# Building Geometry Simplification for Improving Mesh Quality of Numerical Analysis Model
## 7 Conclusions  
This study proposed an automatic simplification methodology of building geometries to improve the accuracy and stability of the FVM model, and analyzed changes in geometry and mesh quality by simplification. The geometry simplification method proposed in this study integrates similar faces through angle and a distance threshold, and removes insignificant faces from the surfaces composing the building model. To evaluate the applicability of the simplification method, the geometries of the building models obtained from the public BIM library were simplified under various conditions. To evaluate the extent of the shape changes from the simplification method, the similarity between the original and simplified geometry was evaluated using the D2 shape distribution and Bhattacharyya coefficient. In addition, the complexity of the building model and hexahedron meshing were evaluated using the ITC. As a result, the similarity of simplified geometry to the original model and the complexity decreased in proportion to the distance threshold. Therefore, it was determined that the degree of geometry changes could be controlled linearly using the threshold of the simplification method. The mesh quality of the building model was evaluated using the maximum non-orthogonality, skewness, and the hexahedron cell ratio as each affects the accuracy and stability of \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Multiple R\({}^{2}\)** & **Adjusted R\({}^{2}\)** & **F-Statistic** & \(p\)**-Value** \\ \hline
0.2143 & 0.2120 & 94.21 & \textless{}2.2e-16 \\ \hline
**Variable** & **Coefficient** & **Standard Error** & \(p\)**-Value** \\ \hline (Intercept) & 103.5349 & 2.3859 & \textless{}2e-16 \\ \(d_{threshold}/L_{\text{CO}}\) & \(-2.3652\) & 0.2556 & \textless{}2e-16 \\ \(s\) & \(-22.6681\) & 2.7056 & \textless{}2e-16 \\ \(s^{2}\) & 3.9979 & 0.6139 & 1.04e-10 \\ \(C_{ITC0}\) & \(-84.6206\) & 5.8553 & \textless{}2e-16 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Regression analysis of maximum non-orthogonality. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Multiple R\({}^{2}\)** & **Adjusted R\({}^{2}\)** & **F-Statistic** & \(p\)**-Value** \\ \hline
0.2370 & 0.2343 & 85.81 & \textless{}2.2e-16 \\ \hline
**Variable** & **Coefficient** & **Standard Error** & \(p\)**-Value** \\ \hline (Intercept) & 3.01519 & 0.16625 & \textless{}2e-16 \\ \(d_{threshold}/L_{\text{CO}}\) & \(-0.11820\) & 0.01290 & \textless{}2e-16 \\ \(s\) & \(-1.20214\) & 0.13649 & \textless{}2e-16 \\ \(s^{2}\) & 0.21268 & 0.03097 & 9.86e-12 \\ \(C_{ITC0}\) & \(-4.63938\) & 0.29573 & \textless{}2e-16 \\ \(L_{\text{CO}}\) & \(-0.71985\) & 0.19068 & 0.000167 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Regression analysis of log-transformed maximum skewness. FVM analysis. The mesh quality metrics showed a significant change based on the distance threshold from the geometry simplification and the complexity of the original geometry. All three mesh quality metrics improved with geometry simplification. In particular, the maximum skewness showed an exponential decrease. To evaluate the priority of the faces to be removed among the building surfaces, an index for evaluating the similarity between the normal vector of a target face and other faces was proposed in this study. The proposed algorithm guarantees identical results with the same input as the results achieved by evaluating the priority order of entire faces with the index. Furthermore, the hexahedral meshing complexity of the geometry is expected to be reduced as Cartesian angles are formed. The experimental results showed that the mesh quality of an FVM model can be quantitatively controlled using the geometry simplification method proposed in this study. In particular, through the linear regression model, it is possible to estimate the mesh quality from the geometrical properties of the original model and the size of the mesh to be designed, as well as to evaluate the required threshold for simplification.