.0010 & \(-\)11.575 & \(-\)11.552 \\
6 & 0.0000 & 0.0030 & \(-\)1.0000 & \(-\)0.9999 & 0.0000 & 0.0019 & \(-\)11.575 & \(-\)11.524 \\
7 & 0.0000 & 0.0006 & 1.0000 & 0.9999 & 0.0000 & \(-\)0.0013 & 11.460 & 11.444 \\
8 & 0.0000 & \(-\)0.0022 & \(-\)1.0000 & \(-\)0.9999 & 0.0000 & \(-\)0.0028 & \(-\)9.760 & \(-\)9.730 \\
9 & 0.0000 & \(-\)0.0013 & \(-\)1.0000 & \(-\)0.9999 & 0.0000 & \(-\)0.0016 & \(-\)10.060 & \(-\)10.042 \\
10 & \(-\)1.0000 & \(-\)0.9999 & 0.0000 & 0.0011 & 0.0000 & 0.0015 & 16.800 & 16.801 \\
11 & 0.0000 & 0.0088 & 1.0000 & 0.9999 & 0.0000 & 0.0002 & 7.375 & 7.209 \\
12 & \(-\)1.0000 & \(-\)0.9999 & 0.0000 & 0.0012 & 0.0000 & 0.0006 & 19.250 & 19.248 \\
13 & 1.0000 & 0.9999 & 0.0000 & 0.0023 & 0.0000 & 0.0003 & \(-\)15.700 & \(-\)15.699 \\ \hline \end{tabular} Where n is the number of the inspected wall, a\({}_{\text{IFC}}\), b\({}_{\text{IFC}}\), c\({}_{\text{IFC}}\), and d\({}_{\text{IFC}}\) are the parameters of the plane from IFC, a\({}_{\text{PoC}}\), b\({}_{\text{IFoC}}\), c\({}_{\text{PoC}}\), and d\({}_{\text{PoC}}\) are the parameters of the plane from IFC.  
\end{table} 
Table 1: Comparison of the plane parameters. Figure 16: Scanned point cloud—wall no. 8. Figure 15: Scanned point cloud—wall no. 7. The maximal difference in orientation \(\alpha\) between the planes is 0.5026\({}^{\circ}\) in the case of plane 11. The difference in orientation of 0.5\({}^{\circ}\) for a wall length of 2.45 m means a deviation of 21 mm. The absolute maximal difference of 41 mm between the IFC plane and the point cloud is in the case of wall no. 13. The average differences reached values from 9 mm to 16 mm. The standard deviation of the results of 4 mm is calculated applying uncertainty propagation law from the registration error and the uncertainty of the 3D position of a single measured point. It means that the deviations under the value of 4 mm are not significant. The deviations between the BIM model and the scanned surfaces, listed in Table 2, are caused by the uncertainty of the measurement (4 mm) and the construction deviation. The construction deviation can be characterized as a sum of the assembly deviation and setting-out deviation of the structures during the construction. Furthermore, the deviations may be caused by the fact that although the LOD of the model is 300, the plasters with a thickness of 10 mm were not modeled. Figures 17 and 18 show the deviation maps between the BIM model and the segmented point cloud for selected walls. The colors from green to red represents positive values in the color bars.